If a and b are both positive integers, is a^2b^2 divisible by 8?

Question

If a and b are both positive integers, is  a^2*b^2  divisible by 8?

(1) a^2 = 4x
(2) x is an integer greater than 1

Kudos for a correct  solution .

funkyleaf · Answer

The original equation can be re written as (a^2b)^2 I believe which would be a^4b (but I think if it is (a^2)*(b^2) the answer will still be the same.). The question is asking us a definite yes or definite no if the original equation is divisible by 8. This will only be solvable if we have the information for both variable a and b.

1) plugging a^2=4x we would get 16x^2b. We still have no information on the new variable X or the original variable B so we do not have sufficient information to answer. Eliminate A and D.
2) This only gives us information about the variable X which is not even in the original equation so this is not sufficient to answer. Eliminate B.

Together: we still have no information about variable b so we can not tell what the value of the solved equation will come out to. select answer choice E.

Harley1980 · Answer

I am not completely assured but I think if it equal to a^(2b)^2 than it should be equal to a^(4(b^2))
and in this case we can write as (a^2)^(2(b^2)) and as we know from 1 statement that a^2=4x we can rewrite it as (4x)^(2(b^2)) and received 16(x^(2(b^2)) and 16 will be divisible by 8.
And 1 statement sufficient.
And answer is A

But if it  a^2*b^2  than answer will be E as you already wrote.

funkyleaf · Answer

I still think that if X is an odd number that we multiply 16 by then the whole answer could be non-divisible by 8 therefore my answer remains the same.

sabineodf · Answer

I think it is E.

1) tells us that a^2 is divisible by at least 4 < not sufficient because even if a^2 = 16, it can be multiplied by any number for b^2 rendering in indivisible by 8.
2) tells us that x can be any number over 1 <- still gives us no idea of the value of b

sudh · Answer

a and b are both positive integers
is  a^2   b^2  divisible by  8 ?

for the above condition to be true, both  a  and  b  should be even
or, either  a^2  or  b^2  should be divisible by  8

Statement (1)
 a^2  =  4x ;
if  x  is even,  a^2  b^2  is divisible by  8 
but if  x  is odd,  a^2  b^2  is NOT divisible by  8 
Not Sufficient

Statement (2):
 x  is an integer greater than 1; no info about either  a  or  b 
Not Sufficient

From (1) and (2)
No additional information about either  x  or  b 
Not Sufficient

Answer E

EMPOWERgmatRichC · Answer

Hi Bunuel,

The formatting in this question is problematic....

Is "a^2b^2" meant to be interpreted as....

(a^2)(b^2)

or

(a^2b)^2

or

a^

GMAT assassins aren't born, they're made,
Rich

Tmoni26 · Answer

Since i am not sure what the actual question is, i would wait for the solution

Right now, I have two different answers for 2 different prompts..

Bunuel · Answer

Mathematically a^2b^2 can ONLY mean (a^2)(b^2). If it were something else it would be written differently.

P.S. Still edited to avoid ambiguity.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: E

Statement (1) allows us to rewrite the equation as (4x)(b^2). Since we don’t know whether x is an integer, don’t know whether this equation is divisible by 8: if x = 2, for example, then the equation is (8)(b^2), which must be divisible by 8; if x = 2/3, the equation is (8/3)(b^2), which is not necessarily divisible by 8; INSUFFICIENT. Statement (2) on its own is useless – what is x, after all? – so it too is INSUFFICIENT. Together, x > 1, but if x is equal to, say, 9, then 4x(b^2) = 36(b^2), which still isn’t necessarily divisible by 8. (E).

stonecold · Answer

Amazing Question
Here We need to check whether A^2*B^2 is divisible by 8 
So we need three two's
Statement 1 => x=√4x=> 2√x => x =1 => no 
x=2 => yes => insuff
statement 2 => no clue of A,B=> insuff
Combining them => x=2*2 or 2*3 => insuff
SMASH THAT E

hatemnag · Answer

Hi Bunuel
I have a question. we know from the question stem that a & b are +ve interger. so a2 must be perfect square since if x = 2 
then a2 = 8 and a = 2 square root of 2 which means that a is not integer.
therefore combining st.1 and st.2 a bust be 16 at least.
Please correct my thinking.

Bunuel · Answer

When combining the least value of x can be 4. In this case a^2 = 4*4 = 16 --> a = 4. Basically x must also be a perfect square so, for (1)+(2) x can be 4, 9, 16, 25, ...

hatemnag · Answer

OK. so if b=1 and a= 5, 6, 7, 9, 11.. answer is no
But if b=1 and a=4, 8, 12, 16, 20 ,... answer if yes 
So combining is insuff.

kanusha · Answer

Is  \frac{a^2b^2}{8}  = ?
1, a^2 = 4x
4x b^2/8 = ??
Nothing about b ;  Insufficient 
2, x > 1
 Insufficient  
3, a^2 = 4x2 = 8
Nothing about b 
 Insufficient 
E

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If a and b are both positive integers, is a^2b^2 divisible by 8?

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If a and b are both positive integers, is a^2b^2 divisible by 8?

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