gmatt1476 wrote:
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.
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 = 144Target 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-data-sufficiency?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 = 1.6wWe also have this equation:
Ww + Mm = 144Do 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
MmStatement 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 = 0.5WWe also have this equation:
Ww + Mm = 144Is 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
MmStatement 2 is NOT SUFFICIENT
Statements 1 and 2 combined From the given information we know that
Ww + Mm = 144Statement 1 tells us that
m = 1.6wStatement 2 tells us that
M = 0.5WReplace m and M to get:
Ww + (0.5W)(1.6w) = 144Simplify:
Ww + 0.8Ww = 144Simplify:
1.8Ww = 144Divide both sides by 1.8 to get: Ww = 80
In other words we now have:
80 + Mm = 144Subtract 80 from both sides to get:
Mm = 64Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent