• EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • examPAL
    Most awarded test prep in the world
    Now free for 30 days

    Available with Beat the GMAT members only code

    MORE DETAILS
    examPAL
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Exponent problem - what is the units digit of n?

This topic has 7 member replies
tritrantran Senior | Next Rank: 100 Posts Default Avatar
Joined
23 Oct 2008
Posted:
62 messages

Exponent problem - what is the units digit of n?

Post Fri Dec 05, 2008 9:16 pm
If [(243)^x]*[(463)^y] = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

OA A

  • +1 Upvote Post
  • Quote
  • Flag
uwhusky Legendary Member
Joined
28 Apr 2010
Posted:
1172 messages
Followed by:
4 members
Upvotes:
74
Test Date:
Target GMAT Score:
GMAT Score:
Post Fri Sep 03, 2010 11:52 pm
You are correct!

  • +1 Upvote Post
  • Quote
  • Flag
Pavan M Newbie | Next Rank: 10 Posts Default Avatar
Joined
25 Jan 2012
Posted:
3 messages
Post Tue Mar 06, 2012 4:45 am
I finally understood the logic. Thanks guys for your detailed explaination. since x+y=7 and both the digits are ending with 3, we don't care what x and what y will be. Smile

  • +1 Upvote Post
  • Quote
  • Flag
logitech Legendary Member
Joined
20 Oct 2008
Posted:
2136 messages
Followed by:
25 members
Upvotes:
237
GMAT Score:
730
Post Fri Dec 05, 2008 10:02 pm
tritrantran wrote:
If [(243)^x]*[(463)^y] = n, where x and y are positive integers, what is the units digit of n?

(1) x + y = 7

(2) x = 4

OA A
243 = 3^5

463 ends with a 3. So we have to know how many times we will multiply 3's at the end of each numbers.

1) 7 times - SUF
2) we dont know Y - INSUF

Choose (a)

_________________
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

  • +1 Upvote Post
  • Quote
  • Flag
tritrantran Senior | Next Rank: 100 Posts Default Avatar
Joined
23 Oct 2008
Posted:
62 messages
Post Fri Dec 05, 2008 10:25 pm
I'm still not seeing it. Is there a rule for numbers ending in 3?

  • +1 Upvote Post
  • Quote
  • Flag
logitech Legendary Member
Joined
20 Oct 2008
Posted:
2136 messages
Followed by:
25 members
Upvotes:
237
GMAT Score:
730
Post Fri Dec 05, 2008 10:39 pm
tritrantran wrote:
I'm still not seeing it. Is there a rule for numbers ending in 3?
3^1 = 3
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3
3^6 = 9
3^7 = 7
3^8 = 1

So the unit digits can be 1, 3, 7 or 9 depending on the power of 3.

_________________
LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

  • +1 Upvote Post
  • Quote
  • Flag
cramya Legendary Member Default Avatar
Joined
28 Aug 2008
Posted:
2469 messages
Followed by:
11 members
Upvotes:
331
Post Fri Dec 05, 2008 10:47 pm
Most exponent problems of this type deal with what's called cyclicity of units digit.

As Logitech mentioned in his post above it cylces as follows for 3
3,9,7,1,3,9,7,1,3,9,7,1.......



Stmt I

For 3 it will be 3,9,7,1,3,9,7,1,3,9,7,1.......

Since x+y=7

the units digit of the product will be 7 no matter how u distribute 7 between x and y(x=4 and y=3 or x=6 and y=1 etc...)

SUFFICIENT

Stmt II

x=4

If y=1 then the units digit of the product will be 3

3,9,7,1,3,9,7,1,3,9,7,1.......

If y =2 then the units digit of the product will be 9

3,9,7,1,3,9,7,1,3,9,7,1.......

Any of the 4 values from 3,9,7,1(abive I have given 2 examples) possible

Cannot get to one defnite answer for the units digit

INSUFFICIENT


A)


Hope this helps also!
[/b]

  • +1 Upvote Post
  • Quote
  • Flag
rohit_gmat Master | Next Rank: 500 Posts
Joined
16 Jun 2010
Posted:
158 messages
Followed by:
1 members
Upvotes:
13
Post Fri Sep 03, 2010 11:45 pm
Took me ages to understand this one...
(please correct me if my logic is wrong here)...

Since we are concerned only abt the unit's digits, lets focus on those only...
243 & 463 both have 3 in the units place...
to solve for the units digit's value, we can boil the equation down to :
(3^x)(3^y) = last few digits of n ....
so we have x+y to solve for... since we know the cyclic form of 3 to the power smths = 1 3 9 7 1 3 9 7 ...

Stmnt 1) x + y = 7
gives us exactly what we are looking for (x+y)
SUFF

Stmnt 2) x =4
y could be ANY other +ve integer on earth...
INSUFF

So it should be A....

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 lheiannie07 108 topics
2 ardz24 67 topics
3 Roland2rule 63 topics
4 LUANDATO 50 topics
5 swerve 43 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

152 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

106 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

103 posts
4 image description Scott@TargetTestPrep

Target Test Prep

96 posts
5 image description Max@Math Revolution

Math Revolution

86 posts
See More Top Beat The GMAT Experts