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Every box of cookies contains exactly 6 cookies.

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Every box of cookies contains exactly 6 cookies. [#permalink] New post 04 Mar 2018, 13:52
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Question Stats:

29% (01:52) correct 70% (01:01) wrong based on 17 sessions
Every box of cookies contains exactly 6 cookies.

Quantity A
Quantity B
The total number of cookies purchased if Sally purchased 3 more than twice as many boxes of oatmeal cookies as boxes of chocolate chip cookies
The total number of cookies purchased if Sally purchased 2 fewer than 3 times as many boxes of oatmeal cookies as boxes of chocolate chip cookies


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 16
Page: 496
[Reveal] Spoiler: OA

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GMAT Club Legend
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Joined: 07 Jun 2014
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Kudos [?]: 1622 [0], given: 385

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Re: Every box of cookies contains exactly 6 cookies. [#permalink] New post 04 Mar 2018, 14:27
Expert's post
Explanation

First, plug in 1 for the number of boxes of chocolate chip cookies.

In Quantity A, if Sally buys 1 box of chocolate chip cookies, then she buys 2(1) + 3 = 5 boxes of oatmeal cookies, for a total of 6 boxes, or 36 cookies.

In Quantity B, if Sally buys 1 box of chocolate chip cookies, then she buys 3(1) – 2 = 1 box of oatmeal cookies, for a total of 2 boxes, or 12 cookies. Quantity A is greater, so eliminate choices (B) and (C).

Now plug in 10 boxes of chocolate chip cookies:

Quantity A is now 2(10) + 3 = 23 boxes of oatmeal cookies, for a total of 33 boxes, or 198 cookies, and

Quantity B is now 3(10) – 2 = 28 boxes of oatmeal cookies, for a total of 38 boxes, or 228 cookies.

Quantity B is now greater, so eliminate choice (A), and you’re left with choice (D).
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Re: Every box of cookies contains exactly 6 cookies. [#permalink] New post 05 Mar 2018, 18:20
The total number of cookies purchased if Sally purchased 3 more than twice as many boxes of oatmeal cookies as boxes of chocolate chip cookies
oatmeal_cookies = 3 + 2* chocolate_cookies

The total number of cookies purchased if Sally purchased 2 fewer than 3 times as many boxes of oatmeal cookies as boxes of chocolate chip cookies
3*oatmeal_cookies - 2 = chocolate_cookies -> oatmeal_cookies = (chocolate_cookies + 2)/3

and we know that Sally has bought both cookies, their sum is oatmeal + chocolate. Having the relation of these two we calculate their sum in A and B:
A: oatmeal + chocolate = 3 + 2* chocolate_cookies + chocolate_cookies = 3 + 3* chocolate_cookies
B: oatmeal + chocolate = (chocolate_cookies + 2)/3 + chocolate_cookies = 6 + 4/3*chocolate_cookies
comparing A and B we notice for different values of chocolate_cookies A and B are sometimes greater and sometimes less.
3 + 3* chocolate_cookies 6 + 4/3*chocolate_cookies (adding -3)
3* chocolate_cookies 3 + 4/3*chocolate_cookies (deleting 4/3*chocolate)
5/3*chocolate_cookies 3
and these two are not comparable.
if chocolate_cookies is 3 : A > B
if chocolate_cookies is 1 : A < B
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Re: Every box of cookies contains exactly 6 cookies. [#permalink] New post 09 Mar 2018, 12:42
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In Quantity A, it's given that:
O = 2C + 3
Therefore, Quantity A = O + C = 2C + 3 + C = 3C + 3

Similarly, in Quantity B, it's given that:
O = 3C - 2
Thus, Quantity B = O + C = 3C - 2 + C = 4C - 2

Now, let's simplify both quantities. i.e subtract 3C from both quantities and add 2 in both quantities.

Quantity A: 5
Quantity B: C

We don't know what's C, i.e it can be greater than 5 or less than 5 or equals. So

Choice D is correct.

Some people may thing, C as 6. In fact, C is not a single box. There are C boxes, which you can't tell how many boxes. While each box has 6 cookies.
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Re: Every box of cookies contains exactly 6 cookies. [#permalink] New post 11 Mar 2018, 07:15
D
Re: Every box of cookies contains exactly 6 cookies.   [#permalink] 11 Mar 2018, 07:15
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