How would you backsolve this problem.

Expert replies

sellaia: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat Nov 26, 2011 1:17 pm

by sellaia » Sun Dec 18, 2011 10:03 am

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]

Source: Beat The GMAT — GMAT Strategy | Sun Dec 18, 2011 10:03 am

GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Mon Dec 19, 2011 3:18 pm

sellaia wrote: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.

Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review