Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43898

If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
08 Jun 2015, 07:58
Question Stats:
74% (01:23) correct 26% (01:34) wrong based on 194 sessions
HideShow timer Statistics



Retired Moderator
Joined: 06 Jul 2014
Posts: 1269
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
08 Jun 2015, 08:20
2
This post received KUDOS
Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



Intern
Joined: 12 Feb 2013
Posts: 21

If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
08 Jun 2015, 08:58
1
This post received KUDOS
Ans is A Please find the solution below in file attached.
Attachments
Capture2.PNG [ 53.61 KiB  Viewed 2067 times ]



Manager
Joined: 26 Dec 2011
Posts: 120

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
08 Jun 2015, 10:00
1
This post received KUDOS
If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? Lets take a=2. 3^2+3^0=(90)3^b > 10/90=3^b > 3^2=3^b > b=2. Substitute a=2 in answer choices, only A fits correctly. Thanks, Please give me kudos.
_________________
Thanks, Kudos Please



Manager
Joined: 21 Jan 2015
Posts: 149
Location: India
Concentration: Strategy, Marketing
WE: Marketing (Consumer Products)

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
09 Jun 2015, 00:48
1
This post received KUDOS
Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4 Ans : A Solution: generalizing both sides gives us 3^a2 * 5*2 = 3^ b+2 * 5*2 means a2=b+2 b= a4
_________________
 The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks



Current Student
Joined: 29 Mar 2015
Posts: 44
Location: United States

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
10 Jun 2015, 01:15
2
This post received KUDOS
2
This post was BOOKMARKED
If \(3^a + 3^{(a  2)} = (90)(3^b)\), what is b in terms of a?
\(3^a + 3^{(a  2)} = (3^2*10)(3^b)\) > \(3^a(1 + 3^{(2)}) = (3^{(2+b)})(10)\) > \(3^a\frac{10}{9} = (3^{(2+b)})(10)\)> \(3^a = (3^{(2+b)})(9)\)> \(3^a = (3^{(2+b)})(3^2)\)> \(3^a = (3^{(4+b)})\)> \(a=4+b\)> \(b=a4\) or A



Manager
Joined: 01 Jan 2015
Posts: 56

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
14 Jun 2015, 03:42
3^(a2) X (5*2) = 3^ (b+2) X (5*2) a2=b+2 b= a4 Ans A



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 432
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
17 Jun 2015, 03:18
Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2} (3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A Hello could you explain the part in red to me plz? I understand that you took 3^a2 as a common factor. But how did you get that taking the power of "a2" from a power of "a" leaves a square?



Retired Moderator
Joined: 06 Jul 2014
Posts: 1269
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
17 Jun 2015, 03:28
1
This post received KUDOS
pacifist85 wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2} (3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A Hello could you explain the part in red to me plz? I understand that you took 3^a2 as a common factor. But how did you get that taking the power of "a2" from a power of "a" leaves a square? Hello pacifist85If you multiply \(3^{a2}\) on \(3^2\) you receive \(3^{(a2)+2}\) > \(3^a\)
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 432
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
17 Jun 2015, 03:55
Oh ok I think i see it now. So, you basally want to take 3^a2 out, as a common factor. You have 3^a, and from that power (a) you are subtracting a2, as you have already taken this as a fator.
Then you would have 3^a(a2) = 3^aa+2 = 3^2. I hope I got it right...



SVP
Joined: 08 Jul 2010
Posts: 1959
Location: India
GMAT: INSIGHT
WE: Education (Education)

If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
17 Jun 2015, 04:04
pacifist85 wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2} (3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A Hello could you explain the part in red to me plz? I understand that you took 3^a2 as a common factor. But how did you get that taking the power of "a2" from a power of "a" leaves a square? Hi pacifist, Just for your information and better understanding here are Rules of exponents The powers of the numbers add up for the same base when the numbers are multiplied i.e. \(a^x * a^y = a^{(x+y)}\)
Attachments
File comment: www.GMATinsight.com
Rules of Exponents.jpg [ 197.99 KiB  Viewed 1801 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 22 Apr 2015
Posts: 50
Location: United States
GPA: 3.86

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
01 Jul 2015, 14:27
1
This post was BOOKMARKED
Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A I am confused on the first step you took that factored out the \((3^2+1)\)



Senior Manager
Joined: 15 Sep 2011
Posts: 358
Location: United States
WE: Corporate Finance (Manufacturing)

If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
01 Jul 2015, 16:29
xLUCAJx wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A I am confused on the first step you took that factored out the \((3^2+1)\) Hi xLUCAJx, They factored out the whole expression, \(3^{a2}\), so that the \((3^{2}+1)\), or \(10\), would be isolated. Thinking forward, not one but two steps ahead, and it saved them from a fraction.



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
01 Jul 2015, 16:44
xLUCAJx wrote: Harley1980 wrote: Bunuel wrote: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
(A) a – 4 (B) a – 2 (C) a + 4 (D) 3a + 2 (E) 3a + 4
Kudos for a correct solution. \(3^a + 3^{a  2} =3^{a2}(3^2+1)=3^{a2}*10\) \((90)(3^b)=3^2*10*3^b=3^{b+2}*10\) so \(3^{a2}*10=3^{b+2}*10\) \(b+2=a2\) > \(b = a4\) Answer is A I am confused on the first step you took that factored out the \((3^2+1)\) Think of it in this way: \(3^a+ 3^{a  2} =3^{a+22}+3^{a2}=3^{a2}*3^{2}+ 3^{a2} = 3^{a2}(3^2+1)=3^{a2}*10\) Going from 1st part to the second, we added and subtracted 2 from a as we need the power of a2 common. For the second part, we used the property \(a^{x+y} = a^x*a^y\), where x= a2 and y = 2. I hope this clears your doubt.



NonHuman User
Joined: 09 Sep 2013
Posts: 13759

Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a? [#permalink]
Show Tags
26 Mar 2017, 09:59
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If 3^a + 3^(a  2) = (90)(3^b), what is b in terms of a?
[#permalink]
26 Mar 2017, 09:59






