If a and b are integers and (a*b)^5 = 96y, y could be:

Question

(A) 5
(B) 9
(C) 27
(D) 81
(E) 125

Kudos for a correct  solution .

PareshGmat · Accepted Answer

Answer = (D) 81

(a*b)^5 = 96y

a^5 * b^5 = 2^5 * 3y

If  a^5 = 2^5 , then

b^5 = 3y

y = 3^4 = 81

chetan2u · Answer

ans D 81....
(a*b)^5=96y..=2^5*3y.. so y can be 3^4 which is 81

Yash12345 · Answer

(ab)^5=96y
 =3*(2^5) *y

to make both sides equal we need y to be a fourth power of 3 so that we get (ab)^5=2^5*3^5. since we already have one 3 on rhs from 96.

ANS D-81

CCMBA · Answer

Distribute the exponent.

a^5 * b^5 = 96 y

Find the prime factorization of 96. This is 2^5 *3^1.

We need 3^4 (or some other power of 3 that will give us a multiple of 3^5 as our second term).

3^4 = 81

The answer is D.

peachfuzz · Answer

(a*b)^5 = 96y

96=(2^5)(3)

(a*b)^5 = (2^5)(3)(y)
(a^5)*(b^5) = (2^5)(3)(y) 
y must be 3. to make both sides of the equation symmetrical, make y=(3^4) so that (a^5)*(b^5) = (2^5)(3^1)(3^4) 
(3^4) = 81

Answer: D

DesiGmat · Answer

Here we go----

96 can be written as 2^5 * 3

(a * b)^5 = 96Y

2^5 * 3 * 3^4 = 96 * Y-----------------> Y = 3^4 = 81

Option D is correct

OptimusPrepJanielle · Answer

(ab)^5 =96y = 32*3*y = 2^5*3*y
This means a = 2 and b = 3
Now b^5 = 3y.
Therefore, y = b^4 = 81 Option D

law258 · Answer

rewrite equation:

(ab)^5 = 96y
ab = 2 5throot(3y)

We need 4 more 3's to make ab equal to an integer.

81 = 3^4 , Thus this is the correct answer.

D

Nunuboy1994 · Answer

In order to solve this question use exponent properties:

(a*b)^5= a^5 b^5 = 96y

Find prime factorization of 96 y

a^5 b^5 = 2^5*3y

96 has  four  factors of three so

a^5 b^5 = 2^5*3^4

3^4= 81

Thus

D

ydmuley · Answer

(a*b)^5 = 96y

a^5 * b^5 = 2^5 * 3^1 * y

As we can see that we are looking for the value  3^5  and we already have  3  so we would need  3^4 = 81

a^5 * b^5 = 2^5 * 3^1 * 3^4

a^5 * b^5 = 2^5 * 3^5

y = 3^4 = 81

Hence, Answer is D

guireif · Answer

In this case is y the units digit of 96y or is it multiplying 96? I don't get it, because it states before that  a*b , with an "*". What is the pattern in GMAT? It will always state if it's the units digit when it's asking for the units digit?

mvictor · Answer

it doesn't matter, as everything under the parenthesis is raised to the power of 5. We apply PEMDAS - parenthesis/exponents/multiplication/division/addition/subtraction
in this case, we can rewrite (a*b)^5 as (a)^5 * (b)^5 or (ab)^5.
since prime factorization of 96 is 2^5 * 3, we can conclude that either a^5 or b^5 is 2^5, leaving us with the other equal to 3. since we have raised to the power of 5, but only one factor of 3 in the 96, it must be true that y is 3^4, or 81.

guireif · Answer

Hi mvcitor, thanks but I think I wasn't clear enough. 
I'm asking if the question is asking "96*y" or "96y", which "y" is the units digit of the number "96y". And what would be the pattern in GMAT? Should I assume that 96y = 96*y?

Bunuel · Answer

If 96y were a three-digit number it would have been mentioned explicitly. Without that, 96y can only be 96*y since only multiplication sign (*) is usually omitted.

guireif · Answer

PERFECT! Thank you a lot as always!

EMPOWERgmatRichC · Answer

Hi All,

This question is essentially about prime-factorization - the idea that any positive integer greater than 1 is either prime or the product of a bunch of primes.

Here, we're told that (AB)^5 = 96Y, and that A and B are integers, which means…

(AB)(AB)(AB)(AB)(AB) = 96Y

We can rewrite this as….

(A^5)(B^5) = (2^5)(3)(Y)

We're asked for what Y COULD equal. This means that Y could be MORE than one value…so we should start by looking for the smallest value that Y could equal.

Notice how 2^5 could "account for" either A or B, so we need to make sure that the "Y", when combined with the "3" that's already there, could account for the other variable….

If Y = 3^4, then 96Y would = (2^5)(3^5), which gives us two integers raised to the 5th power.

Y COULD = 3^4 = 81

Final Answer:  D

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

bumpbot · Answer

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If a and b are integers and (a*b)^5 = 96y, y could be:

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If a and b are integers and (a*b)^5 = 96y, y could be:

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