Percentages

Abdulla wrote:In a certain warehouse, 60 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?

(A) 8
(B) 64
(C) 96
(D) 102
(E) 144

OA is C

If 80% of the packages weigh more than 25 pounds, then 20% weigh less. The problem states that there are 48 packages weighing less than 25 pounds.

Thus, 20% of X = 48, where X is the total number of packages
X = 240.

If 60% of the packages weigh less than 75 lbs, then that means 144 packages weigh less.
60% of 240 = 144

Question is how many weigh more than 25 lbs but less than 75 lbs.
Thus, 144 - 48 = 96 packages

The answer is C

80 percent of packages: >25 lbs
That means 20 percent: <25lbs

20 percent is 48 packages.
This gives total # of packages: 240

60 percent of 240 packages are <75lbs i.e 144 packages
This 144 also includes the 48 that are <25lbs.

Hence 144 - 48 = 96, would give you the # of packages that weigh between 25lbs and 75lbs

Ans: C

I used this pic while reading the problem. <25lbs 100%-80% = 20%. X - packages between 25 lbs and 75 lbs. It is clear that X = 40% is 96.