For how many positive integer x is 130/x an integer?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 3
The OA is A.
What is the fastest way to solve this PS question? Should I try number by number?
For how many positive integer x is 130/x an integer?
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Hi Vincen,
For 130/X to be an integer, X must be a factor of 130. There are a couple of different ways to determine all of the different factors of 130: you can 'brute force' the list or use prime-factorization.
If you prime-factor 130, you'll get...
(2)(65)
(2)(5)(13)
Thus, the factors of 130 are:
1
2
5
13
(2)(5) = 10
(2)(13) = 26
(5)(13) = 65
(2)(5)(13) = 130
Total = 8 (you should also notice that this is the largest possible answer among the 5 choices, so there's no way that you 'missed' any of them).
Final Answer: A
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Rich
For 130/X to be an integer, X must be a factor of 130. There are a couple of different ways to determine all of the different factors of 130: you can 'brute force' the list or use prime-factorization.
If you prime-factor 130, you'll get...
(2)(65)
(2)(5)(13)
Thus, the factors of 130 are:
1
2
5
13
(2)(5) = 10
(2)(13) = 26
(5)(13) = 65
(2)(5)(13) = 130
Total = 8 (you should also notice that this is the largest possible answer among the 5 choices, so there's no way that you 'missed' any of them).
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Hi Vincen,Vincen wrote:For how many positive integer x is 130/x an integer?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 3
The OA is A.
What is the fastest way to solve this PS question? Should I try number by number?
Let's take a look at your question.
for 130/x to be a positive integer, the x in the denominator should be one of the factors of 130. Let's factor out 130 using prime factorization.
130 = 2 x 5 x 13
All possible factors could be
1, 2, 5, 13, 130
and
2 x 5 = 10
2 x 13 = 26
5 x 13 = 65
So there are a total of 8 positive integers x so that 130/x is a positive integer.
1, 2, 5, 10, 13, 26, 65, 130
Therefore, Option A is correct.
I am available if you'd like any followup.
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If x is a positive integer and 130/x is an integer, then x must be a factor of 130. Thus, we need to determine the number of factors of 130. To determine the number of factors, we break down 130 into primes and add 1 to the exponent of each unique prime, and then multiply. Thus:Vincen wrote:For how many positive integer x is 130/x an integer?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 3
130 = 10 x 13 = 2^1 x 5^1 x 13^1
Thus, 130 has (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 total factors.
Answer: A
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This is just a funky way of asking "How many distinct factors are there of 130?"
To see a nice way of doing this, check out this link!
To see a nice way of doing this, check out this link!