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

 It is currently 17 Oct 2019, 08:42

### 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

# If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Director
Joined: 18 Feb 2019
Posts: 581
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =  [#permalink]

### Show Tags

29 Mar 2019, 00:23
2
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:18) correct 41% (02:10) wrong based on 17 sessions

### HideShow timer Statistics

If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

A. 1
B. 2
C. 3
D. 4
E. 5
Math Expert
Joined: 02 Aug 2009
Posts: 7969
Re: If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =  [#permalink]

### Show Tags

29 Mar 2019, 00:46
kiran120680 wrote:
If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

A. 1
B. 2
C. 3
D. 4
E. 5

Let us take each separately ..
(I) $$(\frac{1}{2})^a∗(\frac{1}{2})^b=(4)^−2=(\frac{1}{4})^2$$..
$$(\frac{1}{2})^{a+b}=(\frac{1}{4})^2=(\frac{1}{2})^4$$
By equating the power of (1/2) on both sides, we get a+b=4.
(II) $$(\frac{1}{5})^a∗(\frac{1}{125})^b=(5)^−6=(\frac{1}{5})^6$$..
$$(\frac{1}{5})^{a+3b}=(\frac{1}{5})^6$$
By equating the power of (1/5) on both sides, we get a+3b=6

Thus, we have two equations..
a+b=4 and a+3b=6
Subtracting 1 from 2 .. a+3b-(a+b)=6-4=2......2b=2 or b=1
So, a+1=4 or a=3.

Therefore, $$\frac{a}{b}=\frac{3}{1}=3$$

C
_________________
Re: If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =   [#permalink] 29 Mar 2019, 00:46
Display posts from previous: Sort by

# If (1/2)^a∗(1/2)^b=(4)^−2 and (1/5)^a∗(1/125)^b=(5)^−6, then a/b =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne