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Factors

by harsh.champ » Tue Feb 09, 2010 4:59 am
If both 52 and 33 are factors of n x (25) x (62) x (73), what is the smallest possible positive value of n?

(A)75
(B)85
(C)65
(D)55
(E)45

The OA is A.
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by shashank.ism » Tue Feb 09, 2010 5:46 am
harsh.champ wrote:If both 52 and 33 are factors of n x (25) x (62) x (73), what is the smallest possible positive value of n?

(A)75
(B)85
(C)65
(D)55
(E)45

The OA is A.
52=13x 2x2
33=11x3
25=5x5
62=31x2
73=73
so minimum value of N = 13 x 2 x 11 x3 = 858 None of these
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by ajith » Tue Feb 09, 2010 6:31 am
harsh.champ wrote:If both 52 and 33 are factors of n x (25) x (62) x (73), what is the smallest possible positive value of n?

(A)75
(B)85
(C)65
(D)55
(E)45

The OA is A.
To make , 25*62*73 a multiple of 52 and 33 we should multiply it by 2*13*3*11 =858

Is there anything that I am missing here?
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by ldoolitt » Tue Feb 09, 2010 6:48 am
Its a prime factors question. Its asking what prime factors need to be added to the number n x (25) x (62) x (73) such that it contains all the prime factors of the numbers 52 and 33. So write out all the factor boxes.

52 (f) 13,2,2
33 (f) 11,3

25 (f) 5,5
62 (f) 31,2
73 (f) 73

Since the product of 25, 62 and 73 already has one 2 as a prime factor we can eliminate that. Thus we need to add the prime factors of 12, 2, 11 and 3. With the product of that being 858. I agree with shashank.ism.

You can see that 75 doesn't work by plugging it into a calculator. 75*25*62*73 / 33 is not an integer. Unless I'm misunderstanding the question. Are the numbers correct?
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by shashank.ism » Tue Feb 09, 2010 7:01 am
ajith wrote:
harsh.champ wrote:If both 52 and 33 are factors of n x (25) x (62) x (73), what is the smallest possible positive value of n?

(A)75
(B)85
(C)65
(D)55
(E)45

The OA is A.
To make , 25*62*73 a multiple of 52 and 33 we should multiply it by 2*13*3*11 =858

Is there anything that I am missing here?
i think something is missing here..or some wrong options has been put up by mistake..Harsh will you please match it up with the source.
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