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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
PS
This topic has expert replies
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi abhasjha,
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 force-ing" 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: A
GMAT assassins aren't born, they're made,
Rich
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 force-ing" 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: A
GMAT assassins aren't born, they're made,
Rich
-
GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
The phrase to catch here is "could be true?"abhasjha 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
We have to try several possibilities to find the right option
(A) 3+7+9 = 19 PRIME therefore Possible
No need to try other options else we would have have tried values for other options in similar way
Answer: Option A
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
