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by prernamalhotra » Thu Jul 03, 2014 1:33 am
In a certain warehouse, 60% of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80% of the packages weight atleast 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds:

1)8
2)64
3)96
4)102
5)144

Thank you,
Prerna
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by GMATGuruNY » Thu Jul 03, 2014 2:10 am
prernamalhotra wrote:In a certain warehouse, 60% of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80% of the packages weight atleast 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds:

1)8
2)64
3)96
4)102
5)144

Thank you,
Prerna
Since 80% of the packages weigh at least 25 pounds, we get:
(at least 25 pounds) : (less than 25 pounds) = 80:20 = 4:1.

Since 48 packages weigh less than 25 pounds, the MULTIPLIER for the ratio is 48:
(at least 25 pounds) : (less than 25 pounds) = (48*4) : (48*1) = 192:48.
Thus, the total number of packages = 192+48 = 240.

Since 60% of the packages weigh less than 75 pounds, 40% of the 240 packages weigh at least 75 pounds:
(40/100)(240) = 96.

Thus:
Packages that weigh at least 25 pounds but less than 75 pounds = (total) - (less than 25 pounds) - (at least 75 pounds) = 240-48-96 = 96.

The correct answer is C.
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by Brent@GMATPrepNow » Thu Jul 03, 2014 6:01 am
prernamalhotra wrote:In a certain warehouse, 60% of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80% of the packages weight 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
Here's another approach.

If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds

48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve: T = 240

60% of the packages weigh less than 75 pounds
So, 60% of T = number of packages that weigh less than 75 pounds
60% of 240 = 144, so 144 packages weigh less than 75 pounds

OF THOSE 144 packages that weigh less than 75 pounds, 48 packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds = 144 - 48 = [spoiler]96 = C[/spoiler]

Cheers,
Brent
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by GMATinsight » Thu Jul 03, 2014 9:51 am
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