December 17, 2018 December 17, 2018 06:00 PM PST 07:00 PM PST Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong. December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 14 Jan 2014
Posts: 12

Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
28 Jul 2014, 02:57
Question Stats:
56% (02:14) correct 44% (02:14) wrong based on 218 sessions
HideShow timer Statistics
Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true? (i) x is always odd (ii) x is always prime (iii) x is never the square of an integer A. ii only B. iii only C. i and ii only D. i and iii only E. ii and iii only
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 51229

Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
28 Jul 2014, 03:43
Vijayeta wrote: Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A. ii only B. iii only C. i and ii only D. i and iii only E. ii and iii only p(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of p(n). Thus, p(n) + 1 = even + 1 = odd. So, (i) is always true. Now, use logic: If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since only "i and iii only" is among the options, then it must be true. Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.Answer: D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Manager
Joined: 29 May 2013
Posts: 62
Concentration: General Management, International Business
GPA: 4

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
14 Sep 2014, 13:41
Bunuel wrote: Vijayeta wrote: Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A. ii only B. iii only C. i and ii only D. i and iii only E. ii and iii only p(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of p(n). Thus, p(n) + 1 = even + 1 = odd. So, (i) is always true. Now, use logic: If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since only "i and iii only" is among the options, then it must be true. Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.Answer: D. A nice approach. I used the same approach. It took me 1 min 51 sec. I wonder if I could have figured the approach sooner though.



Intern
Joined: 22 Nov 2014
Posts: 32

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
02 May 2015, 02:53
I did not get how to choose between ii and iii. We know x to be prime. How can we dismiss ii then?



Manager
Joined: 07 Dec 2009
Posts: 92
GMAT Date: 12032014

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
01 Jun 2015, 14:03
Gmatdecoder wrote: I did not get how to choose between ii and iii. We know x to be prime. How can we dismiss ii then? You use the answer choices to make your decision. If ii is true than iii has to be true but we don't have any answer choice with all 3 options. Hence we go for i & iii



Intern
Joined: 16 Mar 2014
Posts: 16
GMAT Date: 08182015

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
27 Oct 2016, 09:10
Bunuel wrote: Vijayeta wrote: Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A. ii only B. iii only C. i and ii only D. i and iii only E. ii and iii only p(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of p(n). Thus, p(n) + 1 = even + 1 = odd. So, (i) is always true. Now, use logic: If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since only "i and iii only" is among the options, then it must be true. Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.Answer: D. Hi Bunuel, I'm just wondering whether ii is not true? Is there any case that makes ii is not true? Thanks indeed



Math Expert
Joined: 02 Sep 2009
Posts: 51229

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
27 Oct 2016, 09:35
yenh wrote: Bunuel wrote: Vijayeta wrote: Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer
A. ii only B. iii only C. i and ii only D. i and iii only E. ii and iii only p(n) is always even, because the first prime is 2 and no matter what n is, 2 always will be a divisor of p(n). Thus, p(n) + 1 = even + 1 = odd. So, (i) is always true. Now, use logic: If (ii) is true (so if x is always prime), then (iii) must automatically be true: no prime is the square of an integer. So, the correct answer must be i only; i, ii, and iii only; or i and iii only. since only "i and iii only" is among the options, then it must be true. Or, since (i) is always true, then from options the answer must be either C or D. C cannot be correct because if (ii) is true, then so must be (iii). Thus only D remains.Answer: D. Hi Bunuel, I'm just wondering whether ii is not true? Is there any case that makes ii is not true? Thanks indeed \(p(6) + 1 = 2*3*5*7*11*13+1=30031 = 59*509\) is not a prime.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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: 16 Mar 2014
Posts: 16
GMAT Date: 08182015

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
27 Oct 2016, 09:45
Quote: Hi Bunuel, I'm just wondering whether ii is not true? Is there any case that makes ii is not true?
Thanks indeed
Quote: \(p(6) + 1 = 2*3*5*7*11*13+1=30031 = 59*509\) is not a prime. Thanks for your quick response. Btw, is there any way to be sure (theoretically) in case we cannot figure out by example?



Math Expert
Joined: 02 Sep 2009
Posts: 51229

Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
27 Oct 2016, 09:50



Intern
Joined: 16 Mar 2014
Posts: 16
GMAT Date: 08182015

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
27 Oct 2016, 09:59
Got it, thanks Bunuel.



Current Student
Joined: 26 Jan 2016
Posts: 103
Location: United States
GPA: 3.37

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
27 Oct 2016, 15:45
try plugging in numbers. If n=2 then 2X3+1=7 if n=3 then 2*3*5=30+1=31 the answer will always be odd b/c 2 is a prime and the product will always be an even plus 1
If you try n=4 then you get 2*3*5*7=210 which is not a prime
D



NonHuman User
Joined: 09 Sep 2013
Posts: 9192

Re: Let the function p(n) represent the product of the first n p
[#permalink]
Show Tags
23 Dec 2017, 18:55
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: Let the function p(n) represent the product of the first n p &nbs
[#permalink]
23 Dec 2017, 18:55






