Author 
Message 
TAGS:

Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 521
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
10 Feb 2012, 16:03
5
This post received KUDOS
21
This post was BOOKMARKED
Question Stats:
41% (01:55) correct 59% (02:00) wrong based on 794 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730
Last edited by Bunuel on 08 Oct 2017, 04:15, edited 2 times in total.
Edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
10 Feb 2012, 16:32
11
This post received KUDOS
Expert's post
21
This post was BOOKMARKED
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 nonprime, 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 (282)/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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 521
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
10 Feb 2012, 16:35
1
This post received KUDOS
Many thanks Bunuel  you mean to say answer is B. I take it's a typo at your end
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
10 Feb 2012, 16:36



Manager
Status: Juggg..Jugggg Go!
Joined: 11 May 2012
Posts: 233
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

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
05 Jun 2012, 20:59
2
This post received KUDOS
1
This post was BOOKMARKED
Any odd number can be expressed as 2k+1 or 2k+(32) or 2(K1)+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 =291.
_________________
You haven't failed, if you haven't given up!  bschooladmit Visit my Blog www.bschooladmit.wordpress.com
Check out my other posts: Bschool Deadlines 20132014  Bschool Admission Events 2013 Start your GMAT Prep with Stacey Koprince  Get a head start in MBA finance



Senior Manager
Joined: 13 Jan 2012
Posts: 299
Weight: 170lbs
GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42
WE: Analyst (Other)

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
06 Jun 2012, 00:26
1
This post received KUDOS
asax wrote: Any odd number can be expressed as 2k+1 or 2k+(32) or 2(K1)+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 =291. Definitely very clever. I spent 2 minutes going the long way until I realized that.



Manager
Joined: 12 Feb 2012
Posts: 130

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
21 Aug 2012, 16:15
2
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 nonprime, 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 (282)/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?



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
22 Aug 2012, 01:22
alphabeta1234 wrote: 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 nonprime, 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 (282)/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? 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?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Feb 2012
Posts: 130

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
24 Aug 2012, 13:27
Bunuel wrote: alphabeta1234 wrote: 30 sec approach: Any odd nonprime, 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 (282)/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? 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+CABACBCABC+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 ? Thank you!



Intern
Joined: 22 Sep 2012
Posts: 1

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
22 Sep 2012, 14:56
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!!! =)



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
26 Jun 2013, 02:25



Intern
Joined: 22 May 2013
Posts: 48
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
26 Jun 2013, 09:26
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.



Intern
Joined: 06 Dec 2012
Posts: 25
Concentration: Finance, International Business
GPA: 3.5

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
04 Oct 2013, 23:09
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 nonprime, 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 (282)/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 ???



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
05 Oct 2013, 05:12
sunny3011 wrote: 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 nonprime, 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 (282)/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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 23 Jul 2013
Posts: 21

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
17 Oct 2013, 00:26
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 nonprime, 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 (282)/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. ????



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
17 Oct 2013, 03:09
ishdeep18 wrote: 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 nonprime, 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 (282)/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).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 26 May 2012
Posts: 46
Concentration: Marketing, Statistics

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
24 Dec 2013, 00:03
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...



Math Expert
Joined: 02 Sep 2009
Posts: 44321

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
24 Dec 2013, 01:33



Current Student
Joined: 26 May 2012
Posts: 46
Concentration: Marketing, Statistics

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
24 Dec 2013, 11:48
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 (129 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...



Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98

Re: How many positive integers less than 30 are either a multiple of 2, an [#permalink]
Show Tags
07 Nov 2016, 05:41
1
This post was BOOKMARKED
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 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 91 = 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




Re: How many positive integers less than 30 are either a multiple of 2, an
[#permalink]
07 Nov 2016, 05:41



Go to page
1 2
Next
[ 26 posts ]



