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

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by Vincen » Mon May 11, 2020 3:28 am

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Answers

A

B

C

D

E

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

by Brent@GMATPrepNow » Mon May 11, 2020 9:40 am
Vincen wrote: ↑
Mon May 11, 2020 3:28 am
 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
Given: n + n = (n)(n)
Simplify both sides: 2n = n²
Subtract 2n from both sides to get: 0 = n² - 2n
In other words: n² - 2n = 0
Factor to get: n(n - 2) = 0
So, either n = 0 or n = 2
There are two solutions

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: For how many integers \(n\) is \(n + n = n\cdot n ?\)

by Scott@TargetTestPrep » Wed May 13, 2020 7:19 am
Vincen wrote: ↑
Mon May 11, 2020 3:28 am
 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]

Simplifying the equation, we have:

2n = n^2
n^2 - 2n = 0

n(n - 2) = 0

n = 0 or n = 2

We see that there are two such values.

Answer: C

Scott Woodbury-Stewart
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