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Joined: 06 Nov 2016
Posts: 94
Given Kudos: 15
Location: India
GMAT 1: 710 Q50 V36 
GPA: 2.8
S represents the set of positive integers that are factors of 7200. Ho
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08 Jul 2017, 12:41
08 Jul 2017, 12:41
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S represents the set of positive integers that are factors of 7200. How many integers in S are multiples of 72?
A. 2
B. 5
C. 9
D. 10
E. 100
A. 2
B. 5
C. 9
D. 10
E. 100
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Joined: 24 Jun 2008
Posts: 4126
Given Kudos: 96
Q51 V47
Re: S represents the set of positive integers that are factors of 7200. Ho
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08 Jul 2017, 13:23
08 Jul 2017, 13:23
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Expert Reply
If 72x is a divisor of 7200, then 7200/72x is an integer, so, cancelling, 100/x is an integer. So x needs to be a divisor of 100. So that's the question - how many positive divisors does 100 have? If you know the method for counting divisors, you can get the answer quickly - prime factorize 100:
100 = 2^2 * 5^2
then look only at the exponents (2 and 2) : add 1 to each exponent, and multiply what you get. So 100 has (2 + 1)(2 + 1) = 3*3 = 9 divisors.
Or you could list all nine of the divisors quite easily: 1, 2, 4, 5, 10, 20, 25, 50, 100
100 = 2^2 * 5^2
then look only at the exponents (2 and 2) : add 1 to each exponent, and multiply what you get. So 100 has (2 + 1)(2 + 1) = 3*3 = 9 divisors.
Or you could list all nine of the divisors quite easily: 1, 2, 4, 5, 10, 20, 25, 50, 100
General Discussion
Re: S represents the set of positive integers that are factors of 7200. Ho
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08 Jul 2017, 14:28
08 Jul 2017, 14:28
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sonikavadhera
S represents the set of positive integers that are factors of 7200. How many integers in S are multiples of 72?
A. 2
B. 5
C. 9
D. 10
E. 100
A. 2
B. 5
C. 9
D. 10
E. 100
7200 = (2^5)*(3^2)*(5^2)
72 = (2^3)*(3^2)
Multiple of 72 in set S can have 3 different powers of 2 (0,1,2)
Multiple of 72 in set S can have 3 different powers of 5 (0,1,2)
72 can be multiplied with 3 different powers of 2 and still be a factor of 7200: (2^0), (2^1), (2^2)
72 can be multiplied with 3 different powers of 5 and still be a factor of 7200: (5^0), (5^1), (5^2)
Therefore total combinations of multiples of 72, that are factors of 7200 is 3x3 = 9
