sana.noor wrote:at garcia's market, a certain brand of cocoa is sold in boxes of two sizes, A and B. For which size is the price per ounce of cocoa lets?
1) the weight of the cocoa in the size B box is 12/3 times that in the size A box.
2) the price of a size B box is 80% more than the price of a size A box.
Target question:
Which size has the lower price per ounce?
Let A = price of size A box
Let B = price of size B box
Let a = weight of the size A box (in ounces)
Let b = weight of the size B box (in ounces)
So, the price per ounce for box A equals A/a
Similarly, the price per ounce for box B equals B/b
It's time to rephrase the target question.
Rephrased target question:
Which is greater: A/a or B/b?
ASIDE: Rephrasing the target question is a very important strategy when solving Data Sufficiency questions. In anyone is interested, we have a free video on this topic:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: The weight of the cocoa in the size B box is 12/3 times that in the size A box
This tells us nothing about the prices for each box, so there's no way to determine A/a or B/b.
Since we cannot answer the
rephrased target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The price of a size B box is 80% more than the price of a size A box.
This tells us nothing about the weights of each box, so there's no way to determine A/a or B/b.
Since we cannot answer the
rephrased target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1: the weight of box B is 12/3 times that of box A.
So, if a and b equal the weights of boxes A and B, then we can write:
b = (12/3)a
or
b = 4a
Statement 2: The price of a box B is 80% more than the price of box A.
So, if A and B equal the prices of boxes A and B, then we can write:
B = 1.8A
Now that we've expressed B and b in terms of A and a, we can compare the price per ounce for each box.
Box A: price per ounce = A/a
Box B: price per ounce = B/b = 1.8A/4a = (1.8/4)(A/a)
Since (1.8/4)(A/a) is definitely less than A/a,
we can be certain that B/b is less than A/a
Since we can now answer the
rephrased target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
