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GMAT Official Guide 2019 A certain store will order 25

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by BTGmoderatorDC » Sun Jul 01, 2018 6:26 pm

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Answers

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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
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by Jay@ManhattanReview » Sun Jul 01, 2018 10:12 pm
BTGmoderatorDC wrote: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
We have W + M + R = 25 such that W > M and W > R.

We have to minimize the value of W.

Given, W > M and W > R, we can maximize the values of M and R such that W is minimum.

Say M = R = x

Thus, from W + M + R = 25, we have W + x + x = 25

Had W and x were equal, W = x = 25/3 = 8.33

Since W and x are integers, and W > X, we can have W = 9, and x = 8.

The correct answer: C

Hope this helps!

-Jay
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by regor60 » Mon Jul 02, 2018 8:44 am
To minimize W we need to maximize M and R.

Since both M and R have to be less than W, minimize that difference to maximize W.

The minimum difference, since we're dealing with whole numbers, is 1.

So M = R = W-1

Adding M, R and W: W-1+W-1+W = 25 > 3W = 27 and W = C,9
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by Scott@TargetTestPrep » Wed Jul 04, 2018 6:09 pm
BTGmoderatorDC wrote: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
On average, each variety of apple 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 McIntosh crates

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

Answer Choice B: 8 McIntosh crates

Similar to the above discussion, there are 25 - 8 = 17 crates of Winesap 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 McIntosh crates

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

Answer: C

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