BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

MGMAT

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

Re: MGMAT

by gabriel » Mon Nov 19, 2007 9:27 am
cvs wrote:Which of the following best approximates the value of q if 5^28+3^11=5^q ?

39
30
28
27
17

Pls post your answers with explanations.
The answer is B 30.

First the basics .. 5^n when divided by 3 has a remainder 1 if n is even and a remainder 2 if n is odd ..

Now, the given equation can also be written as 3^11=5^q-5^28, looking at the equation we can say that 5^q-5^28 has to be a multiple of 3(that means when (5^q-5^28) is divided by 3 the remainder is 0) that means 5^q and 5^28 should have similar remainders when divided by 3, so that when we subtract them they cancel out and the overall remainder is 0.

Now, we know that 5^28 has a remainder 1 when divided by 3 (as 28 is even), so 5^q should also have a remainder 1 when divided by 3 and hence we can say that q should also be even. The given answer choices have just 2 even options 30 and 28, obviously 28 cant be the answer therefore we can conclude q has to be 30.

Regards
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Fri Nov 09, 2007 12:02 pm

by cvs » Mon Nov 19, 2007 12:42 pm
Any more thoughts.. The answer is not 30!!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 460
Joined: Sun Mar 25, 2007 7:42 am
Thanked: 27 times

by samirpandeyit62 » Mon Nov 19, 2007 9:43 pm
IMO 28

now 5^28 would be a huge nos itself

& 3^11 = 27*27*27 * 9

to approx we can say it is 30^3 *10 which is 180000

this when added to such a huge nos as 5^28 would not make much of a diff

so q =28
Regards
Samir
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

by gabriel » Tue Nov 20, 2007 12:10 am
samirpandeyit62 wrote:IMO 28

now 5^28 would be a huge nos itself

& 3^11 = 27*27*27 * 9

to approx we can say it is 30^3 *10 which is 180000

this when added to such a huge nos as 5^28 would not make much of a diff

so q =28
Well I had thot about it ... but if we choose q = 28 then we are considering the value of 3^11 as 0, which does not make a lot of sense to me .. but then again the question does say approximate value of q, but dont u think we would be pushing it a bit by assuming 3^11 equal to 0 ..
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 986
Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member
Location: India
Thanked: 51 times

by gabriel » Tue Nov 20, 2007 12:17 am
On second thought I agree the answer should be 28 .. I was sure that the answer should be either 30 or 28, 28 makes more sense now .. good going Samir

Regards
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 460
Joined: Sun Mar 25, 2007 7:42 am
Thanked: 27 times

by samirpandeyit62 » Tue Nov 20, 2007 2:58 am
Hi Gabriel,
My reasoning was like this

5^28 = very large nos say X

3^11 = 180000 approx

now q can be 28 or more, i.e next nos is 30

so if we line them up it would be

X X+180000 25X

now obviously X+180000 would be closer to X
Regards
Samir
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Fri Nov 09, 2007 12:02 pm

by cvs » Tue Nov 20, 2007 12:23 pm
Thanks Samir/Gabrial.

The official answer is 28.

Samir explanation is identical to MGMAT's explanation.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 106
Joined: Tue Oct 09, 2007 12:25 pm
Thanked: 1 times

by xcise_science » Wed Nov 21, 2007 10:47 am
Hi samirpandeyit62,

I don't understand this approximation:
3^11 = 27*27*27 * 9
to approx we can say it is 30^3 *10 which is 180000

Also, can you clarify on this as well:

5^28 = very large nos say X
3^11 = 180000 approx
now q can be 28 or more, i.e next nos is 30
so if we line them up it would be
X X+180000 25X
now obviously X+180000 would be closer to X

Also, I see what you wrote before that adding 3^11 to 5^28 will not make a major difference, so then why can't Q be 30.....to account for the slight increase when we add to 5^28?

Thanks
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1