Can someone explain this answer

[mad.grad]

If n is a positive integer and n^2 [n square ] is divisible by 72, then the largest positive integer that must divide n is

A) 6
B) 12
C) 24
D) 36
E) 48

Answer B

nothing in the question stops you from choosing answer E , 48 . Can someone explain.

TIA.

[cramya]

I think the questions read must and not could.


72 = 2*2*2*3*3

2^3*3^2



n must have atleast 2^2*3 so that when its squared we can safely conclude its divisible by 72.

Eg:

let n= 24

24^2 is divisible by 72 but 24 itslef does not ahve to divisible by 48


Hope this helps!

Regards,
CR

[PAB2706]

@cramya

n must have atleast 2^2*3 so that when its squared we can safely conclude its divisible by 72.

Eg:

let n= 24

24^2 is divisible by 72 but 24 itslef does not ahve to divisible by 48


i am not understanding this...

[cramya]

72 = 2^3 * 3^2

This is not a perfect square

Let say the n^2 is divisible by 36(perfect square) = 2^2*3^2

We can say then the largest positive integer that must divide n is 6.

Lets say n = 6 n^2 divisible by 36

n=3 n^2 not divisible by 36

Similarly since 72 = 2^3*3^2 we must have atleast 2^2*3 in n which when squared

(2^2*3) ^2 = 2^4 * 3^2 ->definitely divisible by 72


Hope this helps!

Regards,
CR

[vamshi294]

hi,

If we see 72 is 2^3*3^2; so to make it a square...we need to multiply it with 2 ---> 2^4*3^2 = 12^2 ; so n=12;
largest number that divides 12 is 12.


So my answer is 12. Isnt that correct?