Latest Elitmus Aptitude Question SOLUTION: Is X^2 divisible by 8? (a)If X^3 divisible by 16. (b)X divisible by 18.

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(#M40156093) ELITMUS Numerical Ability question Data Sufficiency Keep an EYE

Is X^2 divisible by 8?
(a)If X^3 divisible by 16.
(b)X divisible by 18.

Asked In Elitmus Dhrub Singh (8 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

Sayan Mukherjee  (8 years ago)

From (a)
as x^3 is divisible by 16, hence x^3 is even and so x must be even, therefore we can write x^3/16=(2*2*2*something)/16 or (8*something)/16 or (something)/2 which is equal to zero as x^3 is divisible by 16. Therefore x is atleast a multiple of 4. Hence it is clear that x^2 is divisible by 8.
From (b)
x is divisible by 18, we can only guess x is an even number, nothing else. x^2 may or may not be divisible by 8.
So answer is (a) alone is sufficient

Is this solution Helpfull? Yes (13) | No   

K.Hyndavi Reddy  (8 years ago)

a) for ex take 4 or 8 as x and verify both a and b only a is true

Is this solution Helpfull? Yes (8) | No   

Ram Krishna  (8 years ago)

To proof: x^2=a*8(multiple of 8)

checking i). x^3=b*16
take cube root and then square both sides
x^2=2^(8/3) * b^(2/3)
which is not a multiple of 8 certainly.

checking ii). x=c*18=2*3^2*c
square both sides
x^2=4*3^4*c^2
which is not always a multiple of 8 .for it c should be even.
taking both
x^3/x= x^2=8*(b/9c)=8*k

BOTH statements (1) and (2)
TOGETHER are sufficient to
answer the question asked,
but NEITHER statement
ALONE is sufficient to answer
the question asked

Is this solution Helpfull? Yes (2) | No (9)  

Shivam  (7 years ago)

Only a) is correct:
Ex: Take x=4,
if x^3 =64, IS divisible by 16;
than x^2= 16, Is divisible by 8;

So a alone is sufficient...!

Is this solution Helpfull? Yes (2) | No (2)  

sahil aggarwal  (8 years ago)

Both of the statement are sufficient to answer the question.
(Note: it is not given that X is an integer)
So X can be irrational as well

In the first case we can have a number like 2*(2)^(1/3).

But when we combine both the statements, we get that X^2 must be divisible by 8.

Had it been given that X is an integer then statement 1 would have been enough.

Is this solution Helpfull? Yes | No (3)  

mohit  (8 years ago)

Both statement must to ans

Is this solution Helpfull? Yes | No   

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