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What is the positive integer n?

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by BTGmoderatorDC » Sat Jun 01, 2019 5:30 pm

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Answers

A

B

C

D

E

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Difficulty—

What is the positive integer n?

(1) The sum of all of the positive factors of n that are less than n is equal to n
(2) n < 30

OA E

Source: Manhattan Prep
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Source: — Data Sufficiency |

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by Ian Stewart » Sun Jun 02, 2019 6:47 am
Numbers that satisfy Statement 1 are known as "perfect numbers" in math. You certainly don't need to know anything about "perfect numbers" for the GMAT, but I'd imagine if you weren't familiar with them, this question could be time consuming, since using both Statements, there are a lot of numbers to think about.

While perfect numbers are very spread out (there are only four of them less than 10,000), there are two different ones less than 30:

6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14

so the answer to this question is E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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