A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and

[BTGmoderatorDC]

A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?

A. 7
B. 14
C. 21
D. 28
E. 35



OA E

Source: Manhattan Prep

[Brent@GMATPrepNow]

A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?

A. 7
B. 14
C. 21
D. 28
E. 35



OA E

Source: Manhattan Prep

We're looking for the smallest possible number of chocolate chip cookies.
So, let's start by testing answer choice A

A) If we make 7 chocolate chip cookies, then the remaining 88 cookies are peanut cookies.
We're told that peanut cookies are baked in batches of 6
However, 88 is NOT divisible by 6, which means there cannot be 88 peanut cookies.
ELIMINATE A

B) If we make 14 chocolate chip cookies, then the remaining 81 cookies are peanut cookies.
However, 81 is NOT divisible by 6, which means there cannot be 81 peanut cookies.
ELIMINATE B

C) If we make 21 chocolate chip cookies, then the remaining 74 cookies are peanut cookies.
However, 74 is NOT divisible by 6, which means there cannot be 74 peanut cookies.
ELIMINATE C

D) If we make 28 chocolate chip cookies, then the remaining 67 cookies are peanut cookies.
However, 67 is NOT divisible by 6, which means there cannot be 67 peanut cookies.
ELIMINATE D

By the process of elimination, the correct answer is E

Cheers,
Brent

[Scott@TargetTestPrep]

A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?

A. 7
B. 14
C. 21
D. 28
E. 35

OA E

Source: Manhattan Prep

Solution:

We can let c = the number of batches of chocolate chip cookies made and p = the number of batches of peanut cookies made and create the equation:

7c + 6p = 95

7c = 95 - 6p

c = (95 - 6p)/7

In order for c to be an integer, we need (95 - 6p) to be a multiple of 7.

Let’s start with the largest value of p and work our way down.

When p is 15, we have:

c = 5/7... this does not work

When p is 14, we have:

c = 11/7… this does not work

When p is 13, we have:

c = 17/7... this does not work

When p is 12, we have:

c = 23/7… this does not work

When p is 11, we have:

c = 29/7... this does not work

When p is 10, we have:

c = 35/7 = 5... this works!

So, the minimum number of batches of chocolate chip cookies is 5, and, thus, the minimum number of chocolate chip cookies is 5 x 7 = 35.

Alternate Solution:

Let’s test each answer choice, starting with the smallest value:

Answer Choice A: c = 7

If c = 7, then the number of peanut butter cookies is 95 - 7 = 88; however, since 88 is not divisible by 6, c = 7 is not possible.

Answer Choice B: c = 14

If c = 14, then the number of peanut butter cookies is 95 - 14 = 81; however, since 81 is not divisible by 6, c = 14 is not possible.

Answer Choice C: c = 21

If c = 21, then the number of peanut butter cookies is 95 - 21 = 74; however, since 74 is not divisible by 6, c = 21 is not possible.

Answer Choice D: c = 28

If c = 28, then the number of peanut butter cookies is 95 - 28 = 67; however, since 67 is not divisible by 6, c = 28 is not possible.

Since we eliminated every other answer choice, we know by this point that the correct answer is E; however, let’s verify this as an exercise:

Answer Choice E: c = 35

If c = 35, then the number of peanut butter cookies is 95 - 35 = 60, which is a possible value since 60 is divisible by 6.

Answer: E