If n is an integer between 2 and 100 and if n is also the square of an

Question

If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

(1) n is even.
(2) The cube root of n is an integer.

Bunuel · Accepted Answer

SOLUTION

If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

Given: n is a perfect square between 2 and 100 (a perfect square is an integer that can be written as the square of some other integer, for example 16=4^2, is a perfect square).

(1) n is even --> n can be any even perfect square in the given range: 4, 16, 36, ... Not sufficient.

(2) The cube root of n is an integer --> so n is also a perfect cube between 2 and 100. There are 4 perfect cubes in this range: 2^3=8, 3^3=27 and 4^3=64 but only one of them namely 64 is also a perfect square, so n=64=8^2=4^3. Sufficient.

Answer: B.

WoundedTiger · Answer

If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?

(1) n is even.
(2) The cube root of n is an integer.

Sol: Given n= I^2 where I some integer and 2<n<100 or 2<I^2<100

St 1: n is even and only possible squares in the given range are for 4,6,8 which are 16,36, 64  respectively...So n can be 4,6 or 8.
A and D ruled out

St2: Cube root of n= a where " a " is an integer So Taking cube we get
n=a^3.So n is a cube of an integer "a" but " a^3" should be between 2 and 100 so a^3=27 or  64 . Since 2 (n=3 or 4) answers are there so not possible.

Combining we get,

n is even and cube root of n is an integer so only possible value of n=64

Ans is C

AKG1593 · Answer

Option B
From S1:2<n<100 and n is a square.
=>n=4,9,16,25,36,49,64,81
According to S1:n=4,16,36,64.Not suff.

From S2:2<n<100
n=4,9,16,25,36,49,64,81 AND
Cube root of n=integer
Only possible for 64.Hence,Sufficient.

b2bt · Answer

Best part of this question is the piece of sentence  n is also the square of an integer 
It narrow downs the answer to 4,9,16,25,36,49,64,81 (between 2 and 100)

A.) n is even. As seen in the above list there are more than one even no.
INSUFFICIENT
B.) cube root of n is integer. Find the cube root of all above no. Only 64 yields an integer
SUFFICIENT

Answer - B
Difficulty - 650

sunaimshadmani · Answer

What does cube root mean here?? For e.g if n is 16, does it mean that "sqroot(16^3)" is an integer, then its an integer. root of 64^3 is also an integer, and how are we assuming that cube root should also be in the range 2-100. HELP!!!!!!

Bunuel · Answer

The cube root of n is an integer means  \sqrt {n}=integer  --> raise to the third power:  n=integer^3 , so n is the cube of some integer: ..., 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, ... Since n is between 2 and 100 and it's also the square of an integer, then it can only be 64.

Hope it's clear.

MasteringGMAT · Answer

Can 8 be a possible answer too ? Because the question stem doesn't explicitly mention "2 & 100" being exclusive or inclusive of this range.

Bunuel · Answer

n cannot be 8 because we are told that n is the square of an integer and 8 is not the square of an integer. But what this has to do with whether 2 and 100 are inclusive ?

MasteringGMAT · Answer

my bad, I forgot to consider this information while evaluating the statements 2 especially, and i think that's the reason why I asked the question.

For instance, if we remove this info  "if n is also the square of an integer"  then can you say for sure that 64 is the value of N? This is where i had some ambiguity, whether the range 2-100 is inclusive of 2 or not.

Thanks in advance!

Bunuel · Answer

If the question were:

If n is an integer between 2 and 100, what is the value of n?

(1) n is even.
(2) The cube root of n is an integer.

Then the answer would have been E because even when we combine the statements n could take more than one value: 8 and 64.

Hope it helps.

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