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

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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

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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

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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.
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by alanforde800Maximus » Fri Oct 14, 2016 5:50 am
Thanks Guys for amazing solution.
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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

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