Word Problems

[swerve]

Of the first three dozen cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. If 1/2 of the remaining cookies that were baked that day were chocolate chip cookies, how many chocolate chip cookies were baked that day?

1) The bakery made five dozen cookies that day
2) Of all the cookies made that day, 2/5 were chocolate chip

The OA is D

Source: Princeton Review

[Brent@GMATPrepNow]

Of the first three dozen cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. If 1/2 of the remaining cookies that were baked that day were chocolate chip cookies, how many chocolate chip cookies were baked that day?

1) The bakery made five dozen cookies that day
2) Of all the cookies made that day, 2/5 were chocolate chip

The OA is D

Source: Princeton Review

Given: Of the first three dozen (36) cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. 1/2 of the remaining cookies that were baked that day were chocolate chip cookies,
1/3 of 36 = 12. So, 12 chocolate cookies were baked in the first round of baking.

Let x = the number of cookies baked in the second round of baking (AFTER the first 36 cookies were baked)
So, 0.5x = number of chocolate cookies were baked in the second round of baking.

So, the TOTAL number of chocolate cookies baked that day = 12 + 0.5x

Target question: How many chocolate chip cookies were baked that day?
This is a good candidate for rephrasing the target question.
REPHRASED target question: What is the value of 12 + 0.5x?

Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: The bakery made five dozen cookies that day.
If 3 dozen (36) cookies were baked in the FIRST round of baking, and a total of 5 dozen (60) cookies were baked in total, then we can conclude that 2 dozen (24) cookies were baked in the SECOND round.
In other words, x = 24
Now, that we know the value of x, we can see that 12 + 0.5x = 12 + 0.5(24) = 12 + 12 = 24
So, the answer to the REPHRASED target question is 12 + 0.5x = 24
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: Of all the cookies made that day, 2/5 were chocolate chip.
In other words: (total number of chocolate chip cookies baked) = (2/5)(total number of cookies baked)
In other words: total number of chocolate chip cookies baked) = (2/5)(cookies baked in first round + cookies baked in second round)
Or we can write: 12 + 0.5x = (2/5)(36 + x)
Since we COULD solve this equation for x, we COULD answer the REPHRASED target question with certainty.
So, statement 2 is SUFFICIENT

Answer: D