How many positive integers less than 28 are prime numbers,

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Jul 22, 2018 7:11 pm

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How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 23, 2018 3:11 am

BTGmoderatorDC wrote:How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

Any even integer other than 2 and 4 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 4, yielding the following options less than 28:
6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 --> 11 options.

Prime numbers less than 28:
2, 3, 5, 7, 11, 13, 17, 19, 23 --> 9 options.

Odd multiples of 5 not yet listed:
15, 25 --> 2 options.

Total options = 11+9+2 = 22.

The correct answer is D.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Jul 25, 2018 4:33 pm

BTGmoderatorDC wrote:How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

The following are sums of multiples of 2 and 4:

6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

The following are prime numbers less than 28:

2, 3, 5, 7, 11, 13, 17, 19, 23

The following are odd multiples of 5 (excluding 5) that are less than 28:

15 and 25

In the lists above there are 11 + 9 + 2 = 22 values.

Answer: D

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