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Is [m][square_root]7ab[/square_root][/m] an integer? (1) a

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by GMATinsight » Thu Oct 08, 2015 1:48 am
Is [m][square_root]7ab[/square_root][/m] an integer?

(1) a = 7
(2) b is equal to an integer raised to the third power.

Answer: Option E
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by GMATinsight » Thu Oct 08, 2015 1:49 am
GMATinsight wrote:Is Sqrt(7ab) an integer?

(1) a = 7
(2) b is equal to an integer raised to the third power.

Answer: Option E

Question : Is square_root(7ab) an integer?

Statement 1: a = 7
Case 1: @a=7 and b=1, [m][square_root]7ab[/square_root] = [square_root]7*7*1[/square_root]=7[/m] i.e. Integer
Case 2: @a=7 and b=2, [m][square_root]7ab[/square_root] = [square_root]7*7*2[/square_root]=7[square_root]2[/square_root][/m] i.e. NOT an Integer
Hence,
NOT SUFFICIENT

Statement 2: b is equal to an integer raised to the third power.
Case 1: @a=1 and b=7^3, [m][square_root]7ab[/square_root] = [square_root]7*1*7^3[/square_root]=7^2 = 49[/m] i.e. Integer
Case 2: @a=2 and b=7^3, [m][square_root]7ab[/square_root] = [square_root]7*2*7^3[/square_root]=7^2[square_root]2[/square_root][/m] i.e. NOT an Integer
Hence,
NOT SUFFICIENT

Combining the two statements
Case 1: @a=7 and b=1^3, [m][square_root]7ab[/square_root] = [square_root]7*7*1^3[/square_root]=7[/m] i.e. Integer
Case 2: @a=7 and b=2^3, [m][square_root]7ab[/square_root] = [square_root]7*7*2^3[/square_root]=7*2*[square_root]2[/square_root][/m] i.e. NOT an Integer
Hence,
NOT SUFFICIENT

Answer: option E
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