Is the value of 3^a/3^b a prime number?
(1) a + b = 8
(2) a - b = 2
Is the value of 3^a/3^b a prime number?
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
We have to determine whether the value of 3^a/3^b a prime number.BTGmoderatorDC wrote:Is the value of 3^a/3^b a prime number?
(1) a + b = 8
(2) a - b = 2
3^a/3^b can be written as 3^(a - b).
Question rephrased: Is 3^(a - b) a prime number?
3^(a - b) can be a prime number only if (a - b) = 1; for any other value, 3^(a - b) is not prime. You may try for 0, 2, -2, 1/2, etc.
Let's take each statement one by one.
(1) a + b = 8
Case 1: Say a = 4.5 and b = 3.5, then (a - b) = 1; thus, 3^(a - b) is a prime number.
Case 2: Say a = 5 and b = 3, then (a - b) = 2; thus, 3^(a - b) = 3^2 = 9; 9 is NOT a prime number.
No unique answer. Insufficient.
(2) a - b = 2
=> 3^(a - b) = 3^2 = 9; 9 is NOT a prime number. A unique answer. Sufficient.
The correct answer: B
Hope this helps!
-Jay
_________________
Manhattan Review Test Prep
Locations: Manhattan Review Chennai | Free GMAT Practice Test | GRE Prep Hyderabad | Jayanagar GRE Coaching | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.