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# prime numbers/multiples question

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Joined: 20 Apr 2005
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prime numbers/multiples question [#permalink]  20 Apr 2005, 01:36
Hi there folks,

I'm just beginning to prepare for the GMAT by using the Princeton Math Workout book (published 1998) and have a question that doesn't make sense to me.

Here it is,

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

I put the answer and explanation, as well as my question further down in case you want to try to figure it out:

(d) is the correct answer. Here is the explanation for why:

The prime numbers are: 2,3,5,7,11,13,17,19,23 (total 9 )
The odd multiples of 25 are: 5,15,25 (total 3)
The numbers that can be expressed as the sum of a positive multiple of 2 and a postive multiple of four are all the even numbers over 4: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 (total 11)
grand total=9+3+11=23

So how can (d), which is 22, be the correct answer?

I apologize if I've overlooked a *really* obvious error--but I can't find it anywhere!

Any shedable light would be warmly received indeed,
Marzipan
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Senior Manager
Joined: 15 Mar 2005
Posts: 421
Location: Phoenix
Followers: 2

Kudos [?]: 12 [0], given: 0

Re: prime numbers/multiples question [#permalink]  20 Apr 2005, 02:38
marzipan wrote:
Hi there folks,

I'm just beginning to prepare for the GMAT by using the Princeton Math Workout book (published 1998) and have a question that doesn't make sense to me.

Here it is,

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

I put the answer and explanation, as well as my question further down in case you want to try to figure it out:

(d) is the correct answer. Here is the explanation for why:

The prime numbers are: 2,3,5,7,11,13,17,19,23 (total 9 )
The odd multiples of 25 are: 5,15,25 (total 3)
The numbers that can be expressed as the sum of a positive multiple of 2 and a postive multiple of four are all the even numbers over 4: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 (total 11)
grand total=9+3+11=23

So how can (d), which is 22, be the correct answer?

I apologize if I've overlooked a *really* obvious error--but I can't find it anywhere!

Any shedable light would be warmly received indeed,
Marzipan

That's because 5 is common to both prime numbers and odd multiples of 5.

Hope that helps.
_________________

Who says elephants can't dance?

Intern
Joined: 20 Apr 2005
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

[#permalink]  20 Apr 2005, 03:53
mwah ha ha!

thank you
VP
Joined: 25 Nov 2004
Posts: 1495
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Kudos [?]: 38 [0], given: 0

[#permalink]  20 Apr 2005, 10:00
marzipan wrote:
mwah ha ha!:lol:
[#permalink] 20 Apr 2005, 10:00
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# prime numbers/multiples question

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