Percentages

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

Percentages

by Abdulla » Fri Dec 12, 2008 2:19 pm

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

Abdulla

Quote

Source: Beat The GMAT — Problem Solving | Fri Dec 12, 2008 2:19 pm

bdemps15: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Fri Dec 12, 2008 1:52 pm

Re: Percentages

by bdemps15 » Fri Dec 12, 2008 2:31 pm

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

Last edited by bdemps15 on Fri Dec 12, 2008 2:32 pm, edited 1 time in total.

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dendude: Master | Next Rank: 500 Posts; Posts: 160; Joined: Fri May 30, 2008 7:10 pm; Thanked: 10 times; GMAT Score:600

by dendude » Fri Dec 12, 2008 2:31 pm

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