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

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Math Expert
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If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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23 Jan 2015, 07:14
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If a and b are integers and (a*b)^5 = 96y, y could be:

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

Kudos for a correct solution.

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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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03 Feb 2015, 19:45
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2

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

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

If $$a^5 = 2^5$$, then

$$b^5 = 3y$$

$$y = 3^4 = 81$$
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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23 Jan 2015, 07:21
1
ans D 81....
(a*b)^5=96y..=2^5*3y.. so y can be 3^4 which is 81
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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23 Jan 2015, 07:28
1
Bunuel wrote:
If a and b are integers and (a*b)^5 = 96y, y could be:

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

Kudos for a correct solution.

(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
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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23 Jan 2015, 18:15
1
1
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

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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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23 Jan 2015, 20:58
1
1
Bunuel wrote:
If a and b are integers and (a*b)^5 = 96y, y could be:

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

Kudos for a correct solution.

(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

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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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24 Jan 2015, 01:00
1
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
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If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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05 Feb 2016, 21:26
zxcvbnmas wrote:
If a and b are integers and $$(ab)^5$$=96y, y could be

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

$$(ab)^5$$=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
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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29 Oct 2016, 09:07
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.

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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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16 Apr 2017, 20:49
Bunuel wrote:
If a and b are integers and (a*b)^5 = 96y, y could be:

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

Kudos for a correct solution.

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

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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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09 Jul 2017, 06:26
1
1
Bunuel wrote:
If a and b are integers and (a*b)^5 = 96y, y could be:

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

Kudos for a correct solution.

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

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

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

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

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

$$y = 3^4 = 81$$

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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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13 Nov 2017, 16:27
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?
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If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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13 Nov 2017, 16:42
guireif wrote:
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.
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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13 Nov 2017, 16:53
mvictor wrote:
guireif wrote:
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?
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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13 Nov 2017, 20:55
guireif wrote:
mvictor wrote:
guireif wrote:
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.
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If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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14 Nov 2017, 05:17
Bunuel wrote:
guireif wrote:
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?

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!
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Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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30 Jan 2018, 15:17
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

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Re: If a and b are integers and (a*b)^5 = 96y, y could be: &nbs [#permalink] 30 Jan 2018, 15:17
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