BTGModeratorVI wrote: ↑

Tue Jul 07, 2020 6:24 am

Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of $144. What was the total pretax price of the metal frames that Tami purchased?

(1) The price of each metal frame was 60% greater than the price of each wooden frame.
(2) Tami purchased twice as many wooden frames as metal frames.

Answer: C
Source: Official guide

Given: Tami purchased several identically priced metal frames and several identically priced wooden frames for a total pretax price of $144.

Let W = the NUMBER of wooden frames purchased
Let w = the PRICE (in dollars) of ONE wooden frame
So, Ww = the COST of buying W wooden frames

Let M = the NUMBER of metal frames purchased
Let m = the PRICE (in dollars) of ONE metal frame
So, Mm = the COST of buying M metal frames

We can now write: Ww + Mm = 144

Target question: What is the value of Mm?
ASIDE: You can see that I rephrased the target question to match the variables I'm using.

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

Statement 1: The price of each metal frame was 60% greater than the price of each wooden frame.
In other words: m = w + (60% of w)
So: m = w + 0.6w
Simplify: m = 1.6w
We also have this equation: Ww + Mm = 144
Do we have enough information to find the value of Mm?
No.
If we replace 1.6w with 1.6w, we get: Ww + M(1.6w) = 144
At this point we can see that we don't have enough information to find the value of Mm
Statement 1 is NOT SUFFICIENT

Statement 2: Tami purchased twice as many wooden frames as metal frames.
We can write: W = 2M or we can write: M = 0.5W
We also have this equation: Ww + Mm = 144
Is this enough information to find the value of Mm?
No.
If we replace M with 0.5W, we get: Ww + (0.5W)m = 144
At this point we can see that we don't have enough information to find the value of Mm
Statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
From the given information we know that Ww + Mm = 144
Statement 1 tells us that m = 1.6w
Statement 2 tells us that M = 0.5W

Replace m and M to get: Ww + (0.5W)(1.6w) = 144
Simplify: Ww + 0.8Ww = 144
Simplify: 1.8Ww = 144
Divide both sides by 1.8 to get: Ww = 80

In other words we now have: 80 + Mm = 144
Subtract 80 from both sides to get: Mm = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent