Author 
Message 
TAGS:

Hide Tags

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 624

If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
22 Oct 2014, 11:26
1
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
65% (01:51) correct 35% (01:51) wrong based on 232 sessions
HideShow timer Statistics
If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true? (A) Each of a, b, and c is prime. (B) Each of a + 3, b + 3, and c + 3 is prime. (C) Each of a + b, a + c, and b + c is prime. (D) The average (arithmetic mean) of a, b, and c is prime. (E) a + b = c From Manhattan's Challenge for this week.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Senior Manager
Joined: 13 Jun 2013
Posts: 278

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
22 Oct 2014, 12:00
2
This post received KUDOS
mau5 wrote: If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of a, b, and c is prime. (B) Each of a + 3, b + 3, and c + 3 is prime. (C) Each of a + b, a + c, and b + c is prime. (D) The average (arithmetic mean) of a, b, and c is prime. (E) a + b = c
From Manhattan's Challenge for this week. we know that all prime numbers are odd except 2. if 2 is also a part of these 3 positive numbers, then sum will always be even. (even+ odd + odd= even) thus sum of a,b,c will be prime only if all 3 of them will be odd. lets consider each option a) 3,5,23 satisfy this condition. hence this option is possible. b) as a,b,c are odd. therefore a+3, b+3, c+3 will always be even. hence this option is not possible c) again as a,b,c are odd. therefore a+b,b+c,a+c will always be even. hence this option is not possible d) sum of a,b,c is a prime number. therefore its sum will never be divisible by 3. (as prime numbers are divisible by 1 and itself). hence it will be a fraction. therefore this options is also not possible e) sum of two odd numbers is always even. thus, this option is not possible at all.



Intern
Joined: 11 Mar 2014
Posts: 2
Concentration: Finance, Accounting

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
11 Dec 2014, 09:27
manpreetsingh86 wrote: mau5 wrote: If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of a, b, and c is prime. (B) Each of a + 3, b + 3, and c + 3 is prime. (C) Each of a + b, a + c, and b + c is prime. (D) The average (arithmetic mean) of a, b, and c is prime. (E) a + b = c
From Manhattan's Challenge for this week. we know that all prime numbers are odd except 2. if 2 is also a part of these 3 positive numbers, then sum will always be even. (even+ odd + odd= even) thus sum of a,b,c will be prime only if all 3 of them will be odd. lets consider each option a) 3,5,23 satisfy this condition. hence this option is possible. b) as a,b,c are odd. therefore a+3, b+3, c+3 will always be even. hence this option is not possible c) again as a,b,c are odd. therefore a+b,b+c,a+c will always be even. hence this option is not possible d) sum of a,b,c is a prime number. therefore its sum will never be divisible by 3. (as prime numbers are divisible by 1 and itself). hence it will be a fraction. therefore this options is also not possible e) sum of two odd numbers is always even. thus, this option is not possible at all. can you please explain as to why you have not taken 2?



Intern
Joined: 03 Dec 2013
Posts: 10
Location: India
Concentration: General Management, Strategy
GMAT 1: 700 Q50 V34 GMAT 2: 740 Q49 V41
WE: Corporate Finance (Manufacturing)

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
11 Dec 2014, 10:48
1
This post received KUDOS
xena123 wrote: manpreetsingh86 wrote: mau5 wrote: If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of a, b, and c is prime. (B) Each of a + 3, b + 3, and c + 3 is prime. (C) Each of a + b, a + c, and b + c is prime. (D) The average (arithmetic mean) of a, b, and c is prime. (E) a + b = c
From Manhattan's Challenge for this week. we know that all prime numbers are odd except 2. if 2 is also a part of these 3 positive numbers, then sum will always be even. (even+ odd + odd= even) thus sum of a,b,c will be prime only if all 3 of them will be odd. lets consider each option a) 3,5,23 satisfy this condition. hence this option is possible. b) as a,b,c are odd. therefore a+3, b+3, c+3 will always be even. hence this option is not possible c) again as a,b,c are odd. therefore a+b,b+c,a+c will always be even. hence this option is not possible d) sum of a,b,c is a prime number. therefore its sum will never be divisible by 3. (as prime numbers are divisible by 1 and itself). hence it will be a fraction. therefore this options is also not possible e) sum of two odd numbers is always even. thus, this option is not possible at all. can you please explain as to why you have not taken 2? I have tried to explain it using number properties  3 different +ve integers (assume a, b, c) – sum is a prime number All prime numbers except 2 are odd. Consider 2 > There is no combination of a, b & c to get a sum of 2. (a, b and c have to be different and positive integers) Now for a, b and c to add up to a prime number (>2) the possibilities are 2 numbers are even positive integers and 1 is an odd positive integer ( E, E, O – i.e. assume a & b are even and c is odd) OR All 3 are odd positive integers (O, O, O – a, b & c are odd) (A) E, E, O (even if 1 of the even numbers is 2 there is another number which cannot be prime) combination not true but O, O, O combination could be true. (B) E+3 could be prime but O+3 is an even integer >2 so cannot be prime So E,E,O combination not true (a+3 OK, b+3 OK but c+3 – cannot be prime ) and O,O,O (a/b/c+3 cannot be prime)combination is also not true. (C) E+O could be prime but O+O cannot be So E,E,O (a+b cannot be prime) combination and O,O,O (a+b, b+c and c+a cannot be prime) combination not true (D) If the average of 3 numbers is a prime number then the sum of the 3 numbers is a multiple of 3 and the arithmetic mean. So the sum cannot be even – therefore this option is also not possible. (E) If a+b=c then a+b+c = 2c which is an even no and hence this option is not possible Answer (A) is the only choice which could be true.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1838
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
12 Dec 2014, 00:21
1
This post received KUDOS
Lets say a = 11, b = 13, c = 17 (A) Each of a, b, and c is prime >>>>>>>>>>>>>>>>>>>>>>>>>>. YES(B) Each of a + 3, b + 3, and c + 3 is prime. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> No in this case (C) Each of a + b, a + c, and b + c is prime. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Not necessary (D) The average (arithmetic mean) of a, b, and c is prime. >>>>>>>>>>>>>>>>>>>> Its fraction in this case (E) a + b = c >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Not required Answer = A
_________________
Kindly press "+1 Kudos" to appreciate



Board of Directors
Joined: 17 Jul 2014
Posts: 2752
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
30 Oct 2015, 07:07
the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be  we know automatically that A is the answer.



Intern
Joined: 08 Mar 2016
Posts: 36

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
01 Mar 2017, 04:34
mvictor wrote: the question asks could be!!!! this means that if at least one option works, it is the answer. 3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be  we know automatically that A is the answer. I understood the question wrong now that you explain what "could" means. I got the meaning. Any other such things that I should remember?



Manager
Joined: 01 Sep 2016
Posts: 207

If a, b, and c are three different positive integers whose sum is [#permalink]
Show Tags
18 Jun 2017, 00:08
If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true? (A) Each of a, b, and c is prime. (B) Each of a + 3, b + 3, and c + 3 is prime. (C) Each of a + b, a + c, and b + c is prime. (D) The average (arithmetic mean) of a, b, and c is prime. (E) a + b = c
_________________
we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2256
Location: India
GPA: 3.12

Re: If a, b, and c are three different positive integers whose sum is [#permalink]
Show Tags
18 Jun 2017, 00:16
Since a,b,c are 3 different postitive integers, and its sum is prime. In Option A, consider a=3,b=5,c=11, sum of a,b and c is 19(which is prime) Hence Option A(Each of a,b and c are prime) is possible.
_________________
Stay hungry, Stay foolish
20172018 MBA Deadlines
Class of 2020: Rotman Thread  Schulich Thread Class of 2019: Sauder Thread



Director
Joined: 04 Dec 2015
Posts: 696
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

If a, b, and c are three different positive integers whose sum is [#permalink]
Show Tags
18 Jun 2017, 00:26
bkpolymers1617 wrote: If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c Let \(a = 3\), \(b = 5\) and \(c = 11\)
\(a + b + c = 3 + 5 + 11 = 19\)  (Prime number)
Lets check the options.
(A) Each of a, b, and c is prime.
Let \(a = 3\), \(b = 5\) and \(c = 11\)  (a,b and c is prime) (Could be true)
(B) Each of a + 3, b + 3, and c + 3 is prime.
From (i) a + 3, b + 3 and c + 3 gives ( 6, 8 and 14) respectively  (Not prime)
(C) Each of a + b, a + c, and b + c is prime.
From (i) \(a + b = 8\)
\(a + c = 14\)
\(b + c = 16\)  (Not prime)
(D) The average (arithmetic mean) of a, b, and c is prime.
From (i) \(\frac{3 + 5 + 11}{3} = \frac{19}{3}\)  (Not prime)
(E) \(a + b = c\) ==> From (i) \(3 + 5 = 8\) not 11  ( Not true)
Therefore Only A could be true . Answer (A)...



Math Expert
Joined: 02 Sep 2009
Posts: 44290

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
18 Jun 2017, 02:46
bkpolymers1617 wrote: If a, b, and c are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of a, b, and c is prime.
(B) Each of a + 3, b + 3, and c + 3 is prime.
(C) Each of a + b, a + c, and b + c is prime.
(D) The average (arithmetic mean) of a, b, and c is prime.
(E) a + b = c Merging topics. You are permanently violating our posting rules ( https://gmatclub.com/forum/rulesforpo ... 33935.html). This post for example, was posted in DS instead of PS and is also a duplicate. Note that ignoring or breaking these rules will likely lead to removed posts, warnings, and eventual bans.
_________________
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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11255
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If a, b, and c are three different positive integers whose sum is prim [#permalink]
Show Tags
03 Mar 2018, 16:27
Hi All, This question has some interesting "restrictions" to it, but it's perfect for TESTing VALUES (even though you'll have to do a bit more work than normal to find a TEST that "fits"). We're told that A, B and C are 3 DIFFERENT positive integers whose SUM is PRIME. Since the sum has to be prime, we should be looking for an ODD total. Since the answer choices emphasize the idea of prime numbers, you should think about "brute forceing" a series of 3 odd numbers (likely primes) to see if you can get a match. Without too much trouble, I got to 3, 5 and 11…. 3+5+11 = 19 = a sum that is prime Using these values, only one answer is true.... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Re: If a, b, and c are three different positive integers whose sum is prim
[#permalink]
03 Mar 2018, 16:27






