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03 Jun 2026, 15:45
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Difficulty:
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Question Stats:
21% (02:17) correct
79%
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wrong
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At a school fundraiser, a snack table sold four types of items: fruit cups, granola bars, sandwich boxes, and salad bowls. A fruit cup cost $3, a granola bar cost $5, a sandwich box cost $9, and a salad bowl cost $14. If the snack table sold 21 items in total, at least one of each type, and collected $180, how many granola bars were sold?
(1) The number of granola bars sold was equal to the number of sandwich boxes sold.
(2) The snack table sold 4 fruit cups and 5 sandwich boxes.
(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) The number of granola bars sold was equal to the number of sandwich boxes sold.
(2) The snack table sold 4 fruit cups and 5 sandwich boxes.
(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.
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M47-184
10 Jun 2026, 01:00
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GMAT Club Official Solution:
At a school fundraiser, a snack table sold four types of items: fruit cups, granola bars, sandwich boxes, and salad bowls. A fruit cup cost $3, a granola bar cost $5, a sandwich box cost $9, and a salad bowl cost $14. If the snack table sold 21 items in total, at least one of each type, and collected $180, how many granola bars were sold?
Let F, G, S, and L be the numbers of fruit cups, granola bars, sandwich boxes, and salad bowls sold, respectively.
Given:
F + G + S + L = 21 (i)
3F + 5G + 9S + 14L = 180 (ii)
The question asks for G.
(1) The number of granola bars sold was equal to the number of sandwich boxes sold.
So G = S.
Then from (i):
F + 2G + L = 21
and from (ii):
3F + 14G + 14L = 180
Multiply the first equation by 3:
3F + 6G + 3L = 63
Subtract from 3F + 14G + 14L = 180:
8G + 11L = 117
Now since G and L must be positive integers, we should check whether this equation gives one or more than one set of solutions for (G, L):
11L = 117 - 8G
So, 117 - 8G must be a positive multiple of 11: 110, 99, 88, 77, ..., 11. Only G = 5 and L = 7 work. So G = 5.
Sufficient.
(2) The snack table sold 4 fruit cups and 5 sandwich boxes.
So F = 4 and S = 5.
From the total number of items:
4 + G + 5 + L = 21
G + L = 12
From the total revenue:
3 * 4 + 5G + 9 * 5 + 14L = 180
12 + 5G + 45 + 14L = 180
5G + 14L = 123
So, we have two distinct linear equations with two unknowns: G + L = 12 and 5G + 14L = 123. We can solve and get the value of G.
Sufficient.
Answer: D.
At a school fundraiser, a snack table sold four types of items: fruit cups, granola bars, sandwich boxes, and salad bowls. A fruit cup cost $3, a granola bar cost $5, a sandwich box cost $9, and a salad bowl cost $14. If the snack table sold 21 items in total, at least one of each type, and collected $180, how many granola bars were sold?
Let F, G, S, and L be the numbers of fruit cups, granola bars, sandwich boxes, and salad bowls sold, respectively.
Given:
F + G + S + L = 21 (i)
3F + 5G + 9S + 14L = 180 (ii)
The question asks for G.
(1) The number of granola bars sold was equal to the number of sandwich boxes sold.
So G = S.
Then from (i):
F + 2G + L = 21
and from (ii):
3F + 14G + 14L = 180
Multiply the first equation by 3:
3F + 6G + 3L = 63
Subtract from 3F + 14G + 14L = 180:
8G + 11L = 117
Now since G and L must be positive integers, we should check whether this equation gives one or more than one set of solutions for (G, L):
11L = 117 - 8G
So, 117 - 8G must be a positive multiple of 11: 110, 99, 88, 77, ..., 11. Only G = 5 and L = 7 work. So G = 5.
Sufficient.
(2) The snack table sold 4 fruit cups and 5 sandwich boxes.
So F = 4 and S = 5.
From the total number of items:
4 + G + 5 + L = 21
G + L = 12
From the total revenue:
3 * 4 + 5G + 9 * 5 + 14L = 180
12 + 5G + 45 + 14L = 180
5G + 14L = 123
So, we have two distinct linear equations with two unknowns: G + L = 12 and 5G + 14L = 123. We can solve and get the value of G.
Sufficient.
Answer: D.
General Discussion
ankushsambare
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Updated on: 06 Jun 2026, 22:19
Originally posted by ankushsambare on 03 Jun 2026, 20:31.
Last edited by ankushsambare on 06 Jun 2026, 22:19, edited 1 time in total.
Last edited by ankushsambare on 06 Jun 2026, 22:19, edited 1 time in total.
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Let:
2G + 6S + 11B = 117
Statement (1): G = S
Substitute S = G:
2G + 6G + 11B = 117
8G + 11B = 117
For integer solutions, 117 − 11B must be divisible by 8.
Trying values of B:
Statement (1) is sufficient.
Statement (2): F = 4 and S = 5
From the total-items equation:
4 + G + 5 + B = 21
G + B = 12
From the revenue equation:
3(4) + 5G + 9(5) + 14B = 180
12 + 45 + 5G + 14B = 180
5G + 14B = 123
Using G + B = 12:
G = 12 − B
Substitute:
5(12 − B) + 14B = 123
60 + 9B = 123
B = 7
Therefore G = 12 − 7 = 5.
Statement (2) is sufficient.
Since each statement alone is sufficient, the answer is D.
- F = fruit cups
- G = granola bars
- S = sandwich boxes
- B = salad bowls
- F + G + S + B = 21
- 3F + 5G + 9S + 14B = 180
2G + 6S + 11B = 117
Statement (1): G = S
Substitute S = G:
2G + 6G + 11B = 117
8G + 11B = 117
For integer solutions, 117 − 11B must be divisible by 8.
Trying values of B:
- B = 7 gives 117 − 77 = 40, so G = 40/8 = 5.
- The next value that works is B = 15, which would make G negative, impossible.
Statement (1) is sufficient.
Statement (2): F = 4 and S = 5
From the total-items equation:
4 + G + 5 + B = 21
G + B = 12
From the revenue equation:
3(4) + 5G + 9(5) + 14B = 180
12 + 45 + 5G + 14B = 180
5G + 14B = 123
Using G + B = 12:
G = 12 − B
Substitute:
5(12 − B) + 14B = 123
60 + 9B = 123
B = 7
Therefore G = 12 − 7 = 5.
Statement (2) is sufficient.
Since each statement alone is sufficient, the answer is D.
