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How many of the positive divisors of 120 are also multiples

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by M7MBA » Wed Jun 06, 2018 1:15 am

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Answers

A

B

C

D

E

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How many of the positive divisors of 120 are also multiples of 4 not including 120?

A. 3.
B. 4.
C. 5.
D. 7.
E. 8.

The OA is the option D.

Could someone give me some help here? Please. I am confused.
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by GMATGuruNY » Wed Jun 06, 2018 2:26 am
M7MBA wrote:How many of the positive divisors of 120 are also multiples of 4 not including 120?

A. 3.
B. 4.
C. 5.
D. 7.
E. 8.
120 = 4*30 = 4 * (2*3*5).
To form a multiple of 4 that divides evenly into 120 but is not equal to 120, we must combine 4 with up to two of the factors in blue:
4
4*2
4*3
4*5
4*2*3
4*2*5
4*3*5
Total options = 7.

The correct answer is D.
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by Brent@GMATPrepNow » Wed Jun 06, 2018 6:05 am
M7MBA wrote:How many of the positive divisors of 120 are also multiples of 4 not including 120?

A. 3.
B. 4.
C. 5.
D. 7.
E. 8.

The OA is the option D.

Could someone give me some help here? Please. I am confused.
Alternatively, we can just list all divisors in an systematic fashion.
We'll list the divisors in PAIRS of numbers that have a product of 120:
1 and 120
2 and 60
3 and 40
4 and 30
5 and 24
6 and 20
8 and 15
10 and 12
DONE

Scanning our list, the multiples of 4 are in red
There are 7 such values.

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Thu Jun 07, 2018 4:12 pm
M7MBA wrote:How many of the positive divisors of 120 are also multiples of 4 not including 120?

A. 3.
B. 4.
C. 5.
D. 7.
E. 8.
120 = 4 x 30

The factors of 30 are:

1, 30, 2, 15, 3, 10, 5, 6

So taking away the factor 30 (since 4 x 30 = 120), there are 7 divisors of 120 (not including 120) that are multiples of 4.

Answer: D

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