TPAT-1 Tests - เชาวน์ปัญญา

Let's solve this step by step:

Let's say number of people who add orange juice is x
Number of people who add sugar is y
We know x is 7 less than twice y
- x = 2y - 7
Number of people who add both = number of people who add neither
- Let's call this number z
Total number of people is 20
- People who add orange only (x-z) + People who add sugar only (y-z) + People who add both (z) + People who add neither (z) = 20
- (x-z) + (y-z) + z + z = 20
- x + y = 20
Substituting x = 2y - 7:
- (2y - 7) + y = 20
- 3y - 7 = 20
- 3y = 27
- y = 9
Therefore x = 2(9) - 7 = 11

The number of people who add orange juice is 11.

{"correct_answer_key":"c"}

Let me solve this step by step:

Let's define:

S = number of people who add sugar to coffee
L = number of people who add lime/orange juice to coffee
B = number of people who add both sugar and lime juice
N = number of people who add neither

Given:

Total people = 20
L = 2S - 7 (lime juice users are 7 fewer than twice sugar users)
B = N (people who add both equals people who add neither)

We know that:

S = (sugar only) + B
L = (lime only) + B
Total = (sugar only) + (lime only) + B + N = 20

Since B = N, and S + L - B = (sugar only) + (lime only) + B, we have: S + L - B + B + N = 20 S + L + N = 20 S + L + B = 20

Substituting L = 2S - 7: S + (2S - 7) + B = 20 3S + B = 27

Since B = N and (sugar only) + (lime only) + B + N = 20: B + N = 20 - (sugar only) - (lime only) 2B = 20 - (S - B) - (L - B) 2B = 20 - S - L + 2B S + L = 20

Substituting L = 2S - 7: S + (2S - 7) = 20 3S = 27 S = 9

Therefore, L = 2(9) - 7 = 18 - 7 = 11

The number of people who add lime/orange juice to their coffee is 11.

{"correct_answer_key":"c"}

Let's define some variables and solve this problem step by step.

Let's denote:

Let S be the set of people who put sugar in their coffee.
Let O be the set of people who put orange juice in their coffee.

We have:

Total number of people = 20
|O| = number of people who put orange juice in their coffee
|S| = number of people who put sugar in their coffee
|O ∩ S| = number of people who put both orange juice and sugar
|O'∩ S'| = number of people who put neither orange juice nor sugar

From the problem:

Number of people who put orange juice is 7 less than twice the number of people who put sugar. |O| = 2|S| - 7
Number of people who put both orange juice and sugar equals the number of people who put neither orange juice nor sugar. |O ∩ S| = |O'∩ S'|

We can use the formula: |O ∪ S| = |O| + |S| - |O ∩ S|

Also, |O'∩ S'| = Total - |O ∪ S|

So, |O ∩ S| = |O'∩ S'| = Total - |O ∪ S| = Total - (|O| + |S| - |O ∩ S|)

This gives us: |O ∩ S| = Total - |O| - |S| + |O ∩ S| 2|O ∩ S| = Total - |O| - |S|

Substituting |O| = 2|S| - 7: 2|O ∩ S| = 20 - (2|S| - 7) - |S| 2|O ∩ S| = 20 - 2|S| + 7 - |S| 2|O ∩ S| = 27 - 3|S|

So, |O ∩ S| = (27 - 3|S|) / 2

Now, let's use another approach. Using set theory: |O| = |O ∩ S| + |O ∩ S'| |S| = |O ∩ S| + |O' ∩ S| |O'∩ S'| = Total - |O| - |S| + |O ∩ S|

From |O| = 2|S| - 7, we get: |O ∩ S| + |O ∩ S'| = 2(|O ∩ S| + |O' ∩ S|) - 7 |O ∩ S| + |O ∩ S'| = 2|O ∩ S| + 2|O' ∩ S| - 7 |O ∩ S'| = |O ∩ S| + 2|O' ∩ S| - 7

I realize I might be getting a bit complex. Let me step back and think about this more directly.

Let's define variables:

a = number of people who put only orange juice
b = number of people who put only sugar
c = number of people who put both orange juice and sugar
d = number of people who put neither

So, we have:

Total: a + b + c + d = 20
Orange juice: a + c = |O|
Sugar: b + c = |S|
From the problem: a + c = 2(b + c) - 7
Also: c = d

From a + c = 2(b + c) - 7, we get: a - 2b - c = -7 a - 2b - d = -7 (since c = d)

From a + b + c + d = 20 and c = d, we get: a + b + 2c = 20 a + b + 2d = 20

Substituting the first equation into the second: (2b + d - 7) + b + 2d = 20 3b + 3d = 27 b + d = 9

Now, from a + b + 2d = 20, we get: a = 20 - b - 2d a = 20 - 9 - d (since b + d = 9) a = 11 - d

Going back to our equation a - 2b - d = -7: (11 - d) - 2b - d = -7 11 - 2d - 2b = -7 11 + 7 = 2d + 2b 18 = 2(d + b) 9 = d + b

So, we have confirmed that b + d = 9.

Now, since c = d, and a + c = |O|, we have: |O| = a + c = a + d = (11 - d) + d = 11

Therefore, the number of people who put orange juice in their coffee is 11, which corresponds to option C.

Actually, let me double-check this.

We have:

a + b + c + d = 20 (Total)
a + c = |O| (Orange juice)
b + c = |S| (Sugar)
a + c = 2(b + c) - 7 (From the problem)
c = d (From the problem)

From a + c = 2(b + c) - 7, we can derive: |O| = 2|S| - 7

Since c = d, we can rewrite the total equation: a + b + c + d = 20 a + b + 2c = 20 (since c = d)

Now, let's use |O| = a + c and |S| = b + c to express a and b: a = |O| - c b = |S| - c

Substituting into the total equation: (|O| - c) + (|S| - c) + 2c = 20 |O| + |S| = 20

We also know |O| = 2|S| - 7.

Substituting this into |O| + |S| = 20: (2|S| - 7) + |S| = 20 3|S| - 7 = 20 3|S| = 27 |S| = 9

Now, using |O| = 2|S| - 7, we get: |O| = 2(9) - 7 = 18 - 7 = 11

Actually, let me do this analysis again for clarity.

We have 20 people. Let's define:

S = set of people who put sugar in their coffee
O = set of people who put orange juice in their coffee

From the problem:

|O| = 2|S| - 7
|O ∩ S| = |O'∩ S'|

Using the formula for the cardinality of the union of two sets: |O ∪ S| = |O| + |S| - |O ∩ S|

Also, |O'∩ S'| = Total - |O ∪ S|

From the second condition: |O ∩ S| = |O'∩ S'| = Total - |O ∪ S| = Total - (|O| + |S| - |O ∩ S|)

Simplifying: |O ∩ S| = Total - |O| - |S| + |O ∩ S| 0 = Total - |O| - |S|

This gives us: |O| + |S| = Total = 20

Substituting |O| = 2|S| - 7: (2|S| - 7) + |S| = 20 3|S| - 7 = 20 3|S| = 27 |S| = 9

Using |O| = 2|S| - 7: |O| = 2(9) - 7 = 18 - 7 = 11

So, the number of people who put orange juice in their coffee is 11, which corresponds to option C.

Actually, let's approach this using a Venn diagram to make it clearer. I'll define the regions of the Venn diagram as follows:

a = number of people who put only orange juice (i.e., |O - S|)
b = number of people who put only sugar (i.e., |S - O|)
c = number of people who put both orange juice and sugar (i.e., |O ∩ S|)
d = number of people who put neither (i.e., |O'∩ S'|)

So, a + b + c + d = 20 (total number of people)

From the problem:

|O| = a + c (total people who put orange juice)
|S| = b + c (total people who put sugar)
|O| = 2|S| - 7
c = d (people who put both equals people who put neither)

From |O| = 2|S| - 7: a + c = 2(b + c) - 7 a + c = 2b + 2c - 7 a = 2b + c - 7

Substituting into a + b + c + d = 20 and using c = d: (2b + c - 7) + b + c + c = 20 3b + 3c - 7 = 20 3b + 3c = 27 b + c = 9

Now, using |S| = b + c: |S| = b + c = 9

And using |O| = 2|S| - 7: |O| = 2(9) - 7 = 18 - 7 = 11

So, the number of people who put orange juice in their coffee is 11, which corresponds to option C.

Let me make one more check:

From |S| = 9 and c = d: b = 9 - c = 9 - d
From |O| = 11 and c = d: a = 11 - c = 11 - d
From a + b + c + d = 20: (11 - d) + (9 - d) + d + d = 20, which gives 20 = 20, which confirms our solution.

Therefore, the answer is 11 people put orange juice in their coffee, which is option C.

This problem is about people's coffee preferences.

Let me solve this step by step:

We have 20 people total
Let's define O = number of people who put orange juice in coffee, and S = number of people who put sugar
The problem states that O = 2S - 7
Also, the number of people who put both orange juice and sugar equals the number who put neither
Using set theory and these conditions, we can derive that O + S = 20
Substituting O = 2S - 7 into O + S = 20: (2S - 7) + S = 20 3S = 27 S = 9
Therefore, O = 2(9) - 7 = 11

So 11 people put orange juice in their coffee.

{"correct_answer_key":"c"}

Let's denote:

( S ) as the number of people who put lemon in their coffee.
( T ) as the number of people who put sugar in their coffee.
( B ) as the number of people who put both lemon and sugar in their coffee.
( N ) as the number of people who put neither lemon nor sugar in their coffee.

From the problem, we have the following information:

( S = 2T - 7 )
( B = N )
The total number of people is 20, so ( S + T - B + N = 20 )

Since ( B = N ), we can substitute ( N ) with ( B ) in the total equation: [ S + T - B + B = 20 ] [ S + T = 20 ]

Now substitute ( S = 2T - 7 ) into ( S + T = 20 ): [ (2T - 7) + T = 20 ] [ 3T - 7 = 20 ] [ 3T = 27 ] [ T = 9 ]

Now find ( S ): [ S = 2T - 7 = 2(9) - 7 = 18 - 7 = 11 ]

Thus, the number of people who put lemon in their coffee is 11, which corresponds to option C.

{"correct_answer_key":"c"}

Let's break down the problem step by step to find the number of people who add orange juice to their coffee.

Given:

Total coffee drinkers surveyed: 20
Let:
- ( S ) = number of people who add sugar to coffee
- ( O ) = number of people who add orange juice to coffee
- ( B ) = number of people who add both sugar and orange juice
- ( N ) = number of people who add neither sugar nor orange juice

Conditions:

The number of people who add orange juice is less than twice the number of people who add sugar by 7: [ O = 2S - 7 ]
The number of people who add both sugar and orange juice is equal to the number who add neither: [ B = N ]

Total people equation:

The total number of people can be expressed using the principle of inclusion-exclusion: [ S + O - B + N = 20 ] Since ( B = N ), substitute: [ S + O - N + N = 20 \implies S + O = 20 ]

Substitute ( O = 2S - 7 ) into ( S + O = 20 ):

[ S + (2S - 7) = 20 \ 3S - 7 = 20 \ 3S = 27 \ S = 9 ]

Now find ( O ):

[ O = 2S - 7 = 2(9) - 7 = 18 - 7 = 11 ]

Verification:

( S = 9 ), ( O = 11 ), ( B = N )
Total: ( S + O - B + N = 9 + 11 - B + B = 20 ) (consistent)
Also, ( O = 2S - 7 \implies 11 = 18 - 7 ) (correct)

Answer:

The number of people who add orange juice to their coffee is 11, which corresponds to option C.

{"correct_answer_key":"c"}

Okay, let's try to solve this problem step by step. So, the question is in Thai, but from what I can gather, it's about a survey of 20 coffee drinkers. The problem gives some relationships between people who add orange juice to their coffee, those who add sugar, and those who don't add either. The goal is to find out how many people add orange juice to their coffee.

First, let me parse the information given. There are 20 people surveyed. The number of people who add orange juice (let's call this O) is less than twice the number of people who add sugar (let's call this S) by 7. So, the first equation would be O = 2S - 7. Wait, but the wording says "น้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟอยู่ 7 คน", which translates to "less than twice the number of people who add sugar by 7 people". So, that would mean O = 2S - 7. Right?

Then, it says the number of people who add both orange and sugar (let's call this B) is equal to the number who add neither (let's call this N). So, B = N.

We know that the total number of people is 20. Using the principle of inclusion-exclusion for sets, the total should be O + S - B + N = 20. Wait, but O and S are the counts of people adding orange and sugar respectively. So, the formula would be:

Total = (People who add O only) + (People who add S only) + (People who add both) + (People who add neither)

But another way to write that is Total = O + S - B + N. Wait, no. Let me think again. If O is the number of people who add orange (including those who also add sugar), and S is the number who add sugar (including those who add both), then the total number of people is O + S - B + N = 20. Because O + S counts the overlap B twice, so we subtract B once. Then add N, the people who don't add either. So yes, O + S - B + N = 20.

But we also know that B = N. So substituting B for N, the equation becomes O + S - B + B = O + S = 20. Wait, that can't be right. Wait, if N = B, then substituting into the equation:

O + S - B + N = O + S - B + B = O + S = 20. So O + S = 20. But that seems conflicting with the first equation O = 2S -7. Let's check.

If O + S = 20, and O = 2S -7, then substituting O into the first equation:

2S -7 + S = 20 → 3S -7 =20 → 3S=27 → S=9. Then O=2*9 -7=18-7=11. So O=11. Then the answer would be 11, which is option C. But wait, let me verify this because maybe I made a mistake in the inclusion-exclusion part.

Wait, the total number of people is 20. The formula should be:

Total = (O only) + (S only) + Both + Neither.

But O only is O - B, S only is S - B, Both is B, Neither is N. So:

(O - B) + (S - B) + B + N = O - B + S - B + B + N = O + S - B + N = 20.

But since B = N, then substituting:

O + S - B + B = O + S = 20. So O + S =20. Then with O=2S -7, solving gives S=9, O=11. So the answer is 11, option C. But let me check if this makes sense with the other conditions.

If O=11, S=9, then B = N. Let's find B and N. From O + S - B + N =20, but since B=N, then O + S - B + B = O + S =20, which we already used. But we need to check if B and N are valid. Let's compute B. The number of people who add both is B, and the number who add neither is also B. So total people would be O + S - B + B = O + S =20. But we need to ensure that B is a non-negative integer and that O and S are also valid. For example, if O=11 and S=9, then the maximum possible B is 9 (since S=9, you can't have more people adding both than those who add sugar). Similarly, B can't exceed O=11. So B can be up to 9. But since B=N, and N must be non-negative, B can be from 0 to 9. But the problem doesn't give more constraints, so as long as O and S satisfy the equations, it's okay. So in this case, the answer is 11, which is option C. So I think that's correct.

Let's break down the problem using set theory and equations:

Definitions:
- Total people = 20
- Let O = number of people who add orange juice (น้ำส้ม)
- Let S = number of people who add sugar (น้ำตาล)
- Let B = number of people who add both
- Let N = number of people who add neither
Given relationships:
- ( O = 2S - 7 ) (Orange users are 7 less than twice sugar users)
- ( B = N ) (Both additives = Neither additives)
Inclusion-Exclusion Principle: Total = ( O + S - B + N ) Substitute ( B = N ): [ 20 = O + S - B + B \implies O + S = 20 ]
Solve the system:
- From ( O = 2S - 7 ) and ( O + S = 20 ): [ 2S - 7 + S = 20 \implies 3S = 27 \implies S = 9 ] [ O = 2(9) - 7 = 11 ]
Verification:
- ( O = 11 ), ( S = 9 ), ( B = N )
- Total = ( 11 + 9 - B + B = 20 ), which holds true.

Answer: The number of people who add orange juice is 11 (option C).

{"correct_answer_key":"c"}

Let's break down this Thai question and solve it:

The question asks: "From a survey of 20 coffee drinkers, it was found that the number of people who put orange juice in their coffee is 7 less than twice the number of people who put sugar in their coffee. The number of people who put both orange juice and sugar in their coffee is equal to the number of people who put neither orange juice nor sugar in their coffee. How many people put orange juice in their coffee?"

Let:

'O' represent the set of people who put orange juice in their coffee.
'S' represent the set of people who put sugar in their coffee.

We are given:

|O| = 2|S| - 7 (The number of orange juice users is 7 less than twice the number of sugar users)
|O ∩ S| = 20 - (|O ∪ S|) (The number of people using both equals the number using neither)

We also know the total number of people surveyed is 20, so:

|O ∪ S| = |O| + |S| - |O ∩ S|

Substituting equation (2) into equation (3):

|O ∪ S| = |O| + |S| - (20 - |O ∪ S|) 2|O ∪ S| = |O| + |S| + 20

Now, let's use a little trick. We know:

|O ∪ S| + (20 - |O ∪ S|) = 20 (Those who use either plus those who use neither equals the total)

Let x = |O ∩ S|. Then 20 - x = number of people using neither, which also equals |O ∩ S|.

So, |O ∪ S| = |O| + |S| - x. And x = 20 - |O ∪ S|.

Substituting equation (1) into the union equation:

|O ∪ S| = (2|S| - 7) + |S| - x |O ∪ S| = 3|S| - 7 - x

We also know 2|O ∪ S| = |O| + |S| + 20. Substituting |O| again:

2|O ∪ S| = (2|S| - 7) + |S| + 20 2|O ∪ S| = 3|S| + 13

Now we have two equations with two unknowns:

|O ∪ S| = 3|S| - 7 - x
2|O ∪ S| = 3|S| + 13

Since x = 20 - |O ∪ S|, substitute this into equation (1):

|O ∪ S| = 3|S| - 7 - (20 - |O ∪ S|) 0 = 3|S| - 27 |S| = 9

Now substitute |S| = 9 into equation (1):

|O| = 2 * 9 - 7 |O| = 18 - 7 |O| = 11

Therefore, 11 people put orange juice in their coffee.

{"correct_answer_key": "c"}

Let's break down the problem:

Let 'x' be the number of people who add sugar to their coffee.
The number of people who add orange juice is less than twice the number of people who add sugar by 7, so the number of people who add orange juice is 2x - 7.
Let 'y' be the number of people who add both orange juice and sugar, and also the number of people who add neither.
Total number of coffee drinkers is 20.

We can use a Venn diagram to visualize this. Let:

A = Number of people who add orange juice only
B = Number of people who add sugar only
y = Number of people who add both orange juice and sugar
y = Number of people who add neither

We know:

A + B + y + y = 20
A + y = 2x - 7 (Total number of people who add orange juice)
B + y = x (Total number of people who add sugar)

Substituting the last two equations into the first equation:

(2x - 7 - y + y) + (x - y + y) + y + y = 20 2x - 7 + x + 2y = 20 3x + 2y = 27

We also know that A, B, x, y must be non-negative integers. Since 2x - 7 represents the number of people who add orange juice, it must be non-negative, so 2x >= 7, meaning x >= 3.5. Since x is an integer, x >= 4.

Let's try different values of x and see if we get integer values for y and A+y (number of people who add orange juice):

If x = 4, 3(4) + 2y = 27 => 2y = 15 => y = 7.5 (not an integer)
If x = 5, 3(5) + 2y = 27 => 2y = 12 => y = 6. A+y = 2(5) - 7 = 3.
If x = 6, 3(6) + 2y = 27 => 2y = 9 => y = 4.5 (not an integer)
If x = 7, 3(7) + 2y = 27 => 2y = 6 => y = 3. A+y = 2(7) - 7 = 7.
If x = 8, 3(8) + 2y = 27 => 2y = 3 => y = 1.5 (not an integer)
If x = 9, 3(9) + 2y = 27 => 2y = 0 => y = 0. A+y = 2(9) - 7 = 11.

Let's check the valid solutions:

x=5, y=6, A+y = 3. This is impossible since A+y must be greater than or equal to y.
x=7, y=3, A+y = 7. A = 4, B = 4, 4+4+3+3 = 14 != 20. This is impossible.
x=9, y=0, A+y = 11. A = 11, B = 9, 11+9+0+0 = 20. This works!

Therefore, the number of people who add orange juice is 11.

{"correct_answer_key":"c"}

Let's break down the problem:

Total: 20 coffee drinkers.
Relationship between orange juice and sugar: Let 's' be the number of people who put sugar in their coffee. Then, the number of people who put orange juice is '2s - 7'.
Equal groups: The number of people who use both orange juice and sugar is equal to the number of people who use neither.
Goal: Find the number of people who put orange juice in their coffee.

Let 'x' be the number of people who use both orange juice and sugar, and also the number of people who use neither.

We can set up an equation using the principle of inclusion-exclusion:

Total = (Orange Juice Only) + (Sugar Only) + (Both) + (Neither)

20 = (2s - 7 - x) + (s - x) + x + x

20 = 3s - 7 + x

Also, we know that the number of people who use orange juice is 2s - 7.

We can't solve this directly without more information. However, we can try to find a solution by testing the answer choices.

Let's test option C (11 people put orange juice in their coffee):

If 2s - 7 = 11, then 2s = 18, and s = 9. Then, 20 = (11 - x) + (9 - x) + x + x 20 = 20 This works.

Therefore, the number of people who put orange juice in their coffee is 11.

{"correct_answer_key":"c"}

คำอธิบาย:

โจทย์กำหนดข้อมูลเกี่ยวกับผู้ดื่มกาแฟ 20 คน และความชอบในการใส่น้ำส้มและน้ำตาลในกาแฟ โดยมีเงื่อนไขดังนี้:

จำนวนผู้ที่ใส่น้ำส้ม น้อยกว่าสองเท่าของผู้ที่ใส่น้ำตาลอยู่ 7 คน
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล เท่ากับจำนวนผู้ที่ไม่ใส่อะไรเลย

ให้:

O = จำนวนผู้ที่ใส่น้ำส้ม
S = จำนวนผู้ที่ใส่น้ำตาล
Both = จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล
Neither = จำนวนผู้ที่ไม่ใส่อะไรเลย

จากเงื่อนไข:

O = 2S - 7
Both = Neither

เรารู้ว่าจำนวนผู้ดื่มกาแฟทั้งหมดคือ 20 คน ซึ่งสามารถแบ่งออกเป็น 4 กลุ่ม:

ใส่เฉพาะน้ำส้ม
ใส่เฉพาะน้ำตาล
ใส่ทั้งน้ำส้มและน้ำตาล (Both)
ไม่ใส่อะไรเลย (Neither)

และเรารู้ว่า: จำนวนผู้ที่ใส่ (อย่างน้อยหนึ่งอย่าง) + จำนวนผู้ที่ไม่ใส่อะไรเลย = 20 (จำนวนผู้ที่ใส่เฉพาะน้ำส้ม + จำนวนผู้ที่ใส่เฉพาะน้ำตาล + Both) + Neither = 20

จากเงื่อนไขที่ 2, Both = Neither ดังนั้น: (จำนวนผู้ที่ใส่เฉพาะน้ำส้ม + จำนวนผู้ที่ใส่เฉพาะน้ำตาล + Both) + Both = 20 จำนวนผู้ที่ใส่เฉพาะน้ำส้ม + จำนวนผู้ที่ใส่เฉพาะน้ำตาล + 2 * Both = 20

นอกจากนี้ เรายังรู้ว่า: จำนวนผู้ที่ใส่น้ำส้ม (O) = จำนวนผู้ที่ใส่เฉพาะน้ำส้ม + Both จำนวนผู้ที่ใส่น้ำตาล (S) = จำนวนผู้ที่ใส่เฉพาะน้ำตาล + Both

ดังนั้น: จำนวนผู้ที่ใส่เฉพาะน้ำส้ม = O - Both จำนวนผู้ที่ใส่เฉพาะน้ำตาล = S - Both

แทนค่าลงในสมการ: (O - Both) + (S - Both) + 2 * Both = 20 O - Both + S - Both + 2 * Both = 20 O + S = 20

จากเงื่อนไขที่ 1: O = 2S - 7 แทนค่า O ในสมการ O + S = 20: (2S - 7) + S = 20 3S - 7 = 20 3S = 27 S = 9

จากนั้นหาค่า O: O = 2S - 7 = 2 * 9 - 7 = 18 - 7 = 11

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟคือ 11 คน

{"correct_answer_key":"c"}

ให้ S แทนจำนวนผู้ที่ใส่น้ำส้มในกาแฟ และ U แทนจำนวนผู้ที่ใส่น้ำตาลในกาแฟ จำนวนผู้ดื่มกาแฟทั้งหมดคือ 20 คน

จากโจทย์ เราได้ข้อมูลดังนี้:

จำนวนผู้ที่ใส่น้ำส้ม (S) น้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาล (U) อยู่ 7 คน: S = 2U - 7
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล (S ∩ U) เท่ากับจำนวนผู้ที่ไม่ใส่ทั้งน้ำส้มและน้ำตาล (Neither): |S ∩ U| = |Neither|
จำนวนผู้ดื่มทั้งหมดคือ 20 คน

เรารู้ว่าจำนวนผู้ดื่มทั้งหมดเท่ากับจำนวนผู้ที่ใส่อย่างน้อยหนึ่งอย่าง (S ∪ U) บวกกับจำนวนผู้ที่ไม่ใส่อะไรเลย (Neither): Total = |S ∪ U| + |Neither| 20 = |S ∪ U| + |Neither|

จากข้อ 2, |Neither| = |S ∩ U|. แทนค่าในสมการข้างบน: 20 = |S ∪ U| + |S ∩ U|

เรารู้สูตรความสัมพันธ์ของเซต: |S ∪ U| = S + U - |S ∩ U| แทนค่า |S ∪ U| ในสมการ 20 = |S ∪ U| + |S ∩ U|: 20 = (S + U - |S ∩ U|) + |S ∩ U| 20 = S + U

ดังนั้น เราได้ระบบสมการสองตัวแปร:

S = 2U - 7
S + U = 20

แทนค่า S จากสมการที่ 1 ลงในสมการที่ 2: (2U - 7) + U = 20 3U - 7 = 20 3U = 20 + 7 3U = 27 U = 27 / 3 U = 9

เมื่อได้ค่า U แล้ว นำไปแทนในสมการที่ 1 เพื่อหาค่า S: S = 2U - 7 S = 2(9) - 7 S = 18 - 7 S = 11

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟคือ 11 คน

ตรวจสอบกับตัวเลือก: a: 15 b: 13 c: 11 d: 9 e: 8

คำตอบคือ 11 ซึ่งตรงกับตัวเลือก c.

{"correct_answer_key":"c"}

This is a word problem involving sets and Venn diagrams. Let S be the set of people who put orange juice in their coffee, and T be the set of people who put sugar in their coffee. We are given the following information:

The total number of coffee drinkers is 20.
The number of people who put orange juice in their coffee is 7 less than twice the number of people who put sugar in their coffee. This can be written as |S| = 2|T| - 7.
The number of people who put both orange juice and sugar in their coffee is equal to the number of people who put neither orange juice nor sugar in their coffee. This can be written as |S ∩ T| = |S' ∩ T'|, where S' and T' are the complements of S and T, respectively.

We know that the total number of people is the sum of those in S only, T only, both S and T, and neither S nor T. Using the principle of inclusion-exclusion, we have:

Total = |S ∪ T| + |S' ∩ T'| Total = (|S| + |T| - |S ∩ T|) + |S' ∩ T'|

From condition 3, |S ∩ T| = |S' ∩ T'|. Let's call this value x. So, 20 = (|S| + |T| - x) + x 20 = |S| + |T|

Now we have a system of two equations:

|S| = 2|T| - 7
20 = |S| + |T|

Substitute the first equation into the second: 20 = (2|T| - 7) + |T| 20 = 3|T| - 7 27 = 3|T| |T| = 9

Now substitute the value of |T| back into the first equation to find |S|: |S| = 2(9) - 7 |S| = 18 - 7 |S| = 11

The number of people who put orange juice in their coffee is 11.

{"correct_answer_key":"c"}

Explanation: Let S be the set of people who add orange juice (น้ำส้ม) and T be the set of people who add sugar (น้ำตาล). The total number of people surveyed is 20. We are given the following information:

|S| = 2|T| - 7 (The number who add orange juice is 7 less than twice the number who add sugar).
|S ∩ T| = |(S ∪ T)'| (The number who add both equals the number who add neither).

Let |S ∩ T| = |(S ∪ T)'| = x. The total number of people is the sum of those in the union and those outside the union: |U| = |S ∪ T| + |(S ∪ T)'| 20 = |S ∪ T| + x So, |S ∪ T| = 20 - x.

Using the Principle of Inclusion-Exclusion: |S ∪ T| = |S| + |T| - |S ∩ T| Substitute the known values: 20 - x = |S| + |T| - x Adding x to both sides gives: 20 = |S| + |T|

Now we have a system of two linear equations:

|S| = 2|T| - 7
|S| + |T| = 20

Substitute the first equation into the second: (2|T| - 7) + |T| = 20 3|T| - 7 = 20 3|T| = 27 |T| = 9

Now substitute the value of |T| back into the first equation to find |S|: |S| = 2(9) - 7 |S| = 18 - 7 |S| = 11

The question asks for the number of people who add orange juice (|S|), which is 11. This corresponds to option C.

{"correct_answer_key":"c"}

This is a word problem in Thai. Here's a breakdown and solution:

Let 'x' be the number of people who put sugar in their coffee.
The number of people who put orange juice in their coffee is 2x - 7.
Let 'both' be the number of people who put both sugar and orange juice in their coffee.
The number of people who put neither sugar nor orange juice is also 'both'.
Total people = 20.

We can set up the following equation based on the principle of inclusion-exclusion:

Total = (Sugar only) + (Orange Juice only) + (Both) + (Neither)

20 = (x - both) + (2x - 7 - both) + both + both 20 = 3x - 7 + both 27 = 3x + both

Also, we know that the total number of people who put something in their coffee is:

Sugar + Orange Juice - Both = (x) + (2x - 7) - both = 3x - 7 - both

Since 'both' people also put something in their coffee, and 'both' people put neither, the number of people who put something in their coffee is 20 - both.

Therefore: 3x - 7 - both = 20 - both 3x = 27 x = 9

Now we can find the number of people who put orange juice in their coffee:

2x - 7 = 2(9) - 7 = 18 - 7 = 11

Therefore, 11 people put orange juice in their coffee.

{"correct_answer_key":"c"}

คำอธิบาย:
กำหนดให้

A = จำนวนผู้ที่ใส่น้ำส้ม
B = จำนวนผู้ที่ใส่น้ำตาล
C = จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล
D = จำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาล

จากโจทย์

A - C = จำนวนผู้ที่ใส่น้ำส้มอย่างเดียว
B - C = จำนวนผู้ที่ใส่น้ำตาลอย่างเดียว
C = D
A - C = 2(B - C) - 7 (แต่โจทย์บอกว่า "น้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟอยู่ 7 คน" หมายถึง (A - C) = 2(B - C) - 7)
A + B - C + D = 20 (จำนวนคนทั้งหมด)

แทน D = C
A + B - C + C = 20 → A + B = 20

แทน (A - C) = 2(B - C) - 7
A - C = 2B - 2C - 7
A = 2B - C - 7

แทน A + B = 20
A = 20 - B

แทนค่า
20 - B = 2B - C - 7
20 - B + 7 = 2B - C
27 - B = 2B - C
27 = 3B - C
C = 3B - 27

แต่ C = D และทุกค่าต้องเป็นจำนวนเต็มบวก
ลองแทนค่าตัวเลือก A (A = จำนวนผู้ใส่น้ำส้ม)

ลอง A = 13
A + B = 20 → B = 7
A = 2B - C - 7
13 = 2×7 - C - 7
13 = 14 - C - 7
13 = 7 - C
C = 7 - 13 = -6 (ไม่เป็นไปได้)

ลอง A = 11
A + B = 20 → B = 9
A = 2B - C - 7
11 = 2×9 - C - 7
11 = 18 - C - 7
11 = 11 - C
C = 0

D = C = 0
ตรวจสอบจำนวนผู้ใส่น้ำส้มอย่างเดียว = A - C = 11
จำนวนผู้ใส่น้ำตาลอย่างเดียว = B - C = 9
A - C = 2(B - C) - 7
11 = 2×9 - 7 = 18 - 7 = 11
ถูกต้อง

ดังนั้น คำตอบคือ 11 คน

{"correct_answer_key":"c"}

Let's analyze the problem step-by-step:

Total coffee drinkers: 20
Let:
- S = number of people who add sugar
- O = number of people who add orange juice
- B = number of people who add both sugar and orange juice
- N = number of people who add neither sugar nor orange juice

Given:

The number of people who add orange juice is 7 less than twice the number of people who add sugar: O = 2S - 7
The number of people who add both sugar and orange juice equals the number of people who add neither: B = N
Total people: S + O - B + N = 20 (since those who add both are counted twice, subtract once)

Substitute O and N with B:

O = 2S - 7
N = B

So: S + (2S - 7) - B + B = 20 S + 2S - 7 = 20 3S = 27 S = 9

Now find O: O = 2(9) - 7 = 18 - 7 = 11

Therefore, the number of people who add orange juice is 11.

{"correct_answer_key":"c"}

คำอธิบาย:
จากโจทย์ ให้กำหนดตัวแปรดังนี้

( S ) = จำนวนผู้ใส่น้ำส้มในกาแฟ
( T ) = จำนวนผู้ใส่น้ำตาลในกาแฟ
( N ) = จำนวนผู้ใส่น้ำส้มและน้ำตาลในกาแฟ (ทั้งสองอย่าง)
( M ) = จำนวนผู้ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ

ข้อมูลจากโจทย์:

มีผู้ดื่มกาแฟ 20 คน
จำนวนผู้ที่ใส่น้ำส้มในกาแฟน้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟ อยู่ 7 คน
(\Rightarrow S = 2T - 7)
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลเท่ากับจำนวนผู้ที่ไม่ใส่ทั้งสอง
(\Rightarrow N = M)
รวมจำนวนผู้ดื่มกาแฟทั้งหมด:
[ S + T - N + M = 20 ] แต่เนื่องจาก ( N = M ), จึงเป็น:
[ S + T - N + N = 20 \Rightarrow S + T = 20 ]

แทน ( S = 2T - 7 ) ลงในสมการ:
[ (2T - 7) + T = 20 \Rightarrow 3T - 7 = 20 \Rightarrow 3T = 27 \Rightarrow T = 9 ]

จากนั้น:
[ S = 2 \times 9 - 7 = 18 - 7 = 11 ]

คำตอบคือ จำนวนผู้ที่ใส่น้ำส้มในกาแฟคือ 11 คน

{"correct_answer_key":"c"}

ขั้นแรกให้กำหนดตัวแปรก่อน:

ให้จำนวนผู้ที่ใส่น้ำตาล = ( x ) คน
จำนวนผู้ที่ใส่น้ำส้ม = ( y ) คน
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล = จำนวนผู้ที่ไม่ใส่อะไรเลย = ( z ) คน

จากโจทย์เราสามารถเขียนสมการได้ดังนี้:

จำนวนผู้ที่ใส่น้ำส้มในกาแฟน้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลอยู่ 7 คน: [ y = 2x - 7 ]
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล (( z )) เท่ากับจำนวนผู้ที่ไม่ใส่อะไรเลย (( z )) ดังนั้นจำนวนผู้ที่ใส่อย่างใดอย่างหนึ่งหรือทั้งสองอย่างหรือไม่ใส่อะไรเลยรวมกันทั้งหมดคือ 20 คน: [ (x + y - z) + z + z = 20 ]

อธิบายเพิ่มเติมสมการที่สอง:

จำนวนผู้ที่ใส่น้ำตาลอย่างเดียว = ( x - z )
จำนวนผู้ที่ใส่น้ำส้มอย่างเดียว = ( y - z )
จำนวนผู้ที่ใส่ทั้งสองอย่าง = ( z )
จำนวนผู้ที่ไม่ใส่อะไรเลย = ( z )

ดังนั้นรวมทั้งหมดคือ: [ (x - z) + (y - z) + z + z = 20 ]

ลดรูปสมการนี้ได้เป็น: [ x + y - z = 20 ]

แทนค่า ( y = 2x - 7 ) ลงในสมการนี้: [ x + (2x - 7) - z = 20 \ 3x - z = 27 \ ]

ดังนั้น: [ z = 3x - 27 ]

เนื่องจาก ( z ) เป็นจำนวนคน ต้องมีค่ามากกว่าหรือเท่ากับ 0 ดังนั้น: [ 3x - 27 \geq 0 \ 3x \geq 27 \ x \geq 9 ]

ลองแทนค่า ( x = 9 ) (ค่าต่ำสุดที่เป็นไปได้) จะได้:

( y = 2(9) - 7 = 18 - 7 = 11 )
( z = 3(9) - 27 = 27 - 27 = 0 )

ตรวจสอบความถูกต้อง:

น้ำตาลอย่างเดียว = ( x - z = 9 - 0 = 9 )
น้ำส้มอย่างเดียว = ( y - z = 11 - 0 = 11 )
ทั้งสองอย่าง = ( z = 0 )
ไม่ใส่อะไรเลย = ( z = 0 )

รวมทั้งหมด ( 9 + 11 + 0 + 0 = 20 ) ถูกต้องตามโจทย์

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟคือ ( y = 11 ) คน ซึ่งตรงกับตัวเลือกข้อ c

{"correct_answer_key":"c"}

จากโจทย์ เรามีข้อมูลดังนี้:

จำนวนผู้ที่ใส่น้ำส้มในกาแฟน้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟอยู่ 7 คน
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ

ให้:

( x ) = จำนวนผู้ที่ใส่น้ำส้มในกาแฟ
( y ) = จำนวนผู้ที่ใส่น้ำตาลในกาแฟ
( z ) = จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟ
( w ) = จำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ

จากข้อ 1: ( x < 2y ) และ ( x = 2y - 7 )

จากข้อ 2: ( z = w )

จากข้อมูลทั้งหมด: ( x + y - z + w = 20 )

แทนค่า ( z = w ) ลงในสมการ: ( x + y = 20 )

แทนค่า ( x = 2y - 7 ) ลงในสมการ: ( 2y - 7 + y = 20 )

แก้สมการ: [ 3y - 7 = 20 ] [ 3y = 27 ] [ y = 9 ]

แทนค่า ( y = 9 ) ลงใน ( x = 2y - 7 ): [ x = 2(9) - 7 = 18 - 7 = 11 ]

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟมีอยู่ 11 คน ซึ่งตรงกับตัวเลือก C.

{"correct_answer_key":"c"}

เพื่อหาจำนวนผู้ที่ใส่น้ำส้มในกาแฟ เราสามารถตั้งสมการจากข้อมูลที่ให้มาได้:

ให้ ( x ) เป็นจำนวนผู้ที่ใส่น้ำตาลในกาแฟ
จำนวนผู้ที่ใส่น้ำส้มในกาแฟจะเป็น ( 2x - 7 ) (น้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาล 7 คน)
จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ

จากข้อมูลที่ให้มา เรามีสมการดังนี้:

จำนวนผู้ที่ใส่น้ำส้ม + จำนวนผู้ที่ใส่น้ำตาล - จำนวนผู้ที่ใส่ทั้งสอง = จำนวนผู้ที่ไม่ใส่ทั้งสอง

เรารู้ว่าจำนวนผู้ดื่มกาแฟทั้งหมดคือ 20 คน ดังนั้นเราสามารถตั้งสมการได้:

[ (2x - 7) + x - (2x - 7) = 20 - (2x - 7 + x) ]

จากการแก้สมการนี้ เราจะได้จำนวนผู้ที่ใส่น้ำส้มในกาแฟ

หลังจากการคำนวณ เราจะพบว่าจำนวนผู้ที่ใส่น้ำส้มในกาแฟคือ 11 คน ซึ่งตรงกับตัวเลือก C

{"correct_answer_key":"c"}

Let's solve this step by step. We are given a survey of 20 coffee drinkers with specific conditions about adding orange juice (O) and sugar (S) to their coffee.

Total people = 20.
Let O be the number of people who add orange juice, S be the number who add sugar, B be the number who add both, and N be the number who add neither.
From the problem, "the number who add orange juice is 7 less than twice the number who add sugar": O = 2S - 7.
Also, "the number who add both is equal to the number who add neither": B = N.
Using the principle of inclusion-exclusion for the total number of people: O + S - B + N = 20.
Since B = N, substitute into the equation: O + S - B + B = O + S = 20.
From step 3, O = 2S - 7. Substitute into O + S = 20: (2S - 7) + S = 20 → 3S - 7 = 20 → 3S = 27 → S = 9.
Then, O = 2S - 7 = 2(9) - 7 = 18 - 7 = 11.

Thus, the number of people who add orange juice to their coffee is 11, which corresponds to option C.

{"correct_answer_key":"c"}

First, the user has provided another multiple-choice question in JSON format. It's in Thai, which might be a bit tricky since I'm an AI trained in English, but I can try to translate and understand it.

Let me translate the question to English:

"จากการสอบทำมผู้ดื่มกาแฟ 20 คน" – This seems misspelled. Probably "จากการสำรวจผู้ดื่มกาแฟ 20 คน" which means "From a survey of 20 coffee drinkers".

"พบว่า จำนวนผู้ที่ใส่น้ำส้มในกาแฟน้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟอยู่ 7 คน" – "Found that the number of people who add orange juice to their coffee is less than twice the number of people who add sugar to their coffee by 7 people."

More precisely: "The number of people who add orange juice is less than twice the number of people who add sugar by 7 people."

Let me denote:

Let S be the number of people who add sugar.

Let O be the number of people who add orange juice.

So, O = 2S - 7 (since it's less than twice by 7)

"น้อยกว่าสองเท่าของ... อยู่ 7 คน" means "is less than twice by 7 people", so yes, O = 2S - 7.

Next: "จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ"

"The number of people who add both orange juice and sugar is equal to the number of people who add neither orange juice nor sugar."

Let me denote:

Let B be the number who add both.

Let N be the number who add neither.

So, B = N.

Total people: 20.

This is a set problem, probably involving Venn diagrams for two sets: sugar (S) and orange juice (O).

Let me define:

Only sugar: S_only
Only orange: O_only
Both: B
Neither: N

Total: S_only + O_only + B + N = 20

Also, total who add sugar: S = S_only + B

Total who add orange: O = O_only + B

From earlier: O = 2S - 7

And B = N

We need to find O, the number who add orange juice.

The question is: "จำนวนผู้ที่ใส่น้ำส้มในกาแฟมีอยู่กี่คน?" which is "How many people add orange juice to their coffee?" So, that's O.

We have:

Total: (people who add only sugar) + (only orange) + both + neither = 20

S = only sugar + both

O = only orange + both

And O = 2S - 7

B = N

Also, since total is 20, and everyone is accounted for: only S + only O + both + neither = 20

Let me express everything in terms of S and O, or perhaps introduce variables.

Let me let:

Let A be the set of people who add sugar. |A| = S

Let B be the set of people who add orange. |B| = O

Then, |B| = 2|A| - 7

The number who add both: |A ∩ B|

The number who add neither: total - |A ∪ B| = 20 - |A ∪ B|

And it's given that |A ∩ B| = number who add neither = 20 - |A ∪ B|

So, |A ∩ B| = 20 - |A ∪ B|

We know |A ∪ B| = |A| + |B| - |A ∩ B| = S + O - |A ∩ B|

So, |A ∩ B| = 20 - (S + O - |A ∩ B|)

Let me denote X = |A ∩ B|

Then, X = 20 - (S + O - X)

X = 20 - S - O + X

Subtract X from both sides: 0 = 20 - S - O

So, S + O = 20

From X = 20 - (S + O - X)

X = 20 - S - O + X

Then, subtract X: 0 = 20 - S - O

Yes, so S + O = 20

We also have O = 2S - 7

Substitute: S + (2S - 7) = 20

3S - 7 = 20

3S = 27

S = 9

Then O = 2*9 - 7 = 18 - 7 = 11

So, the number who add orange juice is 11.

We have S = 9, O = 11, and S + O = 20, which implies |A ∪ B| = S + O - X = 20 - X, but from earlier, total is |A ∪ B| + neither = 20, and neither = X, so |A ∪ B| + X = 20

But S + O = 20, and S + O = |A ∪ B| + X, because S + O = (|A| + |B|) = |A ∪ B| + |A ∩ B| = |A ∪ B| + X

Exactly: S + O = |A ∪ B| + X

And we have S + O = 20

Also, total people = |A ∪ B| + neither = |A ∪ B| + X = 20

So, |A ∪ B| + X = 20

But S + O = |A ∪ B| + X = 20

Yes, consistent.

So, everything checks out.

Therefore, O = 11.

The options are: a:15, b:13, c:11, d:9, e:8

So, c:11

My response should be: First, a brief explanation, then respond in JSON with {"correct_answer_key":"c"}

Explanation: From the survey of 20 coffee drinkers, let S be the number who add sugar, O who add orange. Given O = 2S - 7, and the number who add both equals the number who add neither, leading to S + O = 20. Solving, S=9, O=11.

So, final answer.

Brief Explanation:

จากข้อมูลการสำรวจผู้ดื่มกาแฟ 20 คน ให้กำหนดว่า S เป็นจำนวนผู้ที่ใส่น้ำตาล และ O เป็นจำนวนผู้ที่ใส่น้ำส้ม โดยที่ O = 2S - 7 และจำนวนผู้ที่ใส่ทั้งสองอย่างเท่ากับจำนวนผู้ที่ไม่ใส่ทั้งสองอย่าง นำไปสู่สมการ S + O = 20 เมื่อแก้สมการได้ S = 9 และ O = 11 ดังนั้น จำนวนผู้ที่ใส่น้ำส้มมี 11 คน ซึ่งตรงกับตัวเลือก c.

{"correct_answer_key":"c"}

ให้ x เป็นจำนวนผู้ที่ใส่น้ำตาลในกาแฟ และ y เป็นจำนวนผู้ที่ใส่น้ำส้มในกาแฟ จากโจทย์ให้ y = 2x - 7

จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ ดังนั้นเราจึงสามารถเขียนสมการได้ดังนี้

x + y - (จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล) + (จำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาล) = 20

เนื่องจากจำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาล เราจึงสามารถเขียนสมการใหม่ได้ดังนี้

x + y - (จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล) + (จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาล) = 20

ซึ่งลดรูปเป็น x + y = 20

เมื่อแทน y = 2x - 7 ลงในสมการ x + y = 20 เราจะได้

x + 2x - 7 = 20

รวมเงื่อนไขเช่น

3x - 7 = 20

เพิ่ม 7 ทั้งสองข้าง

3x = 27

หารด้วย 3

x = 9

เมื่อแทน x = 9 ลงใน y = 2x - 7 เราจะได้

y = 2(9) - 7 y = 18 - 7 y = 11

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟคือ 11

{"correct_answer_key":"c"}

Let's denote the number of people who put sugar in their coffee as S, the number of people who put orange juice (น้ำส้ม) in their coffee as J, the number of people who put both as B, and the number of people who put neither as N.

Given:

Total people = 20
J = 2S - 7
B = N
The total number of people who put orange juice or sugar or both can be represented using the principle of inclusion-exclusion as: J + S - B.

We know that the total number of people is the sum of those who put orange juice or sugar or both and those who put neither: (J + S - B) + N = 20. Substituting B for N, we get J + S - B + B = 20, simplifying to J + S = 20.

From (2), we substitute J with 2S - 7 into J + S = 20 to get 2S - 7 + S = 20, which simplifies to 3S = 27, so S = 9.

Substitute S = 9 into J = 2S - 7 to find J: J = 2*9 - 7 = 18 - 7 = 11.

Therefore, the number of people who put orange juice in their coffee is 11.

{"correct_answer_key":"c"}

Let's break down the information:

Let x be the number of people who add sugar to their coffee.
The number of people who add orange juice is less than twice the number of people who add sugar by 7, so it is 2x - 7.
The number of people who add both is equal to the number of people who add neither.

We can use a Venn diagram or basic algebra to solve this, but let's denote:

(S) as the set of people who add sugar,
(O) as the set of people who add orange juice,
(B) as the set of people who add both,
(N) as the set of people who add neither.

Given:

Total people = 20
(|B| = |N|)

We know that: [|S \cup O| + |N| = 20] [|S| + |O| - |B| + |N| = 20] Since (|B| = |N|), [|S| + |O| = 20]

Let's assume (|S| = x), then (|O| = 2x - 7).

The number of people who add only sugar, only orange juice, both, or neither can be represented in terms of (x) and (2x - 7), but we also know that: [|S \cap O| = |B|]

However, without direct information on (|S|), (|O|), or (|B|) separately, let's focus on what we are solving for: the number of people who add orange juice, (|O|).

Let (|O| = 2x - 7) and assume everyone adds either sugar, orange juice, both, or neither. The equation to solve involves understanding that: [|S| + |O| - |B| + |N| = 20] Given (|B| = |N|), we substitute and solve.

But let's simplify with what we actually need to find: If we let (x) be the number of people who add sugar, and (2x - 7) add orange juice, and assuming intersections and unions properly, we'd find a direct solution requires assumptions. However, this problem actually aligns with solving through recognizing relationships.

The correct approach actually calculates through understanding intersections equaling neither group size which leads us directly.

The answer is 13.

{"correct_answer_key":"b"}

Let's break down the problem step by step:

There are 20 people who drink coffee.
The number of people who put orange juice in their coffee is less than twice the number of people who put sugar in their coffee, and this difference is 7 people.
The number of people who put both orange juice and sugar in their coffee is equal to the number of people who put neither orange juice nor sugar in their coffee.

Let:

( x ) be the number of people who put orange juice in their coffee.
( y ) be the number of people who put sugar in their coffee.
( z ) be the number of people who put both orange juice and sugar in their coffee.
( w ) be the number of people who put neither orange juice nor sugar in their coffee.

From the problem, we have the following equations:

( x + y - z = 20 ) (total number of people)
( x - 2y = 7 ) (the difference condition)
( z = w ) (the number of people who put both is equal to the number of people who put neither)

We also know that:

( x = z + (x - z) )
( y = z + (y - z) )
( w = 20 - x - y + z )

Using the equations:

( x + y - z = 20 )
( x - 2y = 7 )

We can solve for ( x ) and ( y ):

From equation 2: [ x = 2y + 7 ]

Substitute ( x ) in equation 1: [ (2y + 7) + y - z = 20 ] [ 3y + 7 - z = 20 ] [ 3y - z = 13 ]

Since ( z = w ), and ( z ) is the number of people who put both, we can assume ( z ) and solve for ( y ): [ 3y - z = 13 ] [ z = w ]

Assuming ( z = w ), we can find ( y ): [ 3y - z = 13 ] [ 3y - w = 13 ]

Since ( z = w ), we can solve for ( y ): [ 3y = 13 + w ]

Since ( z = w ), and ( z ) is the number of people who put both, we can assume ( z ) and solve for ( y ): [ 3y = 13 + z ]

Since ( z = w ), and ( z ) is the number of people who put both, we can assume ( z ) and solve for ( y ):

คำอธิบายแบบสั้น:
กำหนดให้
• x = จำนวนคนที่ใส่น้ำส้มในกาแฟ
• y = จำนวนคนที่ใส่น้ำตาลในกาแฟ
• n = จำนวนคนที่ใส่ทั้งน้ำส้มและน้ำตาล (และเท่ากับจำนวนคนที่ไม่ใส่อะไรเลย)

จากเงื่อนไข:

x = 2y − 7
จำนวนคนที่ใส่ทั้งน้ำส้มและน้ำตาล = จำนวนคนที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาล ทำให้ได้ x + y = 20

แทนค่า x = 2y − 7 ใน x + y = 20 ⇒ 2y − 7 + y = 20 ⇒ 3y = 27 ⇒ y = 9 ⇒ x = 11

ดังนั้นมีผู้ที่ใส่น้ำส้มในกาแฟ 11 คน

{"correct_answer_key":"c"}

ผู้ดื่มกาแฟทั้งหมด 20 คน
ให้
O = ใส่น้ำส้ม, S = ใส่น้ำตาล
x = ใส่ทั้งสอง (O∩S)
y = ใส่เฉพาะน้ำส้ม (O∩¬S)
z = ใส่เฉพาะน้ำตาล (¬O∩S)
w = ไม่ใส่ทั้งสอง (¬O∩¬S)

เงื่อนไข

|O| = x + y
|S| = x + z
|O| = 2|S| – 7 ⇒ x + y = 2(x + z) – 7 → y = x + 2z – 7
x = w
x + y + z + w = 20 → 2x + y + z = 20

แทน (3) ลงใน (5):
2x + (x + 2z – 7) + z = 20 → 3x + 3z = 27 → x + z = 9 → |S| = 9

นำกลับไปหา y: y = –x + 11 (ค่าต้องไม่ลบ)
เมื่อ x = 0‥9 จะได้ y ≥ 0 และทุกกรณีให้ |O| = x + y = 11

ดังนั้นจำนวนผู้ที่ใส่น้ำส้มในกาแฟ คือ 11 คน ⇒ ตัวเลือก c

{"correct_answer_key":"c"}

จำนวนคนที่ใส่น้ำส้ม (A) น้อยกว่าสองเท่าของคนที่ใส่น้ำตาล (B) อยู่ 7 คน
⇒ |A| = 2|B| – 7

กำหนดให้ x = จำนวนคนที่ใส่ทั้งสองอย่าง = จำนวนคนที่ไม่ใส่ทั้งสองอย่าง
สูตรรวมประชากร 20 คน
20 = |A| + |B| − |A∩B| + |neither| = |A| + |B| − x + x = |A| + |B|

จึงมีระบบสมการ

|A| + |B| = 20
|A| = 2|B| − 7

แทน (2) ลง (1)
2|B| − 7 + |B| = 20
3|B| = 27 → |B| = 9
⇒ |A| = 20 − 9 = 11

ดังนั้นจำนวนคนที่ใส่น้ำส้มในกาแฟคือ 11 คน (ตัวเลือก c).

{"correct_answer_key":"c"}

ให้กำหนด O = จำนวนคนใส่น้ำส้ม
S = จำนวนคนใส่น้ำตาล
มีทั้งหมด 20 คน

เงื่อนไข

O น้อยกว่าสองเท่าของ S อยู่ 7 คน ⇒ O = 2S – 7
จำนวนคนใส่ทั้งสองชนิด = จำนวนคนไม่ใส่ทั้งสองชนิด
⇒ ในสูตรเวนน์ |O∪S| + ไม่ใส่ = 20 และเพราะสองกลุ่มสุดท้ายเท่ากัน จึงตัดกันได้เหลือ
O + S = 20

แก้ระบบสมการ
O + S = 20
O = 2S – 7

แทนค่า: 2S – 7 + S = 20 ⇒ 3S = 27 ⇒ S = 9
ดังนั้น O = 2(9) – 7 = 11

จำนวนคนใส่น้ำส้มในกาแฟ = 11 คน → ตัวเลือก c

{"correct_answer_key":"c"}

We let x be the number of people who add orange drink and y be the number of people who add sugar. According to the problem, the number who add orange drink is 7 less than twice the number who add sugar, so x = 2y - 7. Also, because the number of people who add both is equal to those who add neither, the total (20 people) is given by x + y. Therefore, we have x + y = 20. Substituting the first equation in gives (2y - 7) + y = 20, which simplifies to 3y = 27, so y = 9 and then x = 2(9) - 7 = 11.

Thus, the number of people who add orange drink is 11, corresponding to option "c".

{"correct_answer_key": "c"}

เราตั้งให้ S = จำนวนผู้ใส่น้ำตาล (รวมทั้งที่ใส่ทั้งน้ำตาลและน้ำส้ม) และ O = จำนวนผู้ใส่น้ำส้ม (รวมทั้งที่ใส่ทั้งคู่)

จากโจทย์ “จำนวนผู้ที่ใส่น้ำส้มในกาแฟน้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟอยู่ 7 คน” หมายความว่า O = 2S – 7

และจากโจทย์ “จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ” ให้ x = จำนวนที่ใส่ทั้งคู่ = จำนวนที่ใส่ไม่ทั้งสอง

นอกจากนี้ เมื่อนิยาม s = จำนวนผู้ใส่เฉพาะน้ำตาล o = จำนวนผู้ใส่เฉพาะน้ำส้ม x = จำนวนผู้ใส่ทั้งสอง n = จำนวนไม่ใส่ทั้งสอง (n = x) รวมทั้งหมด 20 คน จึงได้ s + o + x + n = s + o + 2x = 20 (1)

จากนิยาม S และ O S = s + x และ O = o + x ดังนั้นเงื่อนไข O = 2S – 7 กลายเป็น o + x = 2(s + x) – 7 (2)

แก้สมการ (2) o + x = 2s + 2x – 7 → o = 2s + x – 7 (3)

แทน (3) ลงใน (1) s + (2s + x – 7) + 2x = 20 3s + 3x – 7 = 20 3(s + x) = 27 → s + x = 9 (4)

ซึ่ง S = s + x = 9 จาก (2) จะได้ O = 2×9 – 7 = 18 – 7 = 11

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟ = O = 11 คน

ตัวเลือก 11 คือ ตัวเลือก C

{"correct_answer_key": "c"}

จากโจทย์ให้ตั้งสมการดังนี้ สมมุติให้ O คือจำนวนผู้ใส่น้ำส้ม และ S คือจำนวนผู้ใส่น้ำตาล โดยข้อมูลบอกว่า

O น้อยกว่าสองเท่าของ S อยู่ 7 คน ซึ่งเขียนได้ว่า O = 2S - 7
จำนวนผู้ใส่น้ำส้มและจำนวนผู้ใส่น้ำตาลรวมกันเท่ากับ 20 คน นั่นคือ O + S = 20 แทนค่า O จากสมการแรกในสมการที่สองจะได้ 2S - 7 + S = 20 ซึ่งคือ 3S = 27 ดังนั้น S = 9 และแทนค่า S กลับไปใน O = 2×9 - 7 จะได้ O = 11 ซึ่งตรงกับตัวเลือกข้อ c

{"correct_answer_key": "c"}

จำนวนผู้ใส่น้ำส้ม S และน้ำตาล T จะได้

S = 2T – 7
ผู้ใส่ทั้งสองอย่างเท่ากับผู้ไม่ใส่เลย ⇒ S + T = 20
แทน S จาก (1) ลงใน (2): (2T – 7) + T = 20 ⇒ 3T = 27 ⇒ T = 9 ⇒ S = 2·9 – 7 = 11

{"correct_answer_key":"c"}

จำนวนผู้ใส่น้ำส้ม = x, ใส่น้ำตาล = y
เงื่อนไขให้ x = 2y – 7 และจากการนับรวมทั้งสองกลุ่ม x + y = 20
แทน x เข้าไป: (2y–7)+y=20 ⇒ 3y=27 ⇒ y=9 ⇒ x=2·9–7=11

{"correct_answer_key":"c"}

จำนวนผู้ใส่น้ำส้ม (A) และน้ำตาล (B) รวมกันได้ 20 คน (A + B = 20) และ A = 2B – 7
แทน B = 20 – A ลงไปในสมการ A = 2B – 7 จะได้ A = 2(20–A) – 7 → 3A = 33 → A = 11

{"correct_answer_key":"c"}

ให้:

( x ) เป็นจำนวนผู้ที่ใส่น้ำตาลในกาแฟ
( y ) เป็นจำนวนผู้ที่ใส่น้ำส้มในกาแฟ
( z ) เป็นจำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟ

จากข้อสอบ:

( y = 2x - 7 )
( z = 20 - (x + y - z) )

จากสมการที่ 2 สามารถเขียนใหม่ได้ว่า: [ z = 20 - x - y + z ] [ 0 = 20 - x - y ] [ x + y = 20 ]

เรามีสมการสองสมการ:

( y = 2x - 7 )
( x + y = 20 )

แทนค่า ( y ) จากสมการที่ 1 ลงในสมการที่ 2: [ x + (2x - 7) = 20 ] [ 3x - 7 = 20 ] [ 3x = 27 ] [ x = 9 ]

แทนค่า ( x = 9 ) กลับไปในสมการ ( y = 2x - 7 ): [ y = 2(9) - 7 ] [ y = 18 - 7 ] [ y = 11 ]

ดังนั้น จำนวนผู้ที่ใส่น้ำส้มในกาแฟมีอยู่ 11 คน ซึ่งตอบคำถามคือ 11 คน ซึ่งตรงกับตัวเลือก C.

{"correct_answer_key":"c"}

To solve this problem, let's define the variables and analyze the situation step by step:

Definitions:

Let $ x $ be the number of people who add sugar to their coffee.
Let $ y $ be the number of people who add orange juice to their coffee.
Let $ z $ be the number of people who add both orange juice and sugar to their coffee.
Let $ w $ be the number of people who add neither orange juice nor sugar to their coffee.

Key Information:

The total number of people surveyed is 20: $$ x + y - z + w = 20 $$ (We subtract $ z $ because those who add both orange juice and sugar are counted twice in $ x + y $.)
The number of people who add orange juice ($ y $) is 7 less than twice the number of people who add sugar ($ x $): $$ y = 2x - 7 $$
The number of people who add both orange juice and sugar ($ z $) is equal to the number of people who add neither ($ w $): $$ z = w $$

Substituting and Solving:

Using the total population equation $ x + y - z + w = 20 $, and substituting $ z = w $, we get: $$ x + y - z + z = 20 \implies x + y = 20 $$

Now substitute $ y = 2x - 7 $ into $ x + y = 20 $: $$ x + (2x - 7) = 20 $$ $$ 3x - 7 = 20 $$ $$ 3x = 27 $$ $$ x = 9 $$

Now substitute $ x = 9 $ into $ y = 2x - 7 $: $$ y = 2(9) - 7 = 18 - 7 = 11 $$

Thus, the number of people who add orange juice ($ y $) is 11.

Verification:

$ x = 9 $, $ y = 11 $, $ z = w $, and $ x + y = 20 $.
Since $ z = w $, the number of people who add both orange juice and sugar ($ z $) and those who add neither ($ w $) must sum to $ 20 - (x + y - z) = z + z = 2z $, which is consistent.

Final Answer:

The number of people who add orange juice to their coffee is 11, corresponding to option C.

{"correct_answer_key":"c"}

Alright, let's tackle this problem step by step. First, I need to understand what's being asked here. The question is in Thai, so I'll translate it to make sure I get all the details right.

The problem states: "From an exam of 20 coffee drinkers, it was found that the number of people who add orange juice to their coffee is 7 less than twice the number of people who add sugar to their coffee. The number of people who add both orange juice and sugar in their coffee is equal to the number of people who add neither. How many people add orange juice to their coffee?"

Okay, so we have 20 people total. Let me break down the information:

Let O be the number of people who add orange juice (น้ำส้ม).
Let S be the number of people who add sugar (น้ำตาล).
The first condition: O = 2S - 7. Because it's 7 less than twice the sugar adders.
The second condition: The number who add both (let's call this B) is equal to the number who add neither (let's call this N). So B = N.
Total people = 20.

We need to find O.

Hmm, to solve this, I should use set theory principles. The total can be broken down into four groups:

Only O (add only orange juice)
Only S (add only sugar)
Both O and S (B)
Neither (N)

We know that B = N. Let's denote B = N = x.

So, the total is: (Only O) + (Only S) + B + N = 20.

But we can also express Only O and Only S in terms of O and S. Let's see:

Only O = O - B Only S = S - B

Therefore, substituting into the total equation:

(O - B) + (S - B) + B + N = 20

Simplify this:

O - B + S - B + B + N = 20 O + S - B + N = 20

But since B = N, substitute N with B:

O + S - B + B = 20 → O + S = 20

Wait, that simplifies to O + S = 20? That can't be right because O and S might overlap. Wait, maybe I made a mistake here.

Wait, let me re-express the total equation again step by step.

Total = (Only O) + (Only S) + Both + Neither

Which is:

(O - B) + (S - B) + B + N = 20

Expanding that:

O - B + S - B + B + N = O + S - B + N = 20

Since B = N, substitute N with B:

O + S - B + B = O + S = 20

Ah, so O + S = 20. That's interesting. So the sum of people who add orange juice and those who add sugar (counting those who add both twice) is 20. But the total number of people is also 20. That suggests that the overlap (those who add both) plus the neither group must account for the difference. Wait, but according to the equation, O + S = 20, so the overlap and neither are already considered here?

Hmm, maybe I need to approach this differently. Let me write down the equations again.

Given:

O = 2S - 7 (from the first condition)
B = N (second condition)
Total = 20

Also, using the principle of inclusion-exclusion for sets:

Total = O + S - B + N

But since B = N, let's substitute N with B:

Total = O + S - B + B = O + S = 20

So that gives O + S = 20. But from the first equation, O = 2S -7. Substitute that into O + S =20:

(2S -7) + S = 20 → 3S -7 =20 → 3S =27 → S=9

Then O = 2*9 -7 = 18-7=11

Wait, so O is 11? Let me check if this makes sense.

If S=9, O=11. Then O + S =20, so according to the inclusion-exclusion formula, the total would be 20, which matches the total number of people. But we also have B = N.

Wait, but how does B and N fit into this?

Wait, the inclusion-exclusion formula says:

Total = O + S - B + N

But since B = N, let me plug in the numbers:

Total = 11 +9 - B + B = 20, which works. But that seems like B cancels out. Hmm, but that might not account for the actual values of B and N.

Wait, perhaps I need another equation here. Let me think again.

We know that B = N. Let me denote N = B.

Also, the total can be written as:

Only O + Only S + Both + Neither = 20

Which is:

(O - B) + (S - B) + B + B = 20

Because Only O is O minus both, Only S is S minus both, and Neither is B (since N=B).

So substituting:

(O - B) + (S - B) + B + B = O + S =20, which is the same as before. So that doesn't add new info.

But since we have O =2S -7 and O + S =20, solving gives S=9, O=11. So the answer would be 11, which is option C.

Wait, but let me check if there's any constraints on B and N. Since B can't be more than the smaller of O and S. Let's see:

If O=11 and S=9, then the maximum possible B is 9 (since S is 9). So B can be up to 9. Since N=B, and total people are 20, let's see if the numbers make sense.

Suppose B is some value between 0 and 9. Let's pick B = x, so N =x.

Then Only O = 11 -x, Only S =9 -x, Both =x, Neither =x.

Total: (11 -x) + (9 -x) +x +x = 11+9 =20. So yes, it works for any x between 0 and 9. But the problem doesn't give more constraints, so the answer is O=11, which is option C. So the answer should be C)11.

Wait, but let me check again the problem's exact wording to make sure I didn't misinterpret anything.

The problem says: "จำนวนผู้ที่ใส่น้ำส้มในกาแฟน้อยกว่าสองเท่าของจำนวนผู้ที่ใส่น้ำตาลในกาแฟอยู่ 7 คน" which translates to "The number of people who add orange juice is 7 less than twice the number who add sugar." So O = 2S -7. That's correct.

Then "จำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟเท่ากับจำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ" which is "The number who add both is equal to the number who add neither." So B = N. That's also correct.

So the equations are set up right, leading to O=11. So the answer is C.

The problem involves 20 coffee drinkers with conditions on those adding orange juice (O), sugar (S), both (B), and neither (N). Key equations derived are:

O = 2S − 7 (orange juice users are 7 less than twice the sugar users).
B = N (those adding both equal those adding neither).
Total: O + S − B + N = 20.

Substituting B = N into the total equation simplifies to O + S = 20. Plugging O = 2S − 7 into this gives:
2S − 7 + S = 20 → 3S = 27 → S = 9.
Thus, O = 2(9) − 7 = 11.

The calculations confirm that 11 people add orange juice, corresponding to option c.

{"correct_answer_key":"c"}

ให้ S เป็นจำนวนผู้ที่ใส่น้ำส้มในกาแฟ, T เป็นจำนวนผู้ที่ใส่น้ำตาลในกาแฟ, และ B เป็นจำนวนผู้ที่ใส่ทั้งน้ำส้มและน้ำตาลในกาแฟ

จากข้อมูลที่ให้มา:

S = 2T - 7
B = จำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ
จำนวนผู้ที่ดื่มกาแฟทั้งหมด = S + T - B + จำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ = 20

เนื่องจาก B = จำนวนผู้ที่ไม่ใส่น้ำส้มและไม่ใส่น้ำตาลในกาแฟ, เราสามารถเขียนสมการได้ว่า: S + T - B + B = 20 S + T = 20

แทนค่า S จากสมการแรก: (2T - 7) + T = 20 3T - 7 = 20 3T = 27 T = 9

แทนค่า T กลับไปในสมการแรก: S = 2(9) - 7 S = 18 - 7 S = 11

ดังนั้น, จำนวนผู้ที่ใส่น้ำส้มในกาแฟมีอยู่ 11 คน, ซึ่งตรงกับตัวเลือก C.

{"correct_answer_key":"c"}

Alright! Let's tackle this problem step by step. The question is about determining the number of people who put lemon in their coffee based on given conditions.

First, let's parse the information provided:

Total participants: 20 people.
The number of people who put lemon (L) is 7 less than twice the number of people who put sugar (S). So, L = 2S - 7.
The number of people who put both lemon and sugar (B) is equal to the number of people who put neither lemon nor sugar (N). So, B = N.
We need to find the value of L.

To solve this, we can use a Venn diagram approach or set theory principles. Let's denote:

Only lemon as L_only,
Only sugar as S_only,
Both lemon and sugar as B,
Neither as N.

The total number of people is the sum of all these groups: L_only + S_only + B + N = 20.

We also know that:

L = L_only + B,
S = S_only + B,
B = N.

From the first condition, L = 2S - 7. Substituting S from above, we get: L = 2(S_only + B) - 7.

But since L = L_only + B, we can set up the equation: L_only + B = 2(S_only + B) - 7.

Simplifying this: L_only + B = 2S_only + 2B - 7, L_only = 2S_only + B - 7.

Now, substituting back into the total equation: L_only + S_only + B + N = 20, (2S_only + B - 7) + S_only + B + B = 20, 3S_only + 3B - 7 = 20, 3S_only + 3B = 27, Divide both sides by 3: S_only + B = 9.

Since B = N, we can say S_only + B = 9 and N = B.

Let’s express everything in terms of B: From S_only + B = 9, we get S_only = 9 - B.

Also, L = L_only + B, and from earlier, L_only = 2S_only + B - 7. Substituting S_only: L_only = 2(9 - B) + B - 7 = 18 - 2B + B - 7 = 11 - B.

Thus, L = (11 - B) + B = 11.

So, the number of people who put lemon in their coffee is 11, which corresponds to option C.

{"correct_answer_key":"c"}

TPAT-1 Tests - เชาวน์ปัญญา - [9]

Question

Answers by AI

Given:

Conditions:

Total people equation:

Substitute ( O = 2S - 7 ) into ( S + O = 20 ):

Now find ( O ):

Verification:

Answer:

Brief Explanation:

Definitions:

Key Information:

Substituting and Solving:

Verification:

Final Answer:

TPAT-1 Tests - เชาวน์ปัญญา - [9]

Question

Answers by AI

C claude-3-5-sonnet-20241022 275 new bootstrap.Tooltip(document.getElementById("😭2"));

C claude-3-7-sonnet-20250219 435 new bootstrap.Tooltip(document.getElementById("😭3"));

C claude-3-7-sonnet-20250219[thinking=16k] 2813 new bootstrap.Tooltip(document.getElementById("😭4"));

C command-a-03-2025 354 new bootstrap.Tooltip(document.getElementById("😭5"));

C deepseek-chat-v3-0324 458 new bootstrap.Tooltip(document.getElementById("😭6"));

Given:

Conditions:

Total people equation:

Substitute ( O = 2S - 7 ) into ( S + O = 20 ):

Now find ( O ):

Verification:

Answer:

C deepseek-r1 1478 new bootstrap.Tooltip(document.getElementById("😭7"));

C gemini-1.5-pro-002 754 new bootstrap.Tooltip(document.getElementById("😭8"));

C gemini-2.0-flash-001 853 new bootstrap.Tooltip(document.getElementById("😭9"));

C gemini-2.0-flash-lite-001 375 new bootstrap.Tooltip(document.getElementById("😭10"));

C gemini-2.0-flash-thinking-exp-01-21 627 new bootstrap.Tooltip(document.getElementById("😭11"));

C gemini-2.5-flash-preview-04-17 6897 new bootstrap.Tooltip(document.getElementById("😭12"));

C gemini-2.5-flash-preview-04-17[no-thinking] 504 new bootstrap.Tooltip(document.getElementById("😭13"));

C gemini-2.5-pro-preview-03-25 2501 new bootstrap.Tooltip(document.getElementById("😭14"));

C gemma-3-27b-it 360 new bootstrap.Tooltip(document.getElementById("😭15"));

C gpt-4.1-2025-04-14 631 new bootstrap.Tooltip(document.getElementById("😭16"));

C gpt-4.1-mini-2025-04-14 281 new bootstrap.Tooltip(document.getElementById("😭17"));

C gpt-4.1-nano-2025-04-14 428 new bootstrap.Tooltip(document.getElementById("😭18"));

C gpt-4.5-preview-2025-02-27 707 new bootstrap.Tooltip(document.getElementById("😭19"));

C gpt-4o-2024-08-06 414 new bootstrap.Tooltip(document.getElementById("😭20"));

C gpt-4o-mini-2024-07-18 328 new bootstrap.Tooltip(document.getElementById("😭21"));

C grok-3-beta 320 new bootstrap.Tooltip(document.getElementById("😭22"));

C grok-3-mini-beta[thinking] 140 new bootstrap.Tooltip(document.getElementById("😭23"));

Brief Explanation:

C llama-3.3-70b-instruct 453 new bootstrap.Tooltip(document.getElementById("😭24"));

C llama-4-maverick 303 new bootstrap.Tooltip(document.getElementById("😭25"));

B llama-4-scout 539 new bootstrap.Tooltip(document.getElementById("😭26"));

? mistral-large-2411 2073 new bootstrap.Tooltip(document.getElementById("😭27"));

C o1-2024-12-17 1706 new bootstrap.Tooltip(document.getElementById("😭28"));

C o3-2025-04-16[high] 1639 new bootstrap.Tooltip(document.getElementById("😭29"));

C o3-2025-04-16[low] 654 new bootstrap.Tooltip(document.getElementById("😭30"));

C o3-2025-04-16[medium] 895 new bootstrap.Tooltip(document.getElementById("😭31"));

C o3-mini-2025-01-31[high] 1666 new bootstrap.Tooltip(document.getElementById("😭32"));

C o3-mini-2025-01-31[low] 1570 new bootstrap.Tooltip(document.getElementById("😭33"));

C o3-mini-2025-01-31[medium] 912 new bootstrap.Tooltip(document.getElementById("😭34"));

C o4-mini-2025-04-16[high] 647 new bootstrap.Tooltip(document.getElementById("😭35"));

C o4-mini-2025-04-16[low] 693 new bootstrap.Tooltip(document.getElementById("😭36"));

C o4-mini-2025-04-16[medium] 509 new bootstrap.Tooltip(document.getElementById("😭37"));

C phi-4 506 new bootstrap.Tooltip(document.getElementById("😭38"));

C qwen-max-2025-01-25 593 new bootstrap.Tooltip(document.getElementById("😭39"));

Definitions:

Key Information:

Substituting and Solving:

Verification:

Final Answer:

C qwq-32b 1896 new bootstrap.Tooltip(document.getElementById("😭40"));

C typhoon-v2-70b-instruct 351 new bootstrap.Tooltip(document.getElementById("😭41"));

C typhoon-v2-r1-70b-preview 592 new bootstrap.Tooltip(document.getElementById("😭42"));