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

Redeem

For how many integers n is n + n = n.n ? a) None b) One c)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Mon Oct 10, 2016 9:39 am
Hi alanforde800Maximus,

I assume that the question is meant to ask "for how many integers N is N+N = (N)(N)?"

In simpler terms, "which number, when added to itself, equals the square of itself?"

This question can be solved with a bit of 'brute force'

0+0 = (0)(0)
2+2 = (2)(2)

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 10, 2016 11:36 am
alanforde800Maximus wrote:For how many integers n is n + n = (n)(n) ?

a) None
b) One
c) Two
d) Three
e) More than three.
When you get a chance, please edit the question so that it reads as Rich suggests.

Another approach:

Given: n + n = (n)(n)
Simplify: 2n = n²
Subtract 2n from both sides to get: n² - 2n = 0
Factor: n(n - 2) = 0
So, EITHER n = 0 OR n = 2
There are two solutions.

Answer: C

RELATED VIDEO
- Solving quadratic equations: https://www.gmatprepnow.com/module/gmat ... /video/964

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Fri Oct 14, 2016 1:52 am
If we have

n + n = n * n

or

2n = n²

We can find any nonzero solutions by dividing by n:

2 = n

and we can find any zero solutions by trying 0:

2*0 = 0*0

So our two solutions are n = 0 and n = 2.
Top
Master | Next Rank: 500 Posts
Posts: 187
Joined: Tue Sep 13, 2016 12:46 am

by alanforde800Maximus » Fri Oct 14, 2016 5:50 am
Thanks Guys for amazing solution.
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Mon Jan 08, 2018 11:18 am
alanforde800Maximus wrote:For how many integers n is n + n = n.n ?

a) None
b) One
c) Two
d) Three
e) More than three.
Simplifying the equation, we have:

2n = n^2

n^2 - 2n = 0

n(n - 2) = 0

n = 0 or n = 2, so there are two possible integer values for n.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1