How would you backsolve this problem.

[sellaia]

Hi, this is my first thread on the forum. I wrote the GMAT a 1 month. At the time I was very confident in my quant skills, however since english is not my first language I focused my efforts toward the verbal section. My strategy had mixed results as I scored in the 99th percentile for the verbal section, but in the 48th percentile in the quant part. The problem was that I didn't manage to answer the last questions. So now I am trying to develop strategies to be faster with the math section. How would you go on backsolving this question ?


Each of the 30 boxes in a certain shipment with either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

A. 4
B. 6
C. 10
D. 20
E. 24

[spoiler]OA: D[/spoiler]

[GmatMathPro]

Hi, this is my first thread on the forum. I wrote the GMAT a 1 month. At the time I was very confident in my quant skills, however since english is not my first language I focused my efforts toward the verbal section. My strategy had mixed results as I scored in the 99th percentile for the verbal section, but in the 48th percentile in the quant part. The problem was that I didn't manage to answer the last questions. So now I am trying to develop strategies to be faster with the math section. How would you go on backsolving this question ?


Each of the 30 boxes in a certain shipment with either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

A. 4
B. 6
C. 10
D. 20
E. 24

[spoiler]OA: D[/spoiler]

You can use the concept of weighted averages to solve this quickly. Here we know that all of the boxes weigh either 10 or 20 pounds, and that the overall average is 18:

10-------18-20

Notice that 18 is 80% of the way from 10 to 20. This means that 80% of the boxes weigh 20 pounds. 0.8*30=24, so there are 24 twenty pound boxes and 6 ten pounds boxes. We need to remove enough 20 pound boxes so that the overall average is 14:

10---14-----20

Note that in this case the overall average is closer to 10 than to 20, which implies that there are more 10 pound boxes than 20 pound boxes. Looking at the answer choices, only D and E accomplish this, but if we remove all 24 twenty-pound boxes, there won't be any left,making the overall average exactly 10, so the answer must be D.