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11 Jul 2022, 08:00
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Difficulty:
95%
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Question Stats:
11% (01:59) correct
89%
(02:19)
wrong
based on 237
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Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?
(1) No suitcase has more red sneakers than the first one.
(2) The first suitcase has between 23% and 27% of his blue sneakers.
M38-04
(1) No suitcase has more red sneakers than the first one.
(2) The first suitcase has between 23% and 27% of his blue sneakers.
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M38-04
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12 Jul 2022, 07:30
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Bunuel
GMAT CLUB Official Explanation:
Mbappé has two types of sneakers: red and blue. When packing for the World Cup, he puts equal number of sneakers in each of his suitcases. The first suitcase has 27% of all his red sneakers. Does the first suitcase have less than 25% of his blue sneakers ?
Say Mbappé has x suitcases. Since he put equal number of sneakers in each of his suitcases, then each suitcase has 100/x% of all his sneakers. For example:
- If Mbappé has 10 suitcases, then each will have 100/10 = 10% of all his sneakers.
Next, notice that, if a suitcase has LESS than 100/x% of Mbappé's red sneakers, it must have MORE than 100/x% of his blue sneakers (and vise-versa). For example:
- If Mbappé has 10 suitcases, each having 10% of all his sneakers, and one specific suitcase has 5% of his red sneakers, then it must have MORE than 10% of his blue sneakers (if a suitcase has less than 10% of red sneakers and less than 10% of blue sneakers, it cannot have 10% of all sneakers).
(1) No suitcase has more red sneakers than the first one.
How many suitcases can Mbappé have? Can he have 3? No, because in this case at least one of his suitcases must have MORE than 100/3 ≈ 33% of his red sneakers (all of his 3 suitcases cannot have less than 33% of his read sneakers). So, Mbappé must have 4 or more suitcases. This means that each of them has LESS than 25% of all his sneakers. For example:
- If he has 4 suitcases then each has 100/4 = 25% of all his sneakers;
If he has 5 suitcases then each has 100/5 = 20% of all his sneakers;
...
From the stem we know that the first suitcase has 27% (more than 25%) of all his red sneakers, thus it must have less than 25% of his blue sneakers. Sufficient.
(2) The first suitcase has between 23% and 27% of his blue sneakers.
From, the stem we now that the first suitcase has 27% of all his red sneakers and from this statement that the first suitcase has more than 23% of his blue sneakers:
- \(0.23 \leq \frac{1}{x} \leq 0.27\)
Only integer which satisfies the above is \(x=4\). So, Mbappé has 4 suitcases and each has 25% of all his sneakers. Since the first suitcase has 27% (more than 25%) of all his red sneakers, then it must have less than 25% of his blue sneakers. Sufficient.
Answer: D.
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11 Jul 2022, 11:18
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Bunuel
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