Question: A perfect number is one which is equal to the sum of all its positive factors that are less than the number itself. Which of the following is a perfect number?

(A) 1
(B) 4
(C) 6
(D) 8
(E) 10

“A perfect number is one which is equal to the sum of all its positive” - is a topic that is covered in the quantitative reasoning section of the GMAT. To successfully execute the GMAT Problem Solving questions, a student must possess a wide range of qualitative skills. The entire GMAT Quant section consists of 31 questions. The problem-solving section of the GMAT Quant topics requires the solution of calculative mathematical problems.

Approach Solution : 1

A positive integer that is equal to the sum of its proper divisors is a perfect number

The formula to be used is, N = [2^(p-1)]*[(2^p) - 1]

Note that P is a prime number

If p = 2, then 2^1(2^2 − 1) = 2 × 3 = 6

If p = 3, then 2^2(2^3 − 1) = 4 × 7 = 28

If p = 5, then 2^4(2^5 − 1) = 16 × 31 = 496

If p = 7, then 2^6(2^7 − 1) = 64 × 127 = 8128

and so on…

Correct Answer : (C)

Approach Solution : 2

Examining the choices could assist us in determining the response to this question.

The first option has 1.

1 cannot be, as 1 is the only factor of 1.
No positive number exists beneath it.

The second option has 4

4 = 1, 2, 4, and we have 1 and 2 in less than 4.
The result of adding these two is 3, which is not an equal number.

The third option has 6

6 = 1, 2, 3, 6; for numbers less than 6, we have 1, 2, 3.
These three added together give us 6, which is the number.

Correct Answer: (C)

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