Numbers

[vijaynarayanan]

I feel the answer should be C. Can anyone explain why it is E?

[selango]

From stmt1,

x is an square of an integer.

X can be 9=3*3,Odd

X can be 4=2*2,Even

Insuff

From stmt2,

x is cube of an integer.

X can be 27=3*3*3,Odd

X can be 64=4*4*4,Even

Insuff

Combining 1 and 2

X is square of integer.X is cube of an integer.

X can be 4,Even

X can be 27,Odd

Still we cant say X is even..Insuff

Hence E

Hope this clarify

[vijaynarayanan]

From stmt1,

x is an square of an integer.

X can be 9=3*3,Odd

X can be 4=2*2,Even

Insuff

From stmt2,

x is cube of an integer.

X can be 27=3*3*3,Odd

X can be 64=4*4*4,Even

Insuff

Combining 1 and 2

X is square of integer.X is cube of an integer.

X can be 4,Even

X can be 27,Odd

Still we cant say X is even..Insuff

Hence E

Hope this clarify

There is only one number - 1 which satisfies both conditions. hence answer should be C. when ur combining shouldn't you combine for same number.

[kvcpk]

I feel the answer should be C. Can anyone explain why it is E?

x is square of integer.

let x= 4 = 2^2...Results in YES
let x=9 = 3^2..Results in NO

x is cube of an integer
let x = 8 = 2^3 ...YES
lest x=27 = 3^3...NO

combining:
let x=1 .. 1^3=1^2 = 1..NO
letx=64 .. 8^2=4^3 .. YES

pick E.

@selango -
Be careful when you are combinign both.
X cannot be 4. because, it is not cube of an integer.
Also, X cannot be 27 because, it is not square of an integer.

Hope this helps!!

[selango]

Yes praveen.Somehow missed it.

thanks for correcting my mistake

[kvcpk]

Yes praveen.Somehow missed it.

thanks for correcting my mistake

That happens.. No Problem

[selango]

We can also have another example.

X can be 729=9^3=81^2,Odd

[gmatmachoman]

We can also have another example.

X can be 729=9^3=81^2,Odd

shouldn't read like 729=9^3=27^2 ???

[selango]

yes

[vijaynarayanan]

Thanks everyone for helping solve this problem

[barcebal]

Another way to look at a x as both a square and a cube of an integer (when combining statements) is to consider x as an integer raised to the sixth power. Any integer raised to the 6th will have both a square root and a cube root.

Knowing that, any integer raised to the 6th means both even and odd integers can be raised which means x can still be even or odd.