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# If the number of different positive factors of (2^y)(3^3) is the same

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Intern
Joined: 08 Jan 2015
Posts: 25
If the number of different positive factors of (2^y)(3^3) is the same  [#permalink]

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Updated on: 14 Apr 2015, 03:31
4
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:09) correct 33% (01:18) wrong based on 114 sessions

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If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

A. 11
B. 12
C. 13
D. 48
E. 51

Originally posted by Awli on 13 Apr 2015, 08:43.
Last edited by Bunuel on 14 Apr 2015, 03:31, edited 1 time in total.
Edited the question.
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Joined: 07 Aug 2011
Posts: 492
GMAT 1: 630 Q49 V27
Re: If the number of different positive factors of (2^y)(3^3) is the same  [#permalink]

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13 Apr 2015, 09:51
2
Awli wrote:
If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

a) 11

b) 12

c) 13

d) 48

e) 51

Number of factors of $$N= a^x * b^y$$ where 'a' and 'b' are prime factors of N is

(X+1) (y+1)

So 4 (y+1)=52
y=12
Intern
Joined: 08 Jan 2015
Posts: 25
Re: If the number of different positive factors of (2^y)(3^3) is the same  [#permalink]

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13 Apr 2015, 10:28
Lucky2783 wrote:
Awli wrote:
If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

a) 11

b) 12

c) 13

d) 48

e) 51

Number of factors of $$N= a^x * b^y$$ where 'a' and 'b' are prime factors of N is

(X+1) (y+1)

So 4 (y+1)=52
y=12

Why 4 (y+1) ??

Thanks
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Posts: 155
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Re: If the number of different positive factors of (2^y)(3^3) is the same  [#permalink]

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13 Apr 2015, 22:38
1
Its the number of factor .....
(x+1) (3+1) = 51+1------------------ equation no 1
(x+1)4 = 52
if you solve it will become
y =12

number of factors theory :
N = (a^n )(b^m)
a, b are prime factors of N raised to power n and m .

and number of factors = (n+1)(m+1) -------- this is what use in equation no 1

kudos appreciated .
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Posts: 62289
Re: If the number of different positive factors of (2^y)(3^3) is the same  [#permalink]

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14 Apr 2015, 03:30
1
Awli wrote:
If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

a) 11

b) 12

c) 13

d) 48

e) 51

Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

According to the above, the number of factors o f (2^y)(3^3) is (y + 1)(3 + 1) = 4y +4 and the number of factors of 2^51 is 51 + 1 = 52. Thus given that 4y +4 = 52 --> y = 12.

Hope it's clear.
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Re: If the number of different positive factors of (2^y)(3^3) is the same  [#permalink]

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11 Jul 2016, 00:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the number of different positive factors of (2^y)(3^3) is the same   [#permalink] 11 Jul 2016, 00:33
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