AAPL wrote: ↑

Mon Nov 16, 2020 5:13 am

Official Guide

A certain store will order 25 crates of apples. The apples will be of three different varieties: McIntosh, Rome, and Winesap, and each crate will contain apples of only one variety. If the store is to order more crates of Winesap than crates of McIntosh and more crates of Winesap than crates of Rome, What is the least possible number of crates of Winesap that the store will order?

A. 7
B. 8
C. 9
D. 10
E. 11

OA C

Solution:

On average, each variety of apples is approximately 25/3 ≈ 8 crates. So we can have 9 crates of Winesap and 8 crates of Rome and 8 crates of McIntosh, for a total of 25 crates. Since 9 is the closest number to the average, it’s the least possible number of crates for the variety of apples - Winesap - that has the greatest number of crates.

Alternate Solution:

Let’s try each answer choice, starting from the smallest.

Answer Choice A: 7 Winesap crates

If there are 7 Winesap crates, then there are 25 - 7 = 18 crates of McIntosh and Rome crates. If there are 18 crates of McIntosh and Rome crates combined, then either one of these crates has to be more than the number of Winesap crates (which is 7). This is because, if both the number of McIntosh and Rome crates are less than 7, then there can be at most 12 remaining crates, but we have 18.

Answer Choice B: 8 Winesap crates

Similar to the above discussion, there are 25 - 8 = 17 crates of McIntosh and Rome crates. Again, if one of these crates is less than 8, then the other one will definitely be greater than 8.

Answer Choice C: 9 Winesap crates

In this case, there are 25 - 9 = 16 crates of McIntosh and Rome crates. In this case, we observe that the store could have ordered 8 crates of the McIntosh and Rome apples each, so it is possible for the store to have ordered 9 Winesap crates. Since we are looking for the smallest value, this is the correct value.

Answer: C