Question: 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

Correct Answer: A
Solution and Explanation:

Approach Solution 1:
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)

Approach Solution 2:

Since 240= 2^4*3*5
Therefore, the total number of divisors= (4+1)(2)(2)= 20 out of these 2,6,10 and 30 are of the form 4n+2.
So option A is correct.

Approach Solution 3:

We can write 240 as 2^4.3^1.5^1
But we want divisors of the form 4n+2
That is, we want even divisor of the form 2(2n+1) and n ⩾ 0
The divisor id 2 (when n=0) or divisor are odd multiples of 2
So the divisors are 2, 6, 10 and 30.

Hence, 4 is the correct answer.

“What is the number of positive divisors of the form (4n + 2) of integer”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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