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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:52) correct
37%
(02:19)
wrong
based on 202
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Of the students who dine in a cafeteria, each student either likes or dislikes coffee and each student either likes or dislikes tea. Of these students, 50% dislike coffee; of those who dislike coffee, 1/3rd also dislike tea. How many students like tea but dislike coffee?
(1) 240 students dine in the cafeteria.
(2) 120 students like coffee.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) 240 students dine in the cafeteria.
(2) 120 students like coffee.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
Updated on: 31 Dec 2025, 02:01
Originally posted by paudomingoo on 30 Dec 2025, 04:37.
Last edited by paudomingoo on 31 Dec 2025, 02:01, edited 1 time in total.
Last edited by paudomingoo on 31 Dec 2025, 02:01, edited 1 time in total.
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As each student either likes or dislikes coffee, 50% like coffee and 50% dislike it.
1/3 of coffee dislikers also dislike tea --> 1/3 · 50% dislike tea and coffee --> 2/3 · 50% like tea but dislike coffee
(1) 240 students dine in the cafeteria --> 2/3 · 50/100 · 240 = 80 ✅
(2) 120 students like coffee --> 50% like coffee so 100% is 120 · 2 = 240. The total students is the same as in (1), so the result is the same ✅
Correct Answer: D (each alone)
1/3 of coffee dislikers also dislike tea --> 1/3 · 50% dislike tea and coffee --> 2/3 · 50% like tea but dislike coffee
(1) 240 students dine in the cafeteria --> 2/3 · 50/100 · 240 = 80 ✅
(2) 120 students like coffee --> 50% like coffee so 100% is 120 · 2 = 240. The total students is the same as in (1), so the result is the same ✅
Correct Answer: D (each alone)
30 Dec 2025, 05:27
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ExpertsGlobal5
Let’s adopt a matrix based approach to this problem. Let’s assume the total to be 6x.
50% don’t like coffee = 50%*(6x) = 3x
People who like Coffee = Total - Dislike Coffee = 6x - 3x = 3x.
Of these 3x, one third dislike tea = (1/3)*3x = x
Like Tea , but Dislike Coffee = 3x - x = 2x
| Like Coffee | Dislike Coffee | Total | |
| Like Tea | 2x | ||
| Dislike Tea | x | ||
| Total | 3x | 3x | 6x |
we need to find : 2x
Statement 1:
240 students dine in the cafeteria.
6x = 240, so, x=40
Therefore, 2x = 2*40 = 80.
Hence, Sufficient
Statement 2:
120 students like coffee.
3x = 120 , x = 40
Therefore, 2x = 2*40 = 80.
Hence, Sufficient
Option D
