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prime numbers/multiples question
[#permalink]
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
Archived Topic
Hi there,
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Re: prime numbers/multiples question
[#permalink]
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.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.