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# For integers x and y, 25^(−10)*100^x=2^y. What is the value of y?

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Math Expert
Joined: 02 Sep 2009
Posts: 50002
For integers x and y, 25^(−10)*100^x=2^y. What is the value of y?  [#permalink]

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10 Feb 2017, 09:37
00:00

Difficulty:

25% (medium)

Question Stats:

86% (02:08) correct 14% (03:07) wrong based on 77 sessions

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For integers x and y, $$25^{(−10)}*100^x=2^y$$. What is the value of y?

A. -10
B. 10
C. 20
D. 25
E. 40

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Joined: 05 Mar 2015
Posts: 995
Re: For integers x and y, 25^(−10)*100^x=2^y. What is the value of y?  [#permalink]

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10 Feb 2017, 11:02
Bunuel wrote:
For integers x and y, $$25^{(−10)}*100^x=2^y$$. What is the value of y?

A. -10
B. 10
C. 20
D. 25
E. 40

25^-10= 1/5^20
100^x= (2^2*5^2) ^x
or 2^2x * 5^2x

substituing each value $$25^{(−10)}*100^x=2^y$$
1/5^20 * 2^2x *5^2x = 2^y

thus x must be 10 such that 1/5^20 gets cancelled by 5^2x
and both side we left with the exponents of similar integer ie 2
thus 2^2x = 2^y
since x=10
y=20

Ans C
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Re: For integers x and y, 25^(−10)*100^x=2^y. What is the value of y?  [#permalink]

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10 Feb 2017, 11:50
Bunuel wrote:
For integers x and y, $$25^{(−10)}*100^x=2^y$$. What is the value of y?

A. -10
B. 10
C. 20
D. 25
E. 40

$$25^{(−10)}*100^x=2^y$$

Or, $$5^{-20} *2^{2x}*5^{2x} = 2^y$$

From the above equation we can safely conclude that the value of $$x = 10$$

Now, $$5^{-20} *2^{2*10}*5^{2*10} = 2^y$$

Or, $$5^{-20} *2^{20}*5^{20} = 2^y$$

Or, $$2^{20}= 2^y$$

So, $$y = 20$$

Thus, correct answer will be (C) y = 20

_________________

Thanks and Regards

Abhishek....

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Re: For integers x and y, 25^(−10)*100^x=2^y. What is the value of y? &nbs [#permalink] 10 Feb 2017, 11:50
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