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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
64% (02:51) correct
36%
(02:31)
wrong
based on 129
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What is the number of positive divisors of the form (4n + 2) of integer 240, where n is an integer ≥ 0 ?
(A) 4
(B) 8
(C) 10
(D) 11
(E) 12
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 4
(B) 8
(C) 10
(D) 11
(E) 12
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
18 Feb 2021, 08:15
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Bunuel
What is the number of positive divisors of the form (4n + 2) of integer 240, where n is an integer ≥ 0 ?
(A) 4
(B) 8
(C) 10
(D) 11
(E) 12
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 4
(B) 8
(C) 10
(D) 11
(E) 12
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Some observations:
4n is divisible by 4 for all integer values of n
So, 4n + 2 is NOT divisible by 4
But 4n + 2 IS divisible by 2
So we're looking for divisors of 420 that are EVEN but NOT divisible by 4
240 = (2)(2)(2)(2)(3)(5)
We can see that the following divisors are EVEN but NOT divisible by 4:
(2)
(2)(3)
(2)(5)
(2)(3)(5)
Evaluate to see that 2, 6, 10 and 30 are the only positive divisors in the form (4n + 2)
Answer: A
13 Apr 2024, 18:57
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Found the factors of 240:
1x240, 2x120, 3x80, 4x60, 5x48, 6x40, 8x30, 10x24, 12x20, 15x16
Now,
starting putting n value from 0 then 1 then 2
So, n=0 : 4(0) + 2 = 2 Yes
n=1 : 4(1) +2 = 6 Yes
n=2: 4(2) + 2 = 10 Yes
n=3: 14 No
n=4 : 18 No
n=5 : 22 No (Increasing by 4 and not divisible by 4)
n=6 : 26 No (Increasing by 4 and not divisible by 4)
n=7 : 30 Yes
n=8..... no value of n from here is not divisble by 4
So answer is 4; Option A
1x240, 2x120, 3x80, 4x60, 5x48, 6x40, 8x30, 10x24, 12x20, 15x16
Now,
starting putting n value from 0 then 1 then 2
So, n=0 : 4(0) + 2 = 2 Yes
n=1 : 4(1) +2 = 6 Yes
n=2: 4(2) + 2 = 10 Yes
n=3: 14 No
n=4 : 18 No
n=5 : 22 No (Increasing by 4 and not divisible by 4)
n=6 : 26 No (Increasing by 4 and not divisible by 4)
n=7 : 30 Yes
n=8..... no value of n from here is not divisble by 4
So answer is 4; Option A
