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# The number of people who purchased book A is twice the number of peopl

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Math Expert
Joined: 02 Sep 2009
Posts: 58323
The number of people who purchased book A is twice the number of peopl  [#permalink]

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29 Jul 2015, 03:18
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Difficulty:

45% (medium)

Question Stats:

65% (01:43) correct 35% (01:40) wrong based on 241 sessions

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The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people who purchased only book A?

A. 250
B. 500
C. 750
D. 1000
E. 1500

Kudos for a correct solution.

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Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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29 Jul 2015, 04:12
2
Bunuel wrote:
The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people who purchased only book A?

A. 250
B. 500
C. 750
D. 1000
E. 1500

Kudos for a correct solution.

IMO: D

Attachment:

1.jpg [ 16.55 KiB | Viewed 3052 times ]

Let A book alone = x
A and B = y
B alone = z

Given No. of ppl purchased A = 2B

x+y = 2(y+z) --(i)
y = 500--(ii)
500 = 2z --(iii)

Sub y = 500 and z = 250 in eq- (i)
we get x = 1000
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Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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29 Jul 2015, 05:54
1
Bunuel wrote:
The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people who purchased only book A?

A. 250
B. 500
C. 750
D. 1000
E. 1500

Kudos for a correct solution.

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The number of people who purchased book A is twice the number of peopl  [#permalink]

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30 Jul 2015, 08:51
Set up a mutual exclusive grid and input the numbers.

_______A_____Not A______Total
B______$$500$$___$$250$$______$$\frac{1}{2}x=750$$
NB_____$$y$$
Total___$$x=1500$$

$$500+y=1500$$
IMO D.
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Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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03 Aug 2015, 06:52
1
1
Information given :
A=2B ----- (1)
Both A and B = 500 which is twice of only B, therefore only B = 250

Overall B = Only B + Both A and B ----(2)

Solution --
From equation (2), we can find Overall B which is 750 = 250 (Only B) + 500 (Both A and B)

Putting Overall B in equation (1), we can find Overall A = 1500

Overall A = Only A + Both A and B
Hence, 1500 = Only A + 500
and Only A = 1500 - 500 i.e. 1000
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Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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03 Aug 2015, 08:00
1
The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people who purchased only book A?

A. 250
B. 500
C. 750
D. 1000
E. 1500

a = book A, b = book B, c = books A and B

a + c = 2 (b+c)
a+c =2b + 2c
a = 2b + c

c = 500 = 2b => b=250

a = 2(250) + 500 = 1000
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The number of people who purchased book A is twice the number of peopl  [#permalink]

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03 Aug 2015, 08:57
1
[quote="Bunuel"]The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people who purchased only book A?

A. 250
B. 500
C. 750
D. 1000
E. 1500

This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, 1000 purchased A only. (This is much simpler to solve using the Venn diagram).

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Posts: 58323
Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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17 Aug 2015, 10:01
1
Bunuel wrote:
The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people who purchased only book A?

A. 250
B. 500
C. 750
D. 1000
E. 1500

Kudos for a correct solution.

800score Official Solution:

The original Venn diagram is the following:

(D) First, let's define some values:
B = number of people who purchased book B
2B = number of people who purchased book A
500 = number of people who purchased both A and B
500/2 = 250 = number of people who purchased only B.
We are looking for the number of people who purchased ONLY book A. The number of people who purchased ONLY A is the total number of people that purchased A minus the number of people that purchased both A and B.
Since 250 people purchased ONLY B, and 500 people purchased both books, 750 people in all must have purchased B.
Thus, 1500 people in all purchased book A.
Since 500 of these people purchased both books, the number who have purchased ONLY A is:
1500 – 500 = 1000.
The correct answer is choice (D).

The solved Venn diagram is the following:

Attachment:

venn_diagram-1.gif [ 9.6 KiB | Viewed 2874 times ]

Attachment:

venn_diagram-2.gif [ 9.63 KiB | Viewed 2855 times ]

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Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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29 Mar 2017, 01:11
i find it much easier to use the table when total number of items is not given directly in the questions stem.
the venn diagram is often quite interesting when lots of calculations are not required.
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Re: The number of people who purchased book A is twice the number of peopl  [#permalink]

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26 Oct 2018, 23:32
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Re: The number of people who purchased book A is twice the number of peopl   [#permalink] 26 Oct 2018, 23:32
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