Author 
Message 
TAGS:

Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 148
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
26 Dec 2012, 02:29
Question Stats:
52% (01:42) correct 48% (01:32) wrong based on 467 sessions
HideShow timer Statistics
If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true? (A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beatitnoonewantstobedefeatedjourney570to149968.html



Math Expert
Joined: 02 Sep 2009
Posts: 46164

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
26 Dec 2012, 03:00
daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd. Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are coprime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1. Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50. Answer: A. Similar question from GMAT Prep: foreverypositiveevenintegernthefunctionhnis126691.htmlHope it helps.
_________________
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
Joined: 17 Dec 2012
Posts: 635
Location: India

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
26 Dec 2012, 03:32
daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 Since each prime number from 3 upto 47 is a factor of (3 Δ 47) , none of them can be a factor of (3 Δ 47) + 2 . Also 48, 49 and 50 are not prime factors. And y cannot be 2 because (3 Δ 47) +2 is odd. Therefore y>50.
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com/bestonlinegrepreparation.php
Improve Intuition and Your Score Systematic Approaches



Director
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
26 Dec 2012, 19:55
Bunuel wrote: daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd. Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are coprime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1. Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50. Answer: A. Similar question from GMAT Prep: foreverypositiveevenintegernthefunctionhnis126691.htmlHope it helps. Hi Bunuel, Thanks for the solution above. Is their a significance of the term " Every Odd prime between 3 & 47"..It can very well be every prime between 3 and 47. Please confirm. Thanks Mridul
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 46164

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
27 Dec 2012, 02:18
mridulparashar1 wrote: Bunuel wrote: daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd. Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are coprime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1. Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50. Answer: A. Similar question from GMAT Prep: foreverypositiveevenintegernthefunctionhnis126691.htmlHope it helps. Hi Bunuel, Thanks for the solution above. Is their a significance of the term " Every Odd prime between 3 & 47"..It can very well be every prime between 3 and 47. Please confirm. Thanks Mridul Yes, that's correct.
_________________
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
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
30 Dec 2012, 08:32
Bunuel wrote: daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd. Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are coprime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1. Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50. Answer: A. Similar question from GMAT Prep: foreverypositiveevenintegernthefunctionhnis126691.htmlHope it helps. Hi Bunuel, I just wanted to undertsand in what case 2 can be a smallest prime factor. For Eg if the Q. said that the smallest prime in (3 Δ 47) + 1.Then, the no (3 Δ 47) + 1 will be odd+1=even. Can we say 2 will be the smallest prime in this case. Also, 2 consecutive integers will also be coprime and therefore none of the factors in (3 Δ 47) will be factors of (3 Δ 47) + 1. Thanks for your reply to my queries earlier. Mridul
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 46164

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
31 Dec 2012, 04:28
mridulparashar1 wrote: Bunuel wrote: daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 (3 Δ 47) + 2 = 3*5*7*...*47+2 = odd + 2 = odd. Now, 3*5*7*...*47 and 3*5*7*...*47 +2 are consecutive odd numbers. Consecutive odd numbers are coprime, which means that they do not share any common factor but 1. For example, 25 and 27 are consecutive odd numbers and they do not share any common factor but 1. Naturally every odd prime between 3 and 47, inclusive is a factor of 3*5*7*...*47, thus none of them is a factor of 3*5*7*...*47 +2. Since 3*5*7*...*47+2 = odd, then 2 is also not a factor of it, which means that the smallest prime factor of 3*5*7*...*47 +2 is greater than 50. Answer: A. Similar question from GMAT Prep: foreverypositiveevenintegernthefunctionhnis126691.htmlHope it helps. Hi Bunuel, I just wanted to undertsand in what case 2 can be a smallest prime factor. For Eg if the Q. said that the smallest prime in (3 Δ 47) + 1.Then, the no (3 Δ 47) + 1 will be odd+1=even. Can we say 2 will be the smallest prime in this case. Also, 2 consecutive integers will also be coprime and therefore none of the factors in (3 Δ 47) will be factors of (3 Δ 47) + 1. Thanks for your reply to my queries earlier. Mridul That is correct. The smallest prime of (3 Δ 47) + 1 is naturally 2, since (3 Δ 47) + 1 = even, and the smallest prime of any positive even integer is 2 (notice that 2 is the smallest prime). Similar question to practice: foreverypositiveevenintegernthefunctionhnis126691.htmlHope it helps.
_________________
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: 13 Oct 2012
Posts: 61
Concentration: General Management, Leadership

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
03 Jan 2013, 22:32
(3*5*7*...*47)/y + 2/y = Integer
2/y is a fraction hence (3*5*7*...*47)/y also has to be a fraction. Only possibility is y>50



Manager
Joined: 02 Sep 2012
Posts: 225
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07252013
GPA: 3.83
WE: Architecture (Computer Hardware)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
23 Mar 2013, 23:49
HEY, (3 Δ 47) AND (3 Δ 47) +1 should be consecutive numbers right? so they dont share the any common factors other than 1 .Hence the smallest prime factor should be more than 47 and hence E. Please can some one explain whether my understanding is right or wrong ? if wrong please say where i made the mistake?
_________________
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything



Manager
Joined: 12 Mar 2012
Posts: 89
Location: India
Concentration: Technology, Strategy
GPA: 3.2
WE: Information Technology (Computer Software)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
24 Mar 2013, 00:01
Since (3 Δ 47) is odd and so (3 Δ 47) +1 is even. All even numbers have smallest factor as 2. Hence E is the answer.
Please give a kudo if my post is useful.



Manager
Joined: 26 Dec 2012
Posts: 146
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
23 Aug 2015, 13:33
HI Bunnel,
Please explain what the smallest prime factor will not be greater than 49? as 48,49,50 &51..... none are prime factors. then why we are taking cut of 50 but not from 49 or 48.
Thanks in advance,



Math Expert
Joined: 02 Sep 2009
Posts: 46164

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
23 Aug 2015, 13:42
lipsi18 wrote: HI Bunnel,
Please explain what the smallest prime factor will not be greater than 49? as 48,49,50 &51..... none are prime factors. then why we are taking cut of 50 but not from 49 or 48.
Thanks in advance, 47 is a prime. The next prime is 53. y (prime number) must be more than 47, so 53 or larger. But it does not matter whether we say that it's more than 47, more than 48, ... or more than 52, it still must be 53 or larger.
_________________
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



Board of Directors
Joined: 17 Jul 2014
Posts: 2730
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
01 Apr 2016, 18:25
daviesj wrote: If a and b are odd integers, a Δ b represents the product of all odd integers between a and b, inclusive. If y is the smallest prime factor of (3 Δ 47) + 2, which of the following must be true?
(A) y > 50 (B) 30 ≤ y ≤ 50 (C) 10 ≤ y < 30 (D) 3 ≤ y < 10 (E) y = 2 (3 Δ 47) + 2  is 100% an odd number, so E is out right away. (3 Δ 47) + 2 is not divisible by ANY of the prime factors between 3 and 47 since the next prime factor after 47 is 53, y must be greater than 50. A



Director
Joined: 26 Oct 2016
Posts: 666
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
07 Mar 2017, 14:12
The function (3 Δ 47) equals the product (3)(5)(7)…(43)(45)(47). This product is a very large odd number, as it is the product of only odd numbers and thus does not have 2 as a factor. Therefore, (3 Δ 47) + 2 = Odd + Even = Odd, and (3 Δ 47) + 2 does not have 2 as a factor either. Every odd prime number between 3 and 47 inclusive is a factor of (3 Δ 47), since each of these primes is a component of the product. For example, (3 Δ 47) is divisible by 3, since dividing by 3 yields an integer — the product (5)(7)(9)…(43)(45)(47). Now, consider the sum (3 Δ 47) + k, where k is an integer. The sum will only be divisible by 3 if k is also divisible by 3. In other words, when we divide (3 Δ 47) + k by 3, we are evaluating (3 Δ 47)/3 + k/3. Because (3 Δ 47)/3 is an integer, k/3 must also be an integer to yield an integer sum. In this problem, k = 2, which is not divisible by any of the odd primes between 3 and 47. Since (3 Δ 47) IS divisible, but 2 is NOT divisible, we conclude that the sum (3 Δ 47) + 2 is NOT divisible by any of the odd primes between 3 and 47. So, (3 Δ 47) + 2 is not divisible by any prime number less than or equal to 47. The smallest prime factor of (3 Δ 47) + 2 must be greater than 47. Thus, the minimum possible prime factor is 53, since that is the smallest prime greater than 47. The correct answer is A.
_________________
Thanks & Regards, Anaira Mitch



NonHuman User
Joined: 09 Sep 2013
Posts: 7002

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
Show Tags
11 Mar 2018, 03:37
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If a and b are odd integers, a Δ b represents the product of
[#permalink]
11 Mar 2018, 03:37






