Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

05 Jun 2012, 18:16

1

This post received KUDOS

How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

is there any shortcut method to solve this type of problem??
_________________

some people are successful, because they have been fortunate enough and some people earn success, because they have been determined.....

please press kudos if you like my post.... i am begging for kudos...lol

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

05 Jun 2012, 19:59

2

This post received KUDOS

1

This post was BOOKMARKED

Any odd number can be expressed as 2k+1 or 2k+(3-2) or 2(K-1)+3. Thus, with the prime number 3, we can express all the odd numbers. Since, 1 i is the only number that cannot be expressed, answer is numbers <30 =29-1.
_________________

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

05 Jun 2012, 23:26

1

This post received KUDOS

asax wrote:

Any odd number can be expressed as 2k+1 or 2k+(3-2) or 2(K-1)+3. Thus, with the prime number 3, we can express all the odd numbers. Since, 1 i is the only number that cannot be expressed, answer is numbers <30 =29-1.

Definitely very clever. I spent 2 minutes going the long way until I realized that.

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

21 Aug 2012, 15:15

1

This post received KUDOS

Bunuel wrote:

enigma123 wrote:

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

Hey Bunuel,

How can this be the entire list?

# of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

Hey Bunuel,

How can this be the entire list?

# of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Your list didn't include all those? What am I missing?

First of all we are asked about the number of positive integers less than 30, which are a multiple of 2 OR an odd prime number OR the sum of a positive multiple of 2 and an odd prime.

Next, EACH numbers from 1 to 30, not inclusive is a multiple of 2 OR an odd prime number OR the sum of a positive multiple of 2 and an odd prime. So, the list is 2, 3, 4, 5, ..., 29 (total of 28 numbers).

So, which number is not included in the list?
_________________

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

24 Aug 2012, 12:27

Bunuel wrote:

alphabeta1234 wrote:

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

Hey Bunuel,

How can this be the entire list?

# of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Your list didn't include all those? What am I missing?

Bunuel's Response: First of all we are asked about the number of positive integers less than 30, which are a multiple of 2 OR an odd prime number OR the sum of a positive multiple of 2 and an odd prime.

Next, EACH numbers from 1 to 30, not inclusive is a multiple of 2 OR an odd prime number OR the sum of a positive multiple of 2 and an odd prime. So, the list is 2, 3, 4, 5, ..., 29 (total of 28 numbers).

So, which number is not included in the list?[/quote]

Hey Bunuel,

Thanks for pointing out my mistake the same numbers that are generated by 2K+odd prime are also included in the same list as the odd primes. In other words A=# of even numbers between 1 and 29, inclusive B=# of odd primes between 1 and 29, inclusive C=# of 2K+odd_prime, between 1 and 29, inclusive

AUBUC=A+B+C-AB-AC-BC-ABC+N

AB=0, since there are no numbers both even and odd primes between 1 and 29, inclusive AC=0, since there are no numbers both even and 2K+odd_prime(=odd) between 1 and 29, inclusive ABC=0 since no numbers are even, and odd prime and a 2K+odd_prime and N=1, since only 1 fits the criteria of being niether an even number, neither an odd prime, and neither a 2K+odd_prime

My question I guess is for BC, numbers both an odd prime and 2K+odd_prime. Is there a way to tell, without actually listing out all the numbers that meet this condition and checking ?

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

22 Sep 2012, 13:56

I can't believe that what made this problem difficult was a "typo error" in the question statement!!!! Instead of "... number, of the sum of a positive multiple..." is "... number, OR the sum of a positive... Thank you for clarifying!!! =)

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

26 Jun 2013, 08:26

1

This post received KUDOS

enigma123 wrote:

How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?

A. 29 B. 28 C. 27 D. 25 E. 23

Qquestion: 0<x<30 so, 1<=x<=29

leave x=1 alone for a while, and consider everything else i.e. 2<=x<=29

integer either multiple of 2 that will be almost half the no's (14) odd prime no, and sum of a positive multiple of 2 and an odd prime => Rest everything else has to be either a prime no or the sum of some multiple of 2(Those 14 no we got earlier)and a odd no

only for x=1, it is neither even, nor prime and definitely not the sum.

Thus ans = total no's - 1 = 29 - 1 = 28

Ans: B
_________________

PS: Like my approach? Please Help me with some Kudos.

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

04 Oct 2013, 22:09

Bunuel wrote:

enigma123 wrote:

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

I did not understand the last condition ? sum of a positive multiple of 2 and an odd prime ? it can be possible: 7=5+2 ???

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

I did not understand the last condition ? sum of a positive multiple of 2 and an odd prime ? it can be possible: 7=5+2 ???

2 is not an odd prime.

But 7 CAN be written as the sum of a positive multiple of 2 and an odd prime: 7 = 4 + 3.
_________________

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

16 Oct 2013, 23:26

Bunuel wrote:

enigma123 wrote:

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

In this # of integers which are the sum of a positive multiple of 2 and an odd prime ,.. why didnt we count 7=5+2 and 13=11+2,19=13+4 .. ??? these all are Sum of multiple of 2 and odd primes. ????

How many positive integers less than 30 are either a multiple of 2, an odd prime number, or the sum of a positive multiple of 2 and an odd prime? (A) 29 (B) 28 (C) 27 (D) 25 (E) 23

Any idea how to solve this guys?

30 sec approach: Any odd non-prime, greater than 1, can be obtained by the sum of an odd prime and a positive even number. So this set plus the set of odd primes basically makes the set of all odd numbers greater than 1 in the range. Now, the set of all odd numbers greater than 1 together with the set of all even numbers makes the set of all numbers from 1 to 30, not inclusive, so total of 28 numbers.

Answer: B.

To illustrate: # of even numbers in the range is (28-2)/2+1=14: 2, 4, 6, ..., 28; # of odd primes in the range is 9: 3, 5, 7, 11, 13, 17, 19, 23, and 29; # of integers which are the sum of a positive multiple of 2 and an odd prime is 5: 9=7+2, 15=13+2, 21=19+2, 25=23+2 and 27=23+4;

Total: 14+9+5=28. You can see that we have all numbers from 1 to 30, not inclusive: 2, 3, 4, 5, 6, ...., 29.

Hope it's clear.

In this # of integers which are the sum of a positive multiple of 2 and an odd prime ,.. why didnt we count 7=5+2 and 13=11+2,19=13+4 .. ??? these all are Sum of multiple of 2 and odd primes. ????

Because 7, 13, and 19 (all primes) are included in the second set (dd primes).
_________________

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

23 Dec 2013, 23:03

What are the actual 2 numbers that answer this question? I know 1 is one of them, but I can't think of the other one...I used to think it was 0 but technically 0 is neither positive nor negative...

What are the actual 2 numbers that answer this question? I know 1 is one of them, but I can't think of the other one...I used to think it was 0 but technically 0 is neither positive nor negative...

I think you misinterpreted the question. It asks: "how many positive integers less than 30 are ..."
_________________

Re: How many positive integers less than 30 are either a [#permalink]

Show Tags

24 Dec 2013, 10:48

Bunuel wrote:

catalysis wrote:

What are the actual 2 numbers that answer this question? I know 1 is one of them, but I can't think of the other one...I used to think it was 0 but technically 0 is neither positive nor negative...

I think you misinterpreted the question. It asks: "how many positive integers less than 30 are ..."

Hi Bunuel - Sorry, I think I misworded my original question. I know the answer is 28, which means 28 numbers less than 30 meet the constraints given. However, I was just curious which values are the numbers that do NOT meet the constraints.

However, I have kind of answered my own question because now I realize that there are only 29 integers to choose from (1-29 inclusive), not 30 like I had originally thought, because 0 is not a positive integer and 30 cannot be included because the question asks for numbers less than 30. Therefore, it makes sense that 1 is the only integer that does not meet the constraints and I should not be looking for a second number. (29 possible integers - 1 integer that does not meet the constraints = 28 integers that meet the constraints, just like the answer says)

Hope this makes sense...

gmatclubot

Re: How many positive integers less than 30 are either a
[#permalink]
24 Dec 2013, 10:48

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...