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For how many integers n is n + n = n*n?

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by Gmat_mission » Sun May 05, 2019 11:19 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

For how many integers \(n\) is \(n + n = n\cdot n?\)

a) None
b) One
c) Two
d) Three
e) More than three.

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
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by Vincen » Sun May 05, 2019 1:41 pm
Hi Gmat_mission.

Let's rewrite the given expression as follows: $$n+n=n\cdot n$$ $$2n=n^2$$ $$n^2-2n=0$$ $$n\left(n-2\right)=0$$ Hence, the given equation is true when \(n=0\) and when \(n=2\).

So, there are two integers that satisfy the given equation. Hence, the correct answer is the option [spoiler]C) Two[/spoiler].

I hope it helps you. <i class="em em---1"></i>
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by Scott@TargetTestPrep » Fri May 10, 2019 4:42 pm
Gmat_mission wrote:For how many integers \(n\) is \(n + n = n\cdot n?\)

a) None
b) One
c) Two
d) Three
e) More than three.

[spoiler]OA=C[/spoiler]

Source: Veritas Prep
Solving the equation, we have:

2n = n^2

n^2 - 2n = 0

n(n - 2) = 0

n = 0 or n = 2

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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