If the number of different positive factors

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figs: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Mon Mar 30, 2009 9:00 am; Thanked: 2 times

by figs » Mon May 25, 2009 4:18 am

If the number of different positive factors(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

if someone know the answer, can explain how to solve it?

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Source: Beat The GMAT — Problem Solving | Mon May 25, 2009 4:18 am

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Re: If the number of different positive factors

by Brent@GMATPrepNow » Mon May 25, 2009 5:22 am

figs wrote:If the number of different positive factors(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

if someone know the answer, can explain how to solve it?

Here's a useful tip:
If K = (a^x)(b^y)(c^z) etc, then the number of factors (divisors) of K will be (x+1)(y+1)(z+1)etc.

So, 2^51 will have 52 factors
(2^y)(3^3) will have (y+1)(3+1) factors.

This means that 52 = (y+1)(4)
Solve to get y=12

Brent Hanneson - Creator of GMATPrepNow.com

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

Re: If the number of different positive factors

by dtweah » Mon May 25, 2009 5:26 am

figs wrote:If the number of different positive factors(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

if someone know the answer, can explain how to solve it?

Number of positive divisors or factors of a^b= b+1. So use this and find the number of all the factors of the three numbers, then equate the two since they are equal and solve the resulting equation. You should be able to solve and get 12 for y.

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