Problem Solving

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?

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.

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?

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?

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.

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.

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?

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.

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?

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!

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?

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?

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

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.