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 350,000 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:

If a and b are odd integers, a Δ b represents the product of [#permalink]
26 Dec 2012, 01:29

1

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

49% (02:40) correct
51% (01:37) wrong based on 209 sessions

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

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
26 Dec 2012, 02:00

5

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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 co-prime, 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.

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
26 Dec 2012, 02:32

2

This post received KUDOS

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. _________________

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
26 Dec 2012, 18:55

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 co-prime, 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.

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.”

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
27 Dec 2012, 01:18

Expert's post

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 co-prime, 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.

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.

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
30 Dec 2012, 07:32

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 co-prime, 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.

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 co-prime 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.”

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
31 Dec 2012, 03:28

Expert's post

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 co-prime, 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.

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 co-prime 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).

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
23 Mar 2013, 22:49

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

Re: If a and b are odd integers, a Δ b represents the product of [#permalink]
10 Sep 2014, 07:30

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. _________________

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...