Query about "every prime factor"

Expert replies

gmatmillenium: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sat Apr 10, 2010 12:46 pmFollowed by: 2 members; Thanked: 2 times; GMAT Score:730

by gmatmillenium » Tue Jun 15, 2010 1:28 am

If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jun 15, 2010 1:28 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Tue Jun 15, 2010 2:36 am

I believe " every prime factor of s is a prime factor of r" doesnt mean that the factors are the same.
Any number can be expressed as a product of prime factors. So I believe still the answer to the question should be INSUFFICIENT. because prime factors are same doesnt convince us on s divides r or r divides s.

Willw ait for expert opinion.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 15, 2010 8:08 am

gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?

Could you please post the entire question?

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

gmatmillenium: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sat Apr 10, 2010 12:46 pmFollowed by: 2 members; Thanked: 2 times; GMAT Score:730

by gmatmillenium » Tue Jun 15, 2010 8:47 am

If r and s are positive integers, is r/s an integer?

1. every factor of s is also a factor of r
2. every prime factor of s is also a prime factor of r

GMATGuruNY wrote:
gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?
Could you please post the entire question?

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 15, 2010 9:01 am

gmatmillenium wrote:If r and s are positive integers, is r/s an integer?

1. every factor of s is also a factor of r
2. every prime factor of s is also a prime factor of r

GMATGuruNY wrote:
gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?
Could you please post the entire question?

Consider the following questions and answers:

"What are the prime factors of 10? Answer: 2 and 5
"What are the prime factors of 100? Answer: 2 and 5

To describe this situation, the GMAT writers would use the language of statement 2 above:

Every prime factor of 10 is also a prime factor of 100. (Because the prime factors of 10 are 2 and 5, and these are both prime factors of 100.)
Every prime factor of 100 is also a prime factor of 10. (Because the prime factors of 100 are 2 and 5, and these are both prime factors of 10.)

So looking at Statement 2:

If r = 100 and s =10, is r divisible by s? Yes, because 100/10 = 10.
If r = 10 and s = 100, is r divisible by s? No, because 10/100 = 1/10.

So statement 2 is INSUFFICIENT.

Like this post

gmatmillenium: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sat Apr 10, 2010 12:46 pmFollowed by: 2 members; Thanked: 2 times; GMAT Score:730

by gmatmillenium » Tue Jun 15, 2010 9:21 am

so unless explicitly stated otherwise, one is to assume only distinct prime factors and not how many times they occur, right?

GMATGuruNY wrote:
gmatmillenium wrote:If r and s are positive integers, is r/s an integer?

1. every factor of s is also a factor of r
2. every prime factor of s is also a prime factor of r

GMATGuruNY wrote:
gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?
Could you please post the entire question?
Consider the following questions and answers:

"What are the prime factors of 10? Answer: 2 and 5
"What are the prime factors of 100? Answer: 2 and 5

To describe this situation, the GMAT writers would use the language of statement 2 above:

Every prime factor of 10 is also a prime factor of 100. (Because the prime factors of 10 are 2 and 5, and these are both prime factors of 100.)
Every prime factor of 100 is also a prime factor of 10. (Because the prime factors of 100 are 2 and 5, and these are both prime factors of 10.)

So looking at Statement 2:

If r = 100 and s =10, is r divisible by s? Yes, because 100/10 = 10.
If r = 10 and s = 100, is r divisible by s? No, because 10/100 = 1/10.

So statement 2 is INSUFFICIENT.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 15, 2010 9:57 am

gmatmillenium wrote:so unless explicitly stated otherwise, one is to assume only distinct prime factors and not how many times they occur, right?

GMATGuruNY wrote:
gmatmillenium wrote:If r and s are positive integers, is r/s an integer?

1. every factor of s is also a factor of r
2. every prime factor of s is also a prime factor of r

GMATGuruNY wrote:
gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?
Could you please post the entire question?
Consider the following questions and answers:

"What are the prime factors of 10? Answer: 2 and 5
"What are the prime factors of 100? Answer: 2 and 5

To describe this situation, the GMAT writers would use the language of statement 2 above:

Every prime factor of 10 is also a prime factor of 100. (Because the prime factors of 10 are 2 and 5, and these are both prime factors of 100.)
Every prime factor of 100 is also a prime factor of 10. (Because the prime factors of 100 are 2 and 5, and these are both prime factors of 10.)

So looking at Statement 2:

If r = 100 and s =10, is r divisible by s? Yes, because 100/10 = 10.
If r = 10 and s = 100, is r divisible by s? No, because 10/100 = 1/10.

So statement 2 is INSUFFICIENT.

The prime factorization of 100 = 2 * 2 * 5 * 5.

The GMAT writers say that 100 has two distinct prime factors: 2 and 5.

The GMAT writers also would say that the prime factors of 100 are 2 and 5.

If the GMAT writers wanted you to count ALL the non-distinct prime factors -- unlikely, but possible -- I suspect they'd make the question explicit:

The integer 100 has how many non-distinct prime factors? Answer: four (2, 2, 5, and 5).

Usually they'd find a sneakier way of asking you to count all the non-distinct prime factors:

Every student in Mitch's GMAT class is either 2 or 5 years old. (Yes, they're starting young these days.) If the product of all the ages of the students is 100, how many students are in Mitch's class?

A. 2
B. 3
C. 4
D. 5
E. 6

Would you know how to solve?

Last edited by GMATGuruNY on Tue Jun 15, 2010 1:15 pm, edited 4 times in total.

Like this post

gmatmillenium: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sat Apr 10, 2010 12:46 pmFollowed by: 2 members; Thanked: 2 times; GMAT Score:730

by gmatmillenium » Tue Jun 15, 2010 10:11 am

Thanks Mitch...appreciate all your help

gmatmillenium wrote:so unless explicitly stated otherwise, one is to assume only distinct prime factors and not how many times they occur, right?

GMATGuruNY wrote:
gmatmillenium wrote:If r and s are positive integers, is r/s an integer?

1. every factor of s is also a factor of r
2. every prime factor of s is also a prime factor of r

GMATGuruNY wrote:
gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?
Could you please post the entire question?
Consider the following questions and answers:

"What are the prime factors of 10? Answer: 2 and 5
"What are the prime factors of 100? Answer: 2 and 5

To describe this situation, the GMAT writers would use the language of statement 2 above:

Every prime factor of 10 is also a prime factor of 100. (Because the prime factors of 10 are 2 and 5, and these are both prime factors of 100.)
Every prime factor of 100 is also a prime factor of 10. (Because the prime factors of 100 are 2 and 5, and these are both prime factors of 10.)

So looking at Statement 2:

If r = 100 and s =10, is r divisible by s? Yes, because 100/10 = 10.
If r = 10 and s = 100, is r divisible by s? No, because 10/100 = 1/10.

So statement 2 is INSUFFICIENT.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 15, 2010 10:16 am

My pleasure. I just added the following sample problem to my earlier post:

Every student in Mitch's GMAT class is either 2 or 5 years old. (Yes, they're starting young these days.) If the product of all the ages of the students is 100, how many students are in Mitch's class?

A. 2
B. 3
C. 4
D. 5
E. 6

Would you know how to approach and solve this problem?

Last edited by GMATGuruNY on Tue Jun 15, 2010 1:15 pm, edited 1 time in total.

Like this post

adt29: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Mon May 04, 2009 6:38 pmFollowed by: 2 members

by adt29 » Tue Jun 15, 2010 1:05 pm

Hi,

Is the answer 4?

2 students who are 2 years old
2 students who are 5 years old.

This is because the prime factorization of 100 is 4 numbers for which you dropped a hint in one of your earlier posts.

Is that the right way to approach the question?

Thanks!

Like this post

gmatmillenium: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Sat Apr 10, 2010 12:46 pmFollowed by: 2 members; Thanked: 2 times; GMAT Score:730

by gmatmillenium » Sun Jun 20, 2010 2:22 am

Hi Mitch

Need your help with the underlying concept here...

Source - GMATPrep

Q. Tanya prepared 4 letters to be sent to 4 different addresses. For each letter she prepared an envelope with its correct address. If the 4 letters are to be put into 4 envelopes at random, what is the probability that only 1 letter will be put its envelope with correct address?

One of the answer explanations which came was -

C=correct
I=incorrect
so lets say the order of letters is CIII
now first letter can be put in correct envelope by 1/4
now second letter can be put in incorrect envelope by 2/3
now third letter can be put in incorrect envelope by 1/2
now fourth letter can be put in incorrect envelope by 1
1/4+2/3+1/2+1=1/12

now CIII can be rearranged in 4C1=4 ways

probability=4*1/12=1/3 way[/quote]

My Doubt
let us say the letters and envelopes are L1,E1,L2,E2,L3,E3,L4,E4

now let us take CIII....

Prob of correct envelope for L1 = 1/4
Prob of incorrect envelope for L2 = 2/3....(here L2 can pick E3 or E4)
If L2 picks E3, then prob of incorrect envelope for L3 will be 1 (only E2 and E4 left) and similarly prob of incorrect envelope for L4 will be 1 too...

am i thinking correct??

GMATGuruNY wrote:
gmatmillenium wrote:so unless explicitly stated otherwise, one is to assume only distinct prime factors and not how many times they occur, right?

GMATGuruNY wrote:
gmatmillenium wrote:If r and s are positive integers, is r/s an integer?

1. every factor of s is also a factor of r
2. every prime factor of s is also a prime factor of r

GMATGuruNY wrote:
gmatmillenium wrote:If we are asked whether r/s is an integer and one of the supporting statement says " every prime factor of s is a prime factor of r" - are we to assume that the distinct prime factors or all prime factors regardless of their repetition?....

is there a GMAT consensus on this?
Could you please post the entire question?
Consider the following questions and answers:

"What are the prime factors of 10? Answer: 2 and 5
"What are the prime factors of 100? Answer: 2 and 5

To describe this situation, the GMAT writers would use the language of statement 2 above:

Every prime factor of 10 is also a prime factor of 100. (Because the prime factors of 10 are 2 and 5, and these are both prime factors of 100.)
Every prime factor of 100 is also a prime factor of 10. (Because the prime factors of 100 are 2 and 5, and these are both prime factors of 10.)

So looking at Statement 2:

If r = 100 and s =10, is r divisible by s? Yes, because 100/10 = 10.
If r = 10 and s = 100, is r divisible by s? No, because 10/100 = 1/10.

So statement 2 is INSUFFICIENT.
The prime factorization of 100 = 2 * 2 * 5 * 5.

The GMAT writers say that 100 has two distinct prime factors: 2 and 5.

The GMAT writers also would say that the prime factors of 100 are 2 and 5.

If the GMAT writers wanted you to count ALL the non-distinct prime factors -- unlikely, but possible -- I suspect they'd make the question explicit:

The integer 100 has how many non-distinct prime factors? Answer: four (2, 2, 5, and 5).

Usually they'd find a sneakier way of asking you to count all the non-distinct prime factors:

Every student in Mitch's GMAT class is either 2 or 5 years old. (Yes, they're starting young these days.) If the product of all the ages of the students is 100, how many students are in Mitch's class?

A. 2
B. 3
C. 4
D. 5
E. 6

Would you know how to solve?

Like this post

jube: Master | Next Rank: 500 Posts; Posts: 186; Joined: Fri May 28, 2010 1:05 am; Thanked: 11 times

by jube » Sun Jun 20, 2010 3:19 am

Let's say letter 1 is put in the right envelope. The probability for that is 1/4

The probability that the 2nd letter won't be put in the right envelope: 2/3

The probability that the 3rd letter won't be put in the right envelope: 1/2

The 4th envelope is automatically accounted for when we take the above 3 actions I'm thinking...

therefore answer should be (1/4)(2/3)(1/2) = 1/12

Is that the OA?

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jun 20, 2010 4:02 am

gmatmillenium wrote:Hi Mitch

Need your help with the underlying concept here...

Source - GMATPrep

Q. Tanya prepared 4 letters to be sent to 4 different addresses. For each letter she prepared an envelope with its correct address. If the 4 letters are to be put into 4 envelopes at random, what is the probability that only 1 letter will be put its envelope with correct address?

One of the answer explanations which came was -

C=correct
I=incorrect
so lets say the order of letters is CIII
now first letter can be put in correct envelope by 1/4
now second letter can be put in incorrect envelope by 2/3
now third letter can be put in incorrect envelope by 1/2
now fourth letter can be put in incorrect envelope by 1
1/4+2/3+1/2+1=1/12

now CIII can be rearranged in 4C1=4 ways

probability=4*1/12=1/3 way
My Doubt
let us say the letters and envelopes are L1,E1,L2,E2,L3,E3,L4,E4

now let us take CIII....

Prob of correct envelope for L1 = 1/4
Prob of incorrect envelope for L2 = 2/3....(here L2 can pick E3 or E4)
If L2 picks E3, then prob of incorrect envelope for L3 will be 1 (only E2 and E4 left) and similarly prob of incorrect envelope for L4 will be 1 too...

am i thinking correct??

Could you please post this question in a separate thread so that everyone can benefit from the discussion?

Thanks!

Mitch

Like this post

ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Sun Jun 20, 2010 9:13 am

gmatmillenium wrote:Hi Mitch

Need your help with the underlying concept here...

Hey millenium,
the answer is already written on the forum for this question, just look for it with part of a question as keyword.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review