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# In the figure above circular region A represents the set of all number

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Math Expert
Joined: 02 Sep 2009
Posts: 44321
In the figure above circular region A represents the set of all number [#permalink]

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23 Nov 2017, 01:12
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96% (01:02) correct 4% (00:52) wrong based on 23 sessions

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In the figure above, circular region A represents the set of all numbers of the form 2m, circular region B represents the set of all numbers of the form n^2, and circular region C represents the set of all numbers of the form 10k, where m, n and k are positive integers. Which of the following numbers belongs in the set represented by the shaded region?

(A) 2
(B) 4
(C) 10
(D) 25
(E) 100

[Reveal] Spoiler:
Attachment:

2017-11-22_1023_003.png [ 10.21 KiB | Viewed 426 times ]
[Reveal] Spoiler: OA

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Joined: 26 Sep 2017
Posts: 4
Re: In the figure above circular region A represents the set of all number [#permalink]

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23 Nov 2017, 01:28
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Explanation: we are asked for a number out of the answer choices which fits in the shaded region (AnBnC)

A=2m
B=n^2
C=10k

Hence we are looking for an Even, Perfect square & a multiple of 10.

VP
Joined: 22 May 2016
Posts: 1420
In the figure above circular region A represents the set of all number [#permalink]

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26 Nov 2017, 21:10
Bunuel wrote:

In the figure above, circular region A represents the set of all numbers of the form 2m, circular region B represents the set of all numbers of the form n^2, and circular region C represents the set of all numbers of the form 10k, where m, n and k are positive integers. Which of the following numbers belongs in the set represented by the shaded region?

(A) 2
(B) 4
(C) 10
(D) 25
(E) 100

[Reveal] Spoiler:
Attachment:
2017-11-22_1023_003.png

Interesting question.

The number must belong to all three sets, so it must have form: 2m (even), $$n^2$$ (perfect square), and 10k (ends in 0).

10k = ends in 0 eliminates A, B, and D.

We have C)10 and E)100

10 is not a perfect square.

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In the figure above circular region A represents the set of all number   [#permalink] 26 Nov 2017, 21:10
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