[Math Revolution GMAT math practice question]
There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?
A. 6
B. 12
C. 15
D. 18
E. 36
There are 3 ways to make the number 12 using products of two
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- Max@Math Revolution
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E
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To count the factors of a positive integer:Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
There are 3 ways to make the number 12 using products of two positive integers. These are 1*12, 2*6, and 3*4. In how many ways can 2700 be written as the product of two positive integers?
A. 6
B. 12
C. 15
D. 18
E. 36
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)..
2700 = 2²3³5²
Adding 1 to each exponent and multiplying, we get:
Total number of factors = (2+1)(3+1)(2+1) = 36
These 36 factors can be used to form 18 FACTOR PAIRS, as follows:
1*2700
2*1350
3*300
And so on.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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- Max@Math Revolution
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=>
2700 = 2^2*3^3*5^2
The number of distinct factors of 2700 is (2+1)(3+1)(2+1) = 36.
Since the order of multiplication does not matter (i.e. 30 * 90 = 90*30), the number of pairs of positive integers that multiply to give 2700 is 36/2 = 18.
Therefore, the answer is D.
Answer: D
2700 = 2^2*3^3*5^2
The number of distinct factors of 2700 is (2+1)(3+1)(2+1) = 36.
Since the order of multiplication does not matter (i.e. 30 * 90 = 90*30), the number of pairs of positive integers that multiply to give 2700 is 36/2 = 18.
Therefore, the answer is D.
Answer: D
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