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Manager  Joined: 20 Oct 2004
Posts: 90
In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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17 00:00

Difficulty:   55% (hard)

Question Stats: 70% (02:55) correct 30% (03:17) wrong based on 298 sessions

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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
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4068
Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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4
kdhong 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

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 = 96 = C

Cheers,
Brent
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Math Expert V
Joined: 02 Aug 2009
Posts: 8197
Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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

a)8
b)64
c)96
d)102
e)144

hello,
80% weigh atleast 25, so 20% weigh less than 25, equal to 48 packages...
so 20%=48..
now packages that weigh between 25 and 75= 60%-20%=40%...
since 20%=48, 40%=96..
C
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Director  Joined: 03 Nov 2004
Posts: 586
Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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C
60% < 75 lbs; 48 < 25lbs &
80% >= 25lbs, so 20% = 48packages
Total no. of packages = 240
since 60% < 75 lbs which is 144packages and
48packages < 25 lbs. The required result is 144 - 48 = 96
Director  Joined: 29 Dec 2005
Posts: 933
Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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NTLancer wrote:
In a certain warehouse, 60 % of the packages weigh less than 75 lbs, and a total of 48 packages weigh less than 25 lbs. If 80% of the packages weigh at least 25 pounds, howmany packages weigh at least 25 lbs but less than 75 lbs.

a)8
b)64
c)96
d)102
e)144

no typo this time less than 75 lbs = 60%
at least 25 lbs = 80%
25 lbs or less than 25 lbs = 20% which equivalant = 48 packages
so 100% = 240

at least 25 lbs but less than 75 lbs = 40%
no of packages that weigh at least 25 lbs but less than 75 lbs = 40% of 240 = 96.
Intern  Joined: 12 Feb 2006
Posts: 24
Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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(8/10)x = 48 + (6/10)x Solve for x
x=240

(6/10)240 = 144 Total packages that weigh less than 75 pounds

We know 48 packages weigh less than 25 pounds so subtract those from 144. 144-48=96 packages
Intern  B
Joined: 07 Jan 2018
Posts: 11

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In a certain warehouse, 60 percent of the packages weigh less than 75 lbs, and a total of 48 packages weigh less than 25lbs. If 80 percent of the packages weighat least 25lbs, how many of the packages weigh at least 25lbs but less than 75lbs?
(A) 8
(B) 64
(C) 96
(D) 102
(E) 144

Posted from my mobile device
Manager  S
Joined: 17 Mar 2018
Posts: 71

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I got C, based on below calculations.

Let total number of packages be x

>75lbs= 60% of x, based on the question stem, the following are the parts that together make it 60% of x: includes 48 packages that are less than 25lbs and 80% that are at least 25 lbs (and above).
Question basically is asking for the bold part.
I am writing this equations as .6x=.8(.6x)+48
Solve for x= .6x- (.8P*.6x)= 48---- x=400.
.6x= 120
and .8(120)= 96.
Math Expert V
Joined: 02 Sep 2009
Posts: 59164
Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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mittu wrote:

In a certain warehouse, 60 percent of the packages weigh less than 75 lbs, and a total of 48 packages weigh less than 25lbs. If 80 percent of the packages weighat least 25lbs, how many of the packages weigh at least 25lbs but less than 75lbs?
(A) 8
(B) 64
(C) 96
(D) 102
(E) 144

Posted from my mobile device

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Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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kdhong 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

Since 80 percent of the packages weigh at least 25 pounds, 20% weigh less than 25 pounds. We are given that there are 48 such packages. Thus, if we let n = the total number of packages, we can create the equation:

0.2n = 48

n = 240

Since 60 percent of the packages weigh less than 75 pounds, we have 0.6 x 240 = 144 packages weigh less than 75 pounds, and, therefore, there must be 144 - 48 = 96 packages that weigh at least 25 pounds but less than 75 pounds.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: In a certain warehouse, 60 percent of the packages weigh less than 75   [#permalink] 02 Oct 2018, 19:21
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