GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 09:36

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

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]

Show Tags

10 Feb 2017, 09:37
00:00

Difficulty:

25% (medium)

Question Stats:

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

HideShow timer Statistics

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

_________________
Director
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]

Show Tags

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
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4094
Location: India
GPA: 3.5
Re: For integers x and y, 25^(−10)*100^x=2^y. What is the value of y?  [#permalink]

Show Tags

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....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

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
Display posts from previous: Sort by