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Is C square of an Integer? 1) Sum of the factors of integer

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by GMATinsight » Fri Apr 27, 2018 12:44 am

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Answers

A

B

C

D

E

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Difficulty—

Is C square of an Integer?

1) Sum of the factors of integer C is ODD
2) Number of distinct factors of Integer C is ODD

Source: www.GMATinsight.com

Answer: Option B
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Source: — Data Sufficiency |
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by deloitte247 » Sat Jun 02, 2018 5:39 pm
Statement 1 = Sum of the factors of integers C is ODD.
Factors of 9 = 1, 3, 9, sum = ODD.
Factors of 8 = 1, 2, 4, 8, sum = ODD.
Hence, Statement 1 is not SUFFICIENT.

Statement 2 = Number of distinct factors of integer C is ODD.
For an integer $$N=x^ay^{b\ }\ $$ the number of factors
$$=\left(a+1\right)\cdot\left(b+1\right)$$
if $$\left(a+1\right),\left(b+1\right)$$ will also be ODD or A, B are even. Hence we have
$$N=x^{even}\cdot y^{even}$$
N=square of an integer / numbers
Statement 2 is SUFFICIENT.
Final Answer = Option B because statement 2 alone is SUFFICIENT.
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