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

 It is currently 06 Dec 2019, 13:43

### 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

# Is 81^a=3^9(b-1)?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Jul 2014
Posts: 87
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 660 Q48 V32

### Show Tags

17 Aug 2017, 11:22
1
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:02) correct 25% (01:31) wrong based on 95 sessions

### HideShow timer Statistics

Is 81^a=3^(b-1)?

1) 3a+1=b-a
2) a=3
Retired Moderator
Joined: 25 Feb 2013
Posts: 1159
Location: India
GPA: 3.82
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

17 Aug 2017, 11:40
Bounce1987 wrote:
Is 81^a=3^(b-1)?

1) 3a+1=b-a
2) a=3

$$81^a$$ $$=3^{(b-1)}$$
$$3^{4a} = 3^{(b-1)}$$ or $$4a = b-1$$

Statement 1: $$3a+1=b-a$$, this implies $$4a = b-1$$. Sufficient

Statement 2: does not provide any value of $$b$$. Hence Not Sufficient

Option $$A$$
Senior Manager
Joined: 06 Jul 2016
Posts: 356
Location: Singapore
Concentration: Strategy, Finance
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

17 Aug 2017, 11:59
Bounce1987 wrote:
Is 81^a=3^(b-1)?

$$81^a$$ = 3^(b-1)
=> 3^(4a) = 3^(b-1)
=> 4a = b-1 ?

Quote:
1) 3a+1=b-a
2) a=3

1) 3a + a = b-1
=> 4a = b - 1
Sufficient.

2) a = 3
we know nothing about B.
Insufficient.

A is the answer.
_________________
Put in the work, and that dream score is yours!
Intern
Joined: 05 Sep 2019
Posts: 2
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

26 Nov 2019, 12:56
Hi,
Need a little explanation for why 'D' cannot be the answer. From the question, we get the equation as: 4a = b-1.
From stmt - 1: we get 4a = b-1 . Sufficient.
From stmt 2: a= 3, substituting a's value in the equation that we got from the question 4a = b-1, b = 13. So, 3^4*3 = 3^13-1. Sufficient .
Am I missing something here?

Thanks for the response.
Retired Moderator
Joined: 25 Feb 2013
Posts: 1159
Location: India
GPA: 3.82
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

27 Nov 2019, 07:38
1
gmat2511 wrote:
Hi,
Need a little explanation for why 'D' cannot be the answer. From the question, we get the equation as: 4a = b-1.
From stmt - 1: we get 4a = b-1 . Sufficient.
From stmt 2: a= 3, substituting a's value in the equation that we got from the question 4a = b-1, b = 13. So, 3^4*3 = 3^13-1. Sufficient .
Am I missing something here?

Thanks for the response.

Hi,

Here you are assuming that the question stem is "true" and then you are substituting the value of a to get the value of b. But the question itself is asking you to find if the equation is "true/valid". Read the question stem carefully. This is an "IS" question I.e. asking you to verify and not to assume that it is true.

Posted from my mobile device
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

30 Nov 2019, 00:50
Bounce1987 wrote:
Is 81^a=3^(b-1)?

1) 3a+1=b-a
2) a=3

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
$$81^a = 3^{b-1}$$
$$⇔(3^4)^a= 3^{b-1}$$
$$⇔3^{4a}= 3^{b-1}$$
$$⇔4a= b-1$$

The question asks if $$4q=b-1$$.

Condition 1) tells $$4a = b -1$$ and it means condition 1) is sufficient.

Condition 2)
Since we don't have any information of $$b$$, condition 2) is not sufficient.

Therefore, A is the answer.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 19 Feb 2019
Posts: 95
Concentration: Marketing, Statistics
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

01 Dec 2019, 00:52
From statement 2 u get the answer that the question stem is wrong so isnt that a definite answer?
Math Expert
Joined: 02 Aug 2009
Posts: 8281

### Show Tags

01 Dec 2019, 01:17
devavrat wrote:
From statement 2 u get the answer that the question stem is wrong so isnt that a definite answer?

$$81^a=3^{(b-1)}$$

Now a=3....$$81^a=3^{(b-1)}$$..
$$81^3=3^{12}=3^{(b-1)}.........12=b-1....b=13$$

So if b=13 answer is yes, otherwise NO
So insuff
_________________
Manager
Joined: 19 Feb 2019
Posts: 95
Concentration: Marketing, Statistics
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

01 Dec 2019, 01:23
Hii
Quote:
81a=39(b−1)81a=39(b−1)

Now a=3....81a=39(b−1)81a=39(b−1)..
813=312=39(b−1).........12=9b−9....9b=21......b=7/3

Why have you put in 3^9(b-1)??

The question asks 3^(b-1)
Math Expert
Joined: 02 Aug 2009
Posts: 8281
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

01 Dec 2019, 01:58
devavrat wrote:
Hii
Quote:
81a=39(b−1)81a=39(b−1)

Now a=3....81a=39(b−1)81a=39(b−1)..
813=312=39(b−1).........12=9b−9....9b=21......b=7/3

Why have you put in 3^9(b-1)??

The question asks 3^(b-1)

Hi

I copied from topic name. . Now I have changed it
_________________
Manager
Joined: 19 Feb 2019
Posts: 95
Concentration: Marketing, Statistics
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

01 Dec 2019, 02:03
But when we have calculated the value of B then why will the value change?
Im sorry to ask but i just can't understand why is it that if the calculated value of b is 13 then it is correct otherwise it is not. When we have already calculated the value then where is the question of b not being 13?
Math Expert
Joined: 02 Aug 2009
Posts: 8281
Re: Is 81^a=3^9(b-1)?  [#permalink]

### Show Tags

01 Dec 2019, 04:25
1
devavrat wrote:
But when we have calculated the value of B then why will the value change?
Im sorry to ask but i just can't understand why is it that if the calculated value of b is 13 then it is correct otherwise it is not. When we have already calculated the value then where is the question of b not being 13?

We have NOT calculated the value of B..

The question -- Is $$81^a=3^{(b−1)}$$?-- This is not given but you have to prove it?? and for that you have to know a and b.
Statement II tells us a=3, but we still do NOT know the value of b???
That is why -- If b=13, answer for -- Is $$81^a=3^{(b−1)}$$?--is YES, otherwise answer will be NO
_________________
Re: Is 81^a=3^9(b-1)?   [#permalink] 01 Dec 2019, 04:25
Display posts from previous: Sort by

# Is 81^a=3^9(b-1)?

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

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