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

(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

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.

(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

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

\((ab)^5\)=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

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

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

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

\(a^5 * b^5 = 2^5 * 3^1 * y\)

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

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?

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.

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?

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.

PERFECT! Thank you a lot as always!

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:

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

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