A function * is defined for all even positive integers n as the number

Question

A function * is defined for all even positive integers n as the number of even factors of n other than n itself. What is the value of *(48) ?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions

rajatchopra1994 · Accepted Answer

Explanation: *n = Number of even factors of n other than n = *48 Factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Number of even factors other than 48 = 7 (2,4,6,8,12,16,24) IMO-D

Please give kudos, if you find my explanation Good Enough

GMATWhizTeam · Answer

For any number N which can be written prime factorized and written like this =  2^a * P^b * Q^c *....  , (where 2, P, Q...are all prime numbers)

The total even factors including  N = a * (b+1) * (c+1)....

In this case  N = 48 = 2^4 * 3^1

Thus, total even factors including 48 will be   4* (1+1) = 8

However, we need even factors excluding the number, thus the answer will be  8 - 1 = 7 .

Option D

satya2029 · Answer

48=2^4*3^1 
Total factors=(4+1)*(1+1)=10
Even factors excluding 48 will be Total-  
10-3
=7
D:)

chetan2u · Answer

Formula

48= 2^4*3^1 
Number of factors: (4+1)(1+1)=10
Odd factors = (1+1) or 2, so even factors = 10-2 or 8.
If we take out 48, the remaining factors are 7.

Calculate the factors  
48 being a small and friendly integer, we can find the factors directly 
48 can be written as
1*48
2*24
3*16
4*12
6*8

Even factors other than 48 = 2,4,6,8,12,16,24, that is 7 in number.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

A function * is defined for all even positive integers n as the number

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A function * is defined for all even positive integers n as the number

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards