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Which of the following has as many positive factors as 300 have? A) 20
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25 Jun 2021, 08:50
25 Jun 2021, 08:50
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65% (01:42) correct
35% (01:09) wrong based on 20 sessions
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Which of the following has as many positive factors as 300 have?
A) 200
B) 400
C) 500
D) 600
E) 700
A) 200
B) 400
C) 500
D) 600
E) 700
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Which of the following has as many positive factors as 300 have? A) 20
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25 Jun 2021, 08:56
25 Jun 2021, 08:56
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Carcass wrote:
Which of the following has as many positive factors as 300 have?
A) 200
B) 400
C) 500
D) 600
E) 700
A) 200
B) 400
C) 500
D) 600
E) 700
---------ASIDE---------------------------------
If N = (p^a)(q^b)(r^c)..., where p, q, r,...(etc.) are prime numbers, then the total number of positive divisors of N is equal to (a+1)(b+1)(c+1)...
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) = (5)(4)(2) = 40
---------NOW ONTO THE QUESTION--------------------------
300 = (2^2)(3^1)(5^2)
So, the number of positive divisors of 300 = (2+1)(1+1)(2+1) = (3)(2)(3) = 18
Now check the answer choices....
NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.
E) 700
700 = (2^2)(5^2)(7^1)
So, the number of positive divisors of 700 = (2+1)(2+1)(1+1) = (3)(3)(2) = 18
We have a MATCH!!
Answer: E
gmatclubot
Which of the following has as many positive factors as 300 have? A) 20 [#permalink]
25 Jun 2021, 08:56
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