The LCM of two positive integers x and y is 576. Is x a perfect square

Question

The LCM of two positive integers x and y is 576. Is x a perfect square?
1) y is a perfect square
2) y is divisible by 9

Archit3110 · Answer

576 = 2^6*3^2 
is x a perfect square
#1
y is a perfect square ; 
y can be 2^6 or 3^2 ; insufficient to say which is x
#2
y is divisible by 9
we have 2^6*3^2 ; so x=2^6 , perfect sqaure or 
2^5*18 ; x =2^5 ; not a perfect square
insufficient
from 1 & 2
2^4*36 ; y = 36 and x sufficient yes perfect square 
2*288 ; x is not a perfect square ; insufficient
IMO E

CareerGeek · Answer

1) y is a perfect square

Eg: y = 9, x = 64 or 64x3 so on ...

Insufficient.

2) y is divisible by 9

Eg: y can be 9 or 9x2 or 9x4 etc

If y = 9, x can be 64 or 64x3 or 64x9
If y = 18, x can be 64 or 64x3 or 64x9

Insufficient

Combining 1) and 2)
Eg: y can be 9, 36 etc

If y = 9, If y = 9, x can be 64 or 64x3 or 64x9

Insufficient.

Hence, Answer is E

anilesh10 · Answer

why st 1 is not sufficient since both the numbers are perfect square??
our main is to find whether X is a perfect square or not ??right?,whether you take 64 or 9 both are perfect square ...

CareerGeek · Answer

So, an example of statement 1 is

If y=9, then x can take 3 values 64 or 192 or 576 that would give LCM of x and y as 576.
So, it’s insufficient

Take a simpler example.
Instead of 576, take 36.
If statement 1 says,
 y is 4. X can take values 9 or 18 or 36 for LCM to be 36
If y is 9, X can take values 4 or 12 or 36.

Hope it’s clear

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The LCM of two positive integers x and y is 576. Is x a perfect square

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