Last visit was: 20 Nov 2025, 02:53 It is currently 20 Nov 2025, 02:53
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   
User avatar
enigma123
User avatar
Joined: 25 Jun 2011
Last visit: 16 Mar 2016
Posts: 392
Own Kudos:
19,303
 [100]
Given Kudos: 217
Status:Finally Done. Admitted in Kellogg for 2015 intake
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
GMAT 1: 730 Q49 V45
Posts: 392
Kudos: 19,303
 [100]
How many positive integers less than 30 are either a multiple of 2, an Updated on: 08 Oct 2017, 04:15
Originally posted by enigma123 on 10 Feb 2012, 16:03.
Last edited by Bunuel on 08 Oct 2017, 04:15, edited 2 times in total.
Edited the question.
10
Kudos
Add Kudos
89
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

39% (02:40) correct 61% (02:38) wrong based on 1341 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
 [57]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
 [57]
How many positive integers less than 30 are either a multiple of 2, an 10 Feb 2012, 16:32
20
Kudos
Add Kudos
37
Bookmarks
Bookmark this Post
enigma123
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?
Show more

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.
User avatar
bschooladmit
User avatar
Joined: 11 May 2012
Last visit: 30 Mar 2014
Posts: 159
Own Kudos:
106
 [8]
Given Kudos: 239
Status:Juggg..Jugggg Go!
Location: India
GC Meter: A.W.E.S.O.M.E
Concentration: Entrepreneurship, General Management
GMAT 1: 620 Q46 V30
GMAT 2: 720 Q50 V38
Products:
My Reviews
GMAT 2: 720 Q50 V38
Posts: 159
Kudos: 106
 [8]
How many positive integers less than 30 are either a multiple of 2, an 05 Jun 2012, 20:59
7
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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.
General Discussion
User avatar
geometric
User avatar
Joined: 13 Jan 2012
Last visit: 15 Feb 2017
Posts: 244
Own Kudos:
891
 [2]
Given Kudos: 38
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE:Analyst (Other)
GMAT 2: 760 Q50 V42
Posts: 244
Kudos: 891
 [2]
How many positive integers less than 30 are either a multiple of 2, an 06 Jun 2012, 00:26
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
asax
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.
Show more

Definitely very clever. I spent 2 minutes going the long way until I realized that.
User avatar
alphabeta1234
User avatar
Joined: 12 Feb 2012
Last visit: 03 Jun 2016
Posts: 105
Own Kudos:
282
 [2]
Given Kudos: 28
Posts: 105
Kudos: 282
 [2]
How many positive integers less than 30 are either a multiple of 2, an 21 Aug 2012, 16:15
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
enigma123
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.
Show more

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;

Shouldnt be:

2(1)+3<30
2(1)+5<30
2(1)+7<30
2(1)+11<30
....
2(1)+23<30

Now


2(2)+3<30
2(2)+5<30
2(2)+7<30
2(2)+11<30
....
2(2)+23<30

etc

Your list didn't include all those? What am I missing?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
 [2]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
 [2]
How many positive integers less than 30 are either a multiple of 2, an 22 Aug 2012, 01:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
alphabeta1234
Bunuel
enigma123
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;

Shouldnt be:

2(1)+3<30
2(1)+5<30
2(1)+7<30
2(1)+11<30
....
2(1)+23<30

Now


2(2)+3<30
2(2)+5<30
2(2)+7<30
2(2)+11<30
....
2(2)+23<30

etc

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

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?
User avatar
sunny3011
User avatar
Joined: 06 Dec 2012
Last visit: 22 Dec 2014
Posts: 20
Own Kudos:
250
Given Kudos: 18
Concentration: Finance, International Business
GMAT 1: 510 Q46 V21
GPA: 3.5
GMAT 1: 510 Q46 V21
Posts: 20
Kudos: 250
How many positive integers less than 30 are either a multiple of 2, an 04 Oct 2013, 23:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
enigma123
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.
Show more


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 ???
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
How many positive integers less than 30 are either a multiple of 2, an 05 Oct 2013, 05:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sunny3011
Bunuel
enigma123
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 ???
Show more

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.
avatar
ishdeep18
avatar
Joined: 23 Jul 2013
Last visit: 20 Jan 2014
Posts: 13
Own Kudos:
19
Given Kudos: 63
Posts: 13
Kudos: 19
How many positive integers less than 30 are either a multiple of 2, an 17 Oct 2013, 00:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
enigma123
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.
Show more

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. ????
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
 [2]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
 [2]
How many positive integers less than 30 are either a multiple of 2, an 17 Oct 2013, 03:09
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ishdeep18
Bunuel
enigma123
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. ????
Show more

Because 7, 13, and 19 (all primes) are included in the second set (dd primes).
User avatar
catalysis
User avatar
Joined: 26 May 2012
Last visit: 03 Jan 2017
Posts: 39
Own Kudos:
33
Given Kudos: 11
Concentration: Marketing, Statistics
Schools: Wharton '19 (A) Kellogg '19 (A)
Schools: Wharton '19 (A) Kellogg '19 (A)
Posts: 39
Kudos: 33
How many positive integers less than 30 are either a multiple of 2, an 24 Dec 2013, 00:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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...
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
How many positive integers less than 30 are either a multiple of 2, an 24 Dec 2013, 01:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
catalysis
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...
Show more

I think you misinterpreted the question. It asks: "how many positive integers less than 30 are ..."
User avatar
vitaliyGMAT
User avatar
Joined: 13 Oct 2016
Last visit: 26 Jul 2017
Posts: 297
Own Kudos:
875
 [3]
Given Kudos: 40
GPA: 3.98
Posts: 297
Kudos: 875
 [3]
How many positive integers less than 30 are either a multiple of 2, an 07 Nov 2016, 05:41
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
enigma123
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
Show more

Let’s use PIE principle to solve this question.

\(XUYUZ = X + Y + Z - X⋂Y - X⋂Z - Y⋂Z + X⋂Y⋂Z\)

We have:

\(X\) - “multiples of 2” – even numbers between 1 and 29 = 14

\(Y\) - “odd prime numbers” – 3, 5, 7, 11, 13, 17, 19, 23, 29 = 9

\(Z\)- “sum of positive multiple of 2 and odd prime” (2a+p), where p is odd prime. This function generates all odd numbers except 1 and 3. 1 – because we have positive multiple of 2 (a≠0), and 3 – because we need to add prime number and in order to generate 3 we need to add 1, which is not prime. So we have total # of odd integers in the range minus 1 and 3: 15 – 2 = 13.

\(X⋂Y\) = 0 = because the number cannot be simultaneously even and odd prime

\(X⋂Z\) = 8 - number is simultaneously prime and generated by the function 2a+p, and we know that this function cannot generate prime 3. So we have 9-1 = 8

\(X⋂Z\) = 0 - can’t be simultaneously even and odd.

\(X⋂Y⋂Z\) = 0 – same logic as in previous case.

The resultant # is = 14 + 9 + 13 – 8 = 28
avatar
Shiv2016
avatar
Joined: 02 Sep 2016
Last visit: 14 Aug 2024
Posts: 516
Own Kudos:
211
Given Kudos: 277
Posts: 516
Kudos: 211
How many positive integers less than 30 are either a multiple of 2, an 19 Aug 2017, 02:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
enigma123
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.
Show more


Hello Bunuel

If in such series, we get a number that repeats in both sets. Then do we have to count it once or twice?

For example:
How many positive integers less than 20 are multiple of 2 or a multiple of 3?

Multiple of 2: 2,4,6,8,10,12,14,16,18

Multiple of 3: 3,6,9,12,15,18

So do we have to count 6, 12, and 18 once or twice?

Total would be 15 or 12 ?

Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
How many positive integers less than 30 are either a multiple of 2, an 19 Aug 2017, 03:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shiv2016
Bunuel
enigma123
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.


Hello Bunuel

If in such series, we get a number that repeats in both sets. Then do we have to count it once or twice?

For example:
How many positive integers less than 20 are multiple of 2 or a multiple of 3?

Multiple of 2: 2,4,6,8,10,12,14,16,18

Multiple of 3: 3,6,9,12,15,18

So do we have to count 6, 12, and 18 once or twice?

Total would be 15 or 12 ?

Thanks
Show more

How many positive integers less than 20 are multiple of 2 OR a multiple of 3?

Answer: 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. So, total of 12 numbers.
avatar
Shiv2016
avatar
Joined: 02 Sep 2016
Last visit: 14 Aug 2024
Posts: 516
Own Kudos:
211
Given Kudos: 277
Posts: 516
Kudos: 211
How many positive integers less than 30 are either a multiple of 2, an 19 Aug 2017, 03:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thank you Bunuel for your reply.

Is it because of OR? If there was AND in place of, will the answer still be 12?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,453
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,453
How many positive integers less than 30 are either a multiple of 2, an 19 Aug 2017, 04:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shiv2016
Thank you Bunuel for your reply.

Is it because of OR? If there was AND in place of, will the answer still be 12?
Show more

How many positive integers less than 20 are multiple of both 2 and 3?

Answer: 6, 12, 18. Total of 3 numbers.
User avatar
sahilvijay
User avatar
Joined: 29 Jun 2017
Last visit: 16 Apr 2021
Posts: 295
Own Kudos:
904
 [1]
Given Kudos: 76
GPA: 4
WE:Engineering (Transportation)
Products:
My Reviews
Posts: 295
Kudos: 904
 [1]
How many positive integers less than 30 are either a multiple of 2, an 19 Aug 2017, 04:29
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
multiple of 2 =14 which are even , 2,4,6,8,10........28
odd primes = 3,5,7,11,13,17,19,23,29 =9 numbers
odd prime and sum of multiple of 2 = 5,7,9,11,13,15,17,19,21,23,25,27,29
so total are 14+ (1) + 13 = 28
1 is used because 3 is only which is not there in 3rd list

total 28.
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,739
Own Kudos:
35,358
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,739
Kudos: 35,358
 [2]
How many positive integers less than 30 are either a multiple of 2, an 27 Oct 2018, 08:34
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
enigma123
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
Show more

Multiples of 2: 2, 4, 6, 8, 10, . . .26, 28

Sum of a positive multiple of 2 and an odd prime
3 is the smallest ODD prime
So, let's add multiples of 2 to 3.
We get: 3 + 2, 3 + 4, 3 + 6, 3 + 8, etc
Evaluate to get: 5, 7, 9, 11, . . . 27, 29

At this point, our list of numbers includes 2 as well as all integers from 4 to 29
All we're missing is 1 and 3

An odd prime number
3 is odd, so, now our list becomes: 2, 3, 4, 5, 6, . . . 27, 28, 29

So, the ONLY value that is NOT in the list is 1 (1 is NOT prime)

So, there are 28 numbers that meet the given conditions.

Answer: B

Cheers,
Brent
avatar
mehro023
avatar
Current Student
Joined: 08 Nov 2019
Last visit: 10 Dec 2021
Posts: 55
Own Kudos:
40
Given Kudos: 1,158
Location: United States (MN)
Concentration: Finance, International Business
Schools: INSEAD Aug 22 intake (A) Stern '24 (WL) Tuck '24 (I)
GMAT 1: 580 Q47 V22
GMAT 2: 650 Q49 V29 (Online)
GMAT 3: 680 Q49 V33
GMAT 4: 710 Q49 V38
GMAT 5: 730 Q50 V40
GPA: 3.29
WE:Architecture (Other)
Products:
My Reviews
Schools: INSEAD Aug 22 intake (A) Stern '24 (WL) Tuck '24 (I)
GMAT 5: 730 Q50 V40
Posts: 55
Kudos: 40
How many positive integers less than 30 are either a multiple of 2, an 12 Apr 2020, 14:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATPrepNow

Why did you choose 3 to add to multiples of 2 ?

Thanks,
K
 1   2   
Moderators:
Bunuel
Math Expert
105408 posts
Krunaal
Tuck School Moderator
805 posts