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prime numbers/multiples question

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prime numbers/multiples question [#permalink] New post 20 Apr 2005, 02:36
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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Re: prime numbers/multiples question [#permalink] New post 20 Apr 2005, 03:38
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.
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 [#permalink] New post 20 Apr 2005, 04:53
mwah ha ha!

thank you :lol:
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 [#permalink] New post 20 Apr 2005, 11:00
marzipan wrote:
mwah ha ha!:lol:
:roll:
  [#permalink] 20 Apr 2005, 11:00
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