GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 19:27 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If a and b are prime numbers, is ab even?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58427
If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

1
6 00:00

Difficulty:   55% (hard)

Question Stats: 58% (01:24) correct 42% (01:28) wrong based on 143 sessions

HideShow timer Statistics

If a and b are prime numbers, is ab even?

(1) The sum of a and b is prime

(2) The difference of a and b is prime

_________________
Retired Moderator G
Joined: 26 Nov 2012
Posts: 565
If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

Bunuel wrote:
If a and b are prime numbers, is ab even?

(1) The sum of a and b is prime

(2) The difference of a and b is prime

Given a and b are prime numbers and need to find ab even or not

Stat 1: When a = 2 and b =3

Then sum we get a+b = 5

suppose 3+3 = 6..not our case
4+3 = 7 our case.
4+4 = 8..not our case...

Then from above cases... either a or b has to be even from this...then ab will be even...Sufficient.

Stat 2: difference of a and b is prime

Then we can take 4-2 = 2 prime..fine

6-3 = 3...fine

5-3 = even ( both primes ) the product will be prime...not fine...Insufficient.

IMO option A.
Senior Manager  Joined: 06 Jun 2016
Posts: 254
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23 GMAT 2: 680 Q49 V34 GPA: 3.9
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

A

Statement 1 says sum of prime numbers a and b is prime.
odd+odd= even so it cant be prime. Eg 11+13=24, 3+5=8..
even+odd/ odd+even can only make the sum prime. Eg 2+5=7, 3+2=5, 2+11=13
So the given statement answers the question as Yes.

Statement 2 says difference between 2 primes is prime.
odd-odd=even 13-11=2, ab=143 ab is not even
odd-even=odd 5-2=3, ab=10 ab is even
This answers the question in yes and no.
So statement 1 alone is sufficient
VP  D
Joined: 05 Mar 2015
Posts: 1000
If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

Bunuel wrote:
If a and b are prime numbers, is ab even?

(1) The sum of a and b is prime

(2) The difference of a and b is prime

Points to keep in mind are:-
a) only even prime is 2
b)all primes are odd except 2
c) 0 & 1 is not a prime number.
d) -ve numbers are not primes

Statement (1)
The sum of a and b is prime
it means sum of 2 numbers is odd since a & b are both primes.
Now as even +odd=odd so for prime numbers family we have only one even number is 2 thus ab is even
But for any other primes than 2 obviously which are ODD we get odd+odd=even (not a prime).....suff.

Statement (2)

let a=5 and b=2 than difference is 3 (prime).......YES

let a=13 and b=11 than difference is 2 (prime).......NO............insuff

Ans A

Originally posted by rohit8865 on 29 Sep 2016, 10:24.
Last edited by rohit8865 on 01 Jan 2017, 19:48, edited 1 time in total.
Intern  Joined: 14 Sep 2016
Posts: 1
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

(A) If the sum is prime, that means the sum is odd as the lowest even prime number is 2 and every other prime number is odd. Even + Odd = Odd. Therefore one of the numbers has to be 2 as 2 is the only even prime number. eg: 11+ 2 = 13

(B) The difference being prime could mean the difference is even or odd as it could be 2 eg: 13 - 11 = 2 or 17 - 11 = 6 and is therefore insufficient.

The correct answer is A
Intern  Joined: 23 Jun 2016
Posts: 41
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

Statement 1: we know all primes are odds besides 2. We are told the sum of a and b is a prime or its odd unless the sum is 2 (which is not possible) So one of a or b must be 2. so we get even + odd = odd. and even*odd = even so sufficient

Statement 2: the difference of A and B is prime. even-odd or if the difference is 2 (even) then a and b must be odd. So we A or B could be even or A and B are both odd So insufficient
Current Student D
Joined: 12 Aug 2015
Posts: 2562
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

Tremendous Question.
Here is what i did in this one =>

We need to see if A*B is even or not.
As A,B are prime numbers => A*B can be prime only when at-least one out of A or B is 2.
Notice the use of word at-least as A and B can be equal too.

Statement 1->
A+B => Prime
Least value of A+B will be when both are 2 => 2+2=4
Hence A+B is a prime number >4
But all the primes create than 4 are odd

Hence A+B=odd

This can happen in two cases
A=even
B=odd
OR
A=odd
B=even

In both cases one out of A or B must be 2 because 2 is the only even prime

Hence sufficient

Statement 2->
A-B=odd
Lets use test cases
A=5
B=2
5-2=3=prime
AB=even
A=5
B=3
5-3=2=prime
AB=odd
Hence not sufficient

Hence A

_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13412
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

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.
_________________ Re: If a and b are prime numbers, is ab even?   [#permalink] 25 Jan 2018, 23:45
Display posts from previous: Sort by

If a and b are prime numbers, is ab even?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  