What is the smallest positive integer x, such that 1,152x is a perfect

Question

What is the smallest positive integer x, such that 1,152x is a perfect cube?

A. 4 
B. 6 
C. 8 
D. 12 
E. 18

OptimusPrepJanielle · Answer

We need to make 1152x a perfect cube, hence we need to have the powers a multiple of 3
1152 = 2^7*3^2

The minimum value of x for which 1152x is a perfect cube = 2^2*3 = 12

Correct Option: D

Himanshu9818 · Answer

Take out the factors of 1152 that will come 2*2*2*2*2*2*2*3*3. for perfect cube you need every no. raise to the power 3. for 1,152x to be a perfect cube, you need two 2 and 1 3 that means 12.
D is the answer.

rhine29388 · Answer

prime factorization 0f 1152 = 2*2*2*2*2*2*2*3*3 =  2^{7}  * 3^2 
for a number to be perfect cube it should have powers of its prime factors in multiple of 3 (3,6 ,9 ...etc)
we need  2^2  *3 = 12 to make the given number a perfect cube so x =12
Correct Answer - D

CounterSniper · Answer

1152 =2^7*3^2
for it to be a perfect cube we have to multiply it with 2^2 *3 = 12

syahasa2 · Answer

1,152 is 2^7*3^2

Or 2^3 * 2^3 *2*3^2

We need 2^2 & 3, to make 1152 a perfect cube.
So 4*3=12 D.

RK84 · Answer

It seems the question is asking if x is an integer placed in front of the number making it either a 5 digit perfect cube or a six digit perfect cube.
please post questions with clarity. The language here should have been : what should be the minimum value of integer x when multiplied by 1152 yields a perfect cube?
Thanks!

Bunuel · Answer

1,152x means 1,152*x.

law258 · Answer

1152 = (2^7)(3^2)

To get a perfect cube, we need to get the exponents (listed above) so that they are multiples of 3 --> closest multiple for 2^7 is 2^9 --> we need 2^2 to do this (KEEP)

Let's do the same for 3^2: closest multiple is 3^3 --> we need 3 to do this (KEEP)

X should have both 2^2 & 3 in order to transform 1152 into a perfect cube.

Thus, D is correct.

BrentGMATPrepNow · Answer

------ASIDE--------------------------------------
Let's examine a perfect CUBE.

1000 is a perfect cube since 1000 = 10^3
Now check out the prime factorization of 1000
1000 = (2)(2)(2)(5)(5)(5)
=    
Notice that we can take the prime factorization of 1000 and divide the prime factors into THREE identical groups
-----NOW ONTO THE QUESTION------------------------

1,152 = (2)(2)(2)(2)(2)(2)(2)(3)(3)
So, 1152 x  = (2)(2)(2)(2)(2)(2)(2)(3)(3)( x )
Let's  test the answer choices. ...

A.  x = 4  
We get: 1152 x  = (2)(2)(2)(2)(2)(2)(2)(3)(3)( 4 )
= (2)(2)(2)(2)(2)(2)(2)(3)(3)( 2 )( 2 )
In order for the above to be a perfect CUBE, we must be able to divide the prime factors into THREE identical groups.
Since we cannot do that here, we can ELIMINATE A

B.  x = 6  
We get: 1152 x  = (2)(2)(2)(2)(2)(2)(2)(3)(3)( 6 )
= (2)(2)(2)(2)(2)(2)(2)(3)(3)( 2 )( 3 )
Can we divide the above prime factors into THREE identical groups?
NO! ELIMINATE B

C.  x = 8  
We get: 1152 x  = (2)(2)(2)(2)(2)(2)(2)(3)(3)( 8 )
= (2)(2)(2)(2)(2)(2)(2)(3)(3)( 2 )( 2 )( 2 )
Can we divide the above prime factors into THREE identical groups?
NO! ELIMINATE C

D.  x = 12  
We get: 1152 x  = (2)(2)(2)(2)(2)(2)(2)(3)(3)( 12 )
= (2)(2)(2)(2)(2)(2)(2)(3)(3)( 2 )( 2 )( 3 )
Can we divide the above prime factors into THREE identical groups?
YES!
1152 x  =    
So, if x = 12, then 1152x IS a perfect cube.

Answer: D

RELATED VIDEO
 https://www.youtube.com/watch?v=W72A4b05K9Y

BrushMyQuant · Answer

We need to find the value of x which will make 1152x a perfect cube

Let's start factorizing 1152x. We get
1152x =  2^7 * 3^2 * x 
So, for 1152x to be a perfect cube
x should be equal to  2^2 * 3  
Making 1152x =  2^7 * 3^2 * 2^2 * 3   =  2^9 * 3^3

=> x = 4*3 = 12

So,  Answer will be D 
Hope it helps!

bumpbot · Answer

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What is the smallest positive integer x, such that 1,152x is a perfect

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What is the smallest positive integer x, such that 1,152x is a perfect

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