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Math Expert V
Joined: 02 Sep 2009
Posts: 58398
If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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18 00:00

Difficulty:   15% (low)

Question Stats: 78% (01:42) correct 22% (02:00) wrong based on 356 sessions

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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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Answer = (D) 81

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

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

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

$$b^5 = 3y$$

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

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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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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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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

The answer is 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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1
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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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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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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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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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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

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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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 $$3^4 = 81$$

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

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

$$y = 3^4 = 81$$

Hence, Answer is 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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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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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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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58398
Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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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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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.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a and b are integers and (a*b)^5 = 96y, y could be:  [#permalink]

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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:  [#permalink]

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_________________ Re: If a and b are integers and (a*b)^5 = 96y, y could be:   [#permalink] 06 May 2019, 04:00
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