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If a positive integer is equal to the following product: 2^5b^3c^4, wh

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Joined: 02 Sep 2009
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If a positive integer is equal to the following product: 2^5b^3c^4, wh  [#permalink]

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New post 26 Nov 2019, 00:50
00:00
A
B
C
D
E

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Question Stats:

39% (01:24) correct 61% (01:36) wrong based on 18 sessions

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Joined: 20 Jul 2017
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Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a positive integer is equal to the following product: 2^5b^3c^4, wh  [#permalink]

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New post 26 Nov 2019, 01:03
Bunuel wrote:
If a positive integer is equal to the following product: \(2^5b^3c^4\), where b and c are distinct prime numbers greater than 2, how many distinct even factors does the integer have?

A. 1
B. 5
C. 50
D. 100
E. 120

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Let \(x\) = \(2^5*b^3*c^4\) = \(2*2^4*b^3*c^4\) = \(2y\)
--> \(y = 2^4*b^3*c^4\)

Note that, even factors of \(x\) is same as all positive factors of \(y\), Since \(x = 2y\)

--> Positive factors of y = (4 + 1)*(3 + 1)*(4 + 1) = 100
--> Even factors of x = All factors of y = 100

IMO Option D
GMAT Club Bot
Re: If a positive integer is equal to the following product: 2^5b^3c^4, wh   [#permalink] 26 Nov 2019, 01:03
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If a positive integer is equal to the following product: 2^5b^3c^4, wh

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