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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

If n=2^435, how many factors of n are...

by swerve » Wed Nov 08, 2017 7:22 am

If n=2^4*3*5, how many factors of n are greater than or equal to 8 and less than equal to 30?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 15

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Nov 08, 2017 7:22 am

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Wed Nov 08, 2017 11:43 am

There may be more formulaic strategies that you could use, but in this case (since it's a small-ish range), I'd just list out all the factors, then count:

n=2^4*3*5

Factors:
1
2
3
4
5
6
8
10
12
15
16
20
24
30

There are 8 distinct factors in this range. The answer is A.

Please list the source of your question!

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Oct 29, 2019 6:39 pm

swerve wrote:If n=2^4*3*5, how many factors of n are greater than or equal to 8 and less than equal to 30?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 15

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

The factors of n that are greater than or equal to 8 and less than or equal to 30 are:

3 x 5 = 15

2 x 5 = 10

2 x 3 x 5 = 30

2^2 x 3 = 12

2^2 x 5 = 20

2^3 = 8

2^3 x 3 = 24

and

2^4 = 16

So there are 8 such factors.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
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