MGMAT factors problem

[HPengineer]

This is from the MGMAT flash card set... Im having trouble understanding. Any help would be most appreciated.

x is divisible by 144. If cube root of X is an integer then which of the following is cube root of x definitely divisible by? Chose all that apply.

A.) 4
B.) 8
C.) 9
D.) 12

[kvcpk]

This is from the MGMAT flash card set... Im having trouble understanding. Any help would be most appreciated.

x is divisible by 144. If cube root of X is an integer then which of the following is cube root of x definitely divisible by? Chose all that apply.

A.) 4
B.) 8
C.) 9
D.) 12

x is divisible by 144 means
x is divisible by 2^4 * 3^2
cube root of x is an integer.
Hence another factor of X should be atleast 2^2 * 3 So that X will be divisible by 2^6*3^3
This is to make the cube root of x as integer.

So X is definitely divisible by 2^2 * 3 = 4*3 = 12

Hope this helps!!

[HPengineer]

ok so i think i got it... for cube root of x to be an integer we know that we have to add additional factors to X.

So we can say that X = 2^6 * 3 ^3 now taking the cube root of that our new x = 2^2 *3 i understand how 4 and 12 work now thanks...

I think what tripped me up was taking the cube root of exponents. We just simply divide the exponent by the root we are taking... is that correct?

for example sqrt of 2*4 would be 2^2..

[kvcpk]

ok so i think i got it... for cube root of x to be an integer we know that we have to add additional factors to X.

So we can say that X = 2^6 * 3 ^3 now taking the cube root of that our new x = 2^2 *3 i understand how 4 and 12 work now thanks...

I think what tripped me up was taking the cube root of exponents. We just simply divide the exponent by the root we are taking... is that correct?

for example sqrt of 2*4 would be 2^2..

You are Right on Target!!

[clock60]

This is from the MGMAT flash card set... Im having trouble understanding. Any help would be most appreciated.

x is divisible by 144. If cube root of X is an integer then which of the following is cube root of x definitely divisible by? Chose all that apply.

A.) 4
B.) 8
C.) 9
D.) 12

x is divisible by 144 means
x is divisible by 2^4 * 3^2
cube root of x is an integer.
Hence another factor of X should be atleast 2^2 * 3 So that X will be divisible by 2^6*3^3
This is to make the cube root of x as integer.

So X is definitely divisible by 2^2 * 3 = 4*3 = 12


Hope this helps!!

hi kvcpk
i like your solution , but slightly puzled , why the answer is not 4 , to me it is definitely divisible by 4 can you please explain a litle more

[HPengineer]

I think its just a typo or he means that since 12 is good 4 is also good...

THe correct answer is 4 and 12.... Thanks kvcpk u da man or women not sure

[kvcpk]

I think its just a typo or he means that since 12 is good 4 is also good...

THe correct answer is 4 and 12.... Thanks kvcpk u da man or women not sure

Ofcourse Man

If the number is divisible by 12, it should be divisible by 4. However, because there were 2 correct options, I chose the larger one.