Author 
Message 
TAGS:

Hide Tags

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
Location: Madrid

If s is the sum of two prime numbers and p is the product of [#permalink]
Show Tags
12 Mar 2007, 16:15
2
This post received KUDOS
15
This post was BOOKMARKED
Question Stats:
56% (02:51) correct
44% (01:31) wrong based on 264 sessions
HideShow timer Statistics
If s is the sum of two prime numbers and p is the product of these prime numbers, which of the following could not be the value of ps?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 397
Last edited by kevincan on 13 Mar 2007, 07:33, edited 1 time in total.



VP
Joined: 28 Mar 2006
Posts: 1369

Re: PS: Prime Numbers [#permalink]
Show Tags
12 Mar 2007, 16:48
kevincan wrote: If s is the sum of two prime numbers and p is the product of these prime numbers, which of the following could not be the value of ps?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 393
Should be B
Let the 2 primes be p1,p2
A) p1=37 , p2 =2 so s= 39 p = 74 ps = 35
B) p1=121 , p2 =2 so s= 123 p = 242 ps = 119 but
p1 =121 isnt prime
C) p1=163 and p2=2
D) p1=353 p2=2
E) p1=601 and p2=2
So B
My method is rustic but if anyone has a better way to do it please let me know



Senior Manager
Joined: 11 Feb 2007
Posts: 351

Looking at trivikram's solution, it appears that having p2 = 2 is important here...
Letting p1, p2 be the two primes,
s=p1+p2
p=p1*p2
ps=(p1*p2)(p1+p2)
ps=(p1*p2)p1p2
Since you have to subtract (p1+p2) from their product, it is important that you don't make the product too big, otherwise ps would be too far from p1 chosen. The smallest prime number is 2, so p2=2.
In picking a number for p1, you want to pick a number that when you add 2, is the next prime number of a number in the answer choice. So that when you subtract (p1+p2) from (p1*p2) you get the number in the answer choice (p12).
Ummm....
Basically, you want to see if by adding 2 to a number in the answer choice, you get a prime number.
The only choice that does not meet this requirement is 119, for 119+2=121 which is divisible by 11.
What I wrote above appears pretty much an ANALYSIS of the answer rather than a mathematically justified approach to solve this problem...
I have this feeling that I'm circumventing...I know I'm heading in the right direction(?) but not quite getting there...
Help!



Director
Joined: 13 Dec 2006
Posts: 510
Location: Indonesia

1
This post received KUDOS
3
This post was BOOKMARKED
lets assume X and Y are two prime numbers
P = X*Y and S = X+Y, so PS = XYXY or X(Y1)Y
now make one of the prime number constant and othe variable, lets say Y=2 (prime number). we have x(21)2 = X2 now put different values of prime numbers in place of X to arrive at the solution.
regards,
Amardeep



Manager
Joined: 20 Jun 2005
Posts: 145

Amardeep Sharma wrote: lets assume X and Y are two prime numbers
P = X*Y and S = X+Y, so PS = XYXY or X(Y1)Y
now make one of the prime number constant and othe variable, lets say Y=2 (prime number). we have x(21)2 = X2 now put different values of prime numbers in place of X to arrive at the solution.
regards,
Amardeep
wow! thats cool. )
i am wondering how to solve it within 2 minuts during test...
only analysis of the x2 = 37, 121, 163, 353, 601 numbers could take much time ...
of course i know that 121 is not prime, but i would have to check others...



Director
Joined: 13 Dec 2006
Posts: 510
Location: Indonesia

4
This post was BOOKMARKED
following are the basic tricks to be quicker in maths calculations:
1. take 5 pair of 3 digit numbers and multiply them. calculate your time taken per question (u need stop watch)... ideally u shouldnt take more than 21 secs per multipications ( e.g. 367*765)
2. memorize squares upto 30 ( e.g. 1, 4, 9 , 16 etc..) cubes upto 15
(1,8,27.. etc).
3. prime numbers from 1 to 200.
Besides this you may go throuh vedic mathmatics to understand the tricky shortcuts ... its worth trying.
regards.
Amardeep



Director
Affiliations: FRM Charter holder
Joined: 02 Dec 2006
Posts: 729
Schools: Stanford, Chicago Booth, Babson College

Re: PS: Prime Numbers [#permalink]
Show Tags
13 Mar 2007, 04:04
trivikram wrote: kevincan wrote: If s is the sum of two prime numbers and p is the product of these prime numbers, which of the following could not be the value of ps?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 599 Should be B Let the 2 primes be p1,p2 A) p1=37 , p2 =2 so s= 39 p = 74 ps = 35 B) p1=121 , p2 =2 so s= 123 p = 242 ps = 119 but
p1 =121 isnt primeC) p1=163 and p2=2 D) p1=353 p2=2 E) p1=601 and p2=2 So B My method is rustic but if anyone has a better way to do it please let me know
hey Vikram, what about 11 and 13. Product is 143, sum is 24, and difference is 119. B can be the difference of ps. No?



VP
Joined: 28 Mar 2006
Posts: 1369

Re: PS: Prime Numbers [#permalink]
Show Tags
13 Mar 2007, 04:34
aurobindo wrote: trivikram wrote: kevincan wrote: If s is the sum of two prime numbers and p is the product of these prime numbers, which of the following could not be the value of ps?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 599 Should be B Let the 2 primes be p1,p2 A) p1=37 , p2 =2 so s= 39 p = 74 ps = 35 B) p1=121 , p2 =2 so s= 123 p = 242 ps = 119 but
p1 =121 isnt primeC) p1=163 and p2=2 D) p1=353 p2=2 E) p1=601 and p2=2 So B My method is rustic but if anyone has a better way to do it please let me know hey Vikram, what about 11 and 13. Product is 143, sum is 24, and difference is 119. B can be the difference of ps. No?
Yep you are correct..I didnt see that combo.



GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
Location: Madrid

So, if p1 and p2 are prime numbers, what do we know about their product minus their sum?



Manager
Joined: 20 Jun 2005
Posts: 145

Amardeep Sharma wrote: following are the basic tricks to be quicker in maths calculations:
1. take 5 pair of 3 digit numbers and multiply them. calculate your time taken per question (u need stop watch)... ideally u shouldnt take more than 21 secs per multipications ( e.g. 367*765)
2. memorize squares upto 30 ( e.g. 1, 4, 9 , 16 etc..) cubes upto 15 (1,8,27.. etc).
3. prime numbers from 1 to 200.
Besides this you may go throuh vedic mathmatics to understand the tricky shortcuts ... its worth trying.
regards.
Amardeep
Amardeep, thanx a lot!
appreciate it.
You are right. These simple math operations require much time in the extreme environment.



Intern
Joined: 14 Mar 2007
Posts: 6

whats to say the prime numbers can't be the same? i.e p1 = p2 = 2 ?
has anyone solved this problem



Director
Joined: 14 Jan 2007
Posts: 774

Re: PS: Prime Numbers [#permalink]
Show Tags
06 Apr 2007, 16:43
kevincan wrote: If s is the sum of two prime numbers and p is the product of these prime numbers, which of the following could not be the value of ps?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 397
Kevincan, please give the solution to this problem.



Senior Manager
Joined: 20 Feb 2007
Posts: 256

I was almost stuck here but thanks to Amardeep who gave really a good solution



Senior Manager
Joined: 20 Feb 2007
Posts: 256

wait a minute!!!!
the value written for (E) option keeps changing in this post....
Original post (A) 35 (B) 119 (C) 161 (D) 351 (E) 397
In trivikram's quote (A) 35 (B) 119 (C) 161 (D) 351 (E) 393
then again in trivikram's quote (A) 35 (B) 119 (C) 161 (D) 351 (E) 599
If we take the original poster's values then answer is B and E both
It is only if (E) 599, then we get answer B.



Intern
Joined: 08 Aug 2011
Posts: 22

Re: If s is the sum of two prime numbers and p is the product of [#permalink]
Show Tags
27 May 2014, 06:23
1
This post received KUDOS
7
This post was BOOKMARKED
kevincan wrote: If S is the sum of two prime numbers and P is the product of these prime numbers, which of the following could NOT be the value of P  S ?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 397 If S is the sum of two prime numbers and P is the product of these prime numbers, which of the following could NOT be the value of P  S ?
(A) 35 (B) 119 (C) 161 (D) 351 (E) 397Let the prime numbers be \(a\) and \(b\). Given: \(P=a*b\) Given: \(S=a+b\) \(P  S = ab  (a+b) = ab  a  b\) The key here is to rewrite this as: \(P  S = ab  a  b = ab  a  b +1 1 = (a  1)*(b  1)  1\) Now, we need to find the answer choice that CANNOT be written in this form, so if it can be, it's wrong. Perhaps the best way to go about this is to add one to all the answer choices and then see if it can be written in the form of \((a  1)*(b  1)\), remembering that both \(a\) and \(b\) are prime. Essentially, we are going to write the ways we can express (answer choice +1) as a product of two factors, and if we can find a combination of two factors that are both one less than a prime number, it is the wrong choice. A. \(35+1=36= 6*6=(71)*(7  1)\)> 7 is prime, so this choice is incorrect. B. \(119+1=120=12*10=(131)*(111)\) > 13 and 11 are both prime, so incorrect C. \(161+1=162=1*162= (21)*(1631)\) > 2 and 163 are both prime, so incorrect D. \(351+1 = 352 = 32*11 = 16*22 =(171)*(231)\) > 17 and 23 are both prime, so incorrect. E. \(397+1 = 398 = 1*398 = 2*199\) > This must be the correct answer because we eliminated everything else, but also because \(2*399\) and \(3*200\) are both in the form \(prime*composite\) and there are no other factors combinations. Answer E.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15966

Re: If s is the sum of two prime numbers and p is the product of [#permalink]
Show Tags
26 Sep 2015, 07:28
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



Intern
Joined: 02 Feb 2011
Posts: 42

Re: If s is the sum of two prime numbers and p is the product of [#permalink]
Show Tags
13 Dec 2015, 05:36
Hi Was anyone able to solve this sum within 2 mins? Any other shorter way to do it? Bunuel ,Karishma pls help!



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2185

Re: If s is the sum of two prime numbers and p is the product of [#permalink]
Show Tags
14 Mar 2016, 01:27
Here x=Value *Y/Y1 clearly only B doesnt satisfy Y being 2 is satisfied by all Hence B
_________________
Give me a hell yeah ...!!!!!



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15966

Re: If s is the sum of two prime numbers and p is the product of [#permalink]
Show Tags
26 Apr 2017, 04:47
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 s is the sum of two prime numbers and p is the product of
[#permalink]
26 Apr 2017, 04:47







