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

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Math Expert
Joined: 02 Sep 2009
Posts: 59573
If a positive integer is equal to the following product: 2^5b^3c^4, wh  [#permalink]

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26 Nov 2019, 00:50
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(N/A)

Question Stats:

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

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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

Are You Up For the Challenge: 700 Level Questions

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

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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

Are You Up For the Challenge: 700 Level Questions

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
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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