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# On a certain table is a collection of 45 pens of various col

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GRE Instructor
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Kudos [?]: 2200 [0], given: 27

On a certain table is a collection of 45 pens of various col [#permalink]  10 May 2019, 08:27
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Question Stats:

66% (00:41) correct 33% (00:42) wrong based on 24 sessions
On a certain table is a collection of 45 pens of various colors of ink and various designs. Of these 45 pens, 60% are ballpoint pens. Also, 60% of the pens on the table have blue ink.

 Quantity A Quantity B The number of pens that are ballpoint with blue ink 8

A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com

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Joined: 15 Mar 2019
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WE: Engineering (Manufacturing)
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Kudos [?]: 40 [0], given: 16

Re: On a certain table is a collection of 45 pens of various col [#permalink]  10 May 2019, 08:48
ballpoint pens =45*0.6=27
and blue ink pen =45*0.6=27
so ballpoint pens+blue ink pen=54
but there are actually 45 pen
so 54-45=9
so 9 ballpoint pens must have blue ink.
that is why A is the answer.
GRE Instructor
Joined: 10 Apr 2015
Posts: 2311
Followers: 72

Kudos [?]: 2200 [1] , given: 27

Re: On a certain table is a collection of 45 pens of various col [#permalink]  10 May 2019, 08:50
1
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Expert's post
GreenlightTestPrep wrote:
On a certain table is a collection of 45 pens of various colors of ink and various designs. Of these 45 pens, 60% are ballpoint pens. Also, 60% of the pens on the table have blue ink.

 Quantity A Quantity B The number of pens that are ballpoint with blue ink 8

One approach is to use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).

Here, we have a population of pens, and the two characteristics are:
- ballpoint or not ballpoint
- blue or not blue

So, we can set up our matrix as follows:

NOTE: I placed a star in the box representing pens that are ballpoint AND have blue ink.

From here, let's determine the GREATEST value and the LEAST value that can be placed in the top-left box.

Since the squares in the top row adds to 27, and since the squares in the left-hand column must add to 27, the GREATEST number we can place in the top-left box is 27
We get:

In order the MINIMIZE the value in the top-left box, we must MAXIMIZE the values in the top-right box and in the bottom-left box.
Since the two boxes in the bottom row must add to 18, we can see that 18 is the BIGGEST number to place in the bottom-left box
Since the two boxes in the right-hand column must add to 18, we can see that 18 is the BIGGEST number to place in the top-right box
We get:

When we fill in the remaining boxes, we see that...

...the SMALLEST number we can place in the top-left box is 9

We get:
QUANTITY A: Some value from 9 to 27 inclusive
QUANTITY B: 8

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Brent Hanneson – Creator of greenlighttestprep.com

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Kudos [?]: 25 [1] , given: 21

Re: On a certain table is a collection of 45 pens of various col [#permalink]  19 Aug 2019, 13:38
1
KUDOS
Here is another approach.
Attachments

pens overlapping.png [ 281.86 KiB | Viewed 66 times ]

Re: On a certain table is a collection of 45 pens of various col   [#permalink] 19 Aug 2019, 13:38
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