Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 05 Nov 2009
Posts: 15

Can the positive integer p be expressed as the product of [#permalink]
Show Tags
27 Dec 2009, 05:49
1
This post received KUDOS
2
This post was BOOKMARKED
Question Stats:
65% (01:39) correct
35% (00:41) wrong based on 363 sessions
HideShow timer Statistics
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? 1) 31 < p < 37 2) p is odd
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39757

Re: Positive integer problem [#permalink]
Show Tags
27 Dec 2009, 07:24
6
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
Minotaur wrote: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1 ? (1) 31 < p < 37 (2) p is odd OA: can anyone help me with the explanation to this problem. The wording makes this question harder than it is actually. If positive integer p cannot be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? (1) 31<p<37 > between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient. (2) p is odd > odd numbers can be primes as well as nonprimes. Not sufficient. Answer: A.
_________________
New to the Math Forum? Please read this: 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



Intern
Status: pursuing a dream
Joined: 02 Jun 2011
Posts: 44
Schools: MIT Sloan (LGO)

Re: Positive integer problem [#permalink]
Show Tags
25 Aug 2011, 13:38
1
This post received KUDOS
Bunuel,
This question confuses me big time. When I saw "CAN" I expected as sufficient to be able to prove that yes, there was a way to do so. Hence for statement (2) I'd say that yes, IT CAN BE EXPRESSED AS THE PRODUCT OF TWO INTEGERS. Do you consider the following two statements to have the same meaning?
(i) Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
(ii) Is the positive integer p the product of two integers, each of which is greater than 1?



Math Expert
Joined: 02 Sep 2009
Posts: 39757

Re: Can the positive integer P be expressed as a product of 2... [#permalink]
Show Tags
28 Feb 2012, 16:55



Optimus Prep Instructor
Joined: 06 Nov 2014
Posts: 1845

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
06 Jun 2016, 21:04
Required: Can p be expressed as the product of two integers, each of which is greater than 1 Or is p = x*y, where x and y are greater than 1. This means p can have the numbers that are not prime, since a prime number has only 2 factors: 1 and the number itself. Statement 1: 31 < p < 37 Values of p can be = 32, 33, 34, 35, 36 None of these is prime, hence p can be written as a product of x and y SUFFICIENT Statement 2: p is odd. Odd numbers can both be prime and non prime INSUFFICIENT Correct Option: A
_________________
Janielle Williams
Customer Support



Manager
Joined: 09 May 2009
Posts: 205

Re: Positive integer problem [#permalink]
Show Tags
27 Dec 2009, 08:27
s1)> p can be 32,33,34,35,36 each no. is having at least 2 factors >1 hence yes .....therfore suff s2)> p can be any odd int and for odd like 3 , 5,7 ans is no and for no's such as 15,21,27, ans is yes hence insuff
_________________
GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME



Manager
Joined: 07 Oct 2006
Posts: 71
Location: India

Re: Positive integer problem [#permalink]
Show Tags
17 Jun 2010, 07:45
Thanks for the explanation Buunel and xcusemeplz2009.



Director
Joined: 01 Feb 2011
Posts: 755

Re: Positive integer problem [#permalink]
Show Tags
08 Jul 2011, 20:51
1. Sufficient
p can be 32 or 33 or 34 or 35 or 36
and each of these numbers can be expressed as product of two integers that are >1 . (32 = 2*16 , 33 = 3*11....)
2. Not sufficient
p is odd
p = 1 3 5 15
when p= 1 or 3 or 5 it cannot be expressed as product of two integers greater than 1. (as 5 = 1*5)
when p=15 , p can be expressed as product of two integers greater than 1.
Answer is A.



Manager
Joined: 07 Dec 2010
Posts: 113
Concentration: Marketing, General Management

Re: Positive integer problem [#permalink]
Show Tags
16 Sep 2011, 10:16
Bunuel wrote: Minotaur wrote: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1 ? (1) 31 < p < 37 (2) p is odd OA: can anyone help me with the explanation to this problem. The wording makes this question harder than it is actually. If positive integer p can not be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? (1) 31<p<37 > between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient. (2) p is odd > odd numbers can be primes as well as nonprimes. Not sufficient. Answer: A. If positive integer p can not be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? how can u say this..please elaborate...how p is prime...any no greater than one can be any no..why r u sayin p is prime?



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: Positive integer problem [#permalink]
Show Tags
16 Sep 2011, 11:26
ruturaj wrote: If positive integer p can not be expressed as the product of two integers >1, it simply means that p is a prime number. So, basically question asks is p prime? how can u say this..please elaborate...how p is prime...any no greater than one can be any no..why r u sayin p is prime? Prime number can only be expressed as "1*p", where p is the prime number itself 13=1*13 Can we write any prime number in the form; p=m*n where, p=prime number m=integer greater than 1 n=integer greater than 1 No, right? For prime number, at least one of m and n must be 1. Thus, question is indirectly asking whether p is a prime number.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 11 Apr 2011
Posts: 49

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
23 Feb 2012, 21:08
I don't understand this question. I am getting E.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Statement (1) states that 31<p<37
My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = 9 x 4 and each integer is not greater than 1, so insufficient.
Statement (2), I agree it is insufficient.
(1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be 7x5 so each integer is not greater than 1.
Am I misunderstanding the question?



Math Expert
Joined: 02 Sep 2009
Posts: 39757

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
24 Feb 2012, 01:25
chamisool wrote: I don't understand this question. I am getting E.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Statement (1) states that 31<p<37
My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = 9 x 4 and each integer is not greater than 1, so insufficient.
Statement (2), I agree it is insufficient.
(1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be 7x5 so each integer is not greater than 1.
Am I misunderstanding the question? It seems that you misinterpreted the question. Look at the definition of a prime number: a prime number is a positive integer with exactly two factors: 1 and itself. Now, the questions asks: "can the positive integer p be expressed as the product of two integers, each of which is greater than 1" So, the question basically asks whether p is a prime number, because if it is then p can NOT be expressed as the product of two integers, each of which is greater than 1. (1) states: 31 < p < 37. Between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers, which means that the answer to the question is YES: p can always be expressed as the product of two integers, each of which is greater than 1. Sufficient. Just to illustrate: 32=2*18, 33=3*11, 34=2*17, 35=5*7, 36=2*18. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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



Intern
Joined: 27 Feb 2012
Posts: 3

Can the positive integer P be expressed as a product of 2... [#permalink]
Show Tags
28 Feb 2012, 15:28
Can the positive integer P be expressed as a product of two integers,each of which is greater than 1? (1) 31<p<37 (2) p=odd
The answer according my program is A, but I dont understand why it can not be D. Because if we take 3*3=9 which is odd and integer and greater than 1?
Thank you in advance



Math Expert
Joined: 02 Sep 2009
Posts: 39757

Re: Can the positive integer P be expressed as a product of 2... [#permalink]
Show Tags
28 Feb 2012, 15:35
Merging similar topics. vladkarz wrote: Can the positive integer P be expressed as a product of two integers, each of which is greater than 1? (1) 31<p<37 (2) p=odd
The answer according my program is A, but I dont understand why it can not be D. Because if we take 3*3=9 which is odd and integer and greater than 1?
Thank you in advance P is some particular integer and we are asked whether it can be expressed as a product of two integers, each of which is greater than 1. Now, for (2) if p=9 then the answer is YES, it can be expressed as a product of two integers, each of which is greater than 1 but of p=5 then the answer is NO, it cannot be expressed as a product of two integers, each of which is greater than 1. Two different answers, hence this statement is not sufficient. Does it makes sense? P.S. Please refer for a complete solution to the above posta and ask if anything remains unclear.
_________________
New to the Math Forum? Please read this: 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



Intern
Joined: 27 Feb 2012
Posts: 3

Re: Can the positive integer P be expressed as a product of 2... [#permalink]
Show Tags
28 Feb 2012, 16:51
Bunuel wrote: Merging similar topics. vladkarz wrote: Can the positive integer P be expressed as a product of two integers, each of which is greater than 1? (1) 31<p<37 (2) p=odd
The answer according my program is A, but I dont understand why it can not be D. Because if we take 3*3=9 which is odd and integer and greater than 1?
Thank you in advance P is some particular integer and we are asked whether it can be expressed as a product of two integers, each of which is greater than 1. Now, for (2) if p=9 then the answer is YES, it can be expressed as a product of two integers, each of which is greater than 1 but of p=5 then the answer is NO, it cannot be expressed as a product of two integers, each of which is greater than 1. Two different answers, hence this statement is not sufficient. Does it makes sense? P.S. Please refer for a complete solution to the above posta and ask if anything remains unclear. Thank you very much Bunuel, So basically if there are 2 possible answers (yes/no) it will always be insufficient?



Moderator
Joined: 01 Sep 2010
Posts: 3220

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
08 Apr 2012, 05:51
Bunuel wrote: chamisool wrote: I don't understand this question. I am getting E.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Statement (1) states that 31<p<37
My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = 9 x 4 and each integer is not greater than 1, so insufficient.
Statement (2), I agree it is insufficient.
(1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be 7x5 so each integer is not greater than 1.
Am I misunderstanding the question? It seems that you misinterpreted the question. Look at the definition of a prime number: a prime number is a positive integer with exactly two factors: 1 and itself. Now, the questions asks: "can the positive integer p be expressed as the product of two integers, each of which is greater than 1" So, the question basically asks whether p is a prime number, because if it is then p can NOT be expressed as the product of two integers, each of which is greater than 1. (1) states: 31 < p < 37. Between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers, which means that the answer to the question is YES: p can always be expressed as the product of two integers, each of which is greater than 1. Sufficient. Just to illustrate: 32=2*18, 33=3*11, 34=2*17, 35=5*7, 36=2*18. Hope it's clear. I think as you said, the key to this problem are the words each of which is greater than one
is correct ??? You think the problem can be solved even if you do not see this nuance ?? thanks
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Current Student
Joined: 26 Jul 2012
Posts: 63

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
13 Apr 2013, 08:13
Ah...I struggled with this one at first as well
I originally got D because I thought the question was asking if we can have product of two numbers for p.
Key for me was reminding myself that this is as "Yes or No" question, which means that it's "always yes" or "always no." For some reason, I had interpreted "Can the positive..." as is there a single instance where it can be true.
1) 31 < p < 37... 32 = 8 x 4 33 = 11 x 3 34 = 2 x 17 35 = 5 x7 36= 6 x 6 sufficient
2) p is odd p = 5 p = 15 not sufficient
So, the answer is A because statement 2 is not ALWAYS sufficient



Intern
Joined: 28 Jun 2013
Posts: 3

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
12 Sep 2013, 09:53
chamisool wrote: I don't understand this question. I am getting E.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Statement (1) states that 31<p<37
My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = 9 x 4 and each integer is not greater than 1, so insufficient.
Statement (2), I agree it is insufficient.
(1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be 7x5 so each integer is not greater than 1.
Am I misunderstanding the question? Hi Bunuel, The question asks: can p be expressed as a product of two numbers greater than 1? If I prove that p can be expressed as a product of two numbers which are < 1 and can also be expressed as a product of two numbers > 1 then the statement A) / B) would become insufficient. Right? Now, as quoted above, for statement A), I can express 36= 1*36, 1*36,9*4..... so doesn't it mean that statement A) is insufficient? If A) is sufficient to answer the question, is it because of the fact that the question asks "Can it be expressed as product of two numbers > 1" instead of "Is P a product of two numbers which are always greater than 1?"



Math Expert
Joined: 02 Sep 2009
Posts: 39757

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
12 Sep 2013, 11:18
SurabhiStar wrote: chamisool wrote: I don't understand this question. I am getting E.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Statement (1) states that 31<p<37
My logic was that p can be anything that fits between 31 and 37, so 36 36 = 9 x 4 and each integer is greater than 1, so it is sufficient 36 = 9 x 4 and each integer is not greater than 1, so insufficient.
Statement (2), I agree it is insufficient.
(1) and (2) is still insufficient because 35 (fits statement 2) and 35 can be 7x5 so each integer is greater than 1. 35 can also be 7x5 so each integer is not greater than 1.
Am I misunderstanding the question? Hi Bunuel, The question asks: can p be expressed as a product of two numbers greater than 1? If I prove that p can be expressed as a product of two numbers which are < 1 and can also be expressed as a product of two numbers > 1 then the statement A) / B) would become insufficient. Right?Now, as quoted above, for statement A), I can express 36= 1*36, 1*36,9*4..... so doesn't it mean that statement A) is insufficient? If A) is sufficient to answer the question, is it because of the fact that the question asks "Can it be expressed as product of two numbers > 1" instead of "Is P a product of two numbers which are always greater than 1?" No, the red part is not correct. The question asks "can p be expressed as the product of two integers, each of which is greater than 1". If from a statement you get that EACH possible value of p can be expressed as the product of two integers, each of which is greater than 1, then the answer is YES, and the statement is sufficient. If from a statement you get that NONE of the possible values of p can be expressed as the product of two integers, each of which is greater than 1, then the answer is NO, and the statement is sufficient too. If from a statement you get that some possible values of p cannot but other possible values of p can be expressed as the product of two integers, each of which is greater than 1, then we'd have two answers to the question and the statement wouldn't be sufficient. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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



Intern
Joined: 24 Apr 2013
Posts: 5

Re: Can the positive integer p be expressed as the product of [#permalink]
Show Tags
23 Sep 2013, 13:08
What if i say that P = 33 x 1.
So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?
Mental block..!!!




Re: Can the positive integer p be expressed as the product of
[#permalink]
23 Sep 2013, 13:08



Go to page
1 2
Next
[ 27 posts ]




