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

It is currently 20 Oct 2018, 20:51

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

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
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post 29 Sep 2016, 04:42
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (01:19) correct 45% (01:28) wrong based on 133 sessions

HideShow timer Statistics

Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 593
Premium Member
If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post 29 Sep 2016, 05:03
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
Senior Manager
avatar
Joined: 06 Jun 2016
Posts: 259
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

New post 29 Sep 2016, 05:16
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
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 995
If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post Updated on: 01 Jan 2017, 19:48
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
Intern
avatar
Joined: 14 Sep 2016
Posts: 1
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post 29 Sep 2016, 10:47
(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
Intern
avatar
Joined: 23 Jun 2016
Posts: 41
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post 29 Sep 2016, 11:08
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
User avatar
D
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post 01 Jan 2017, 13:24
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

_________________


MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8486
Premium Member
Re: If a and b are prime numbers, is ab even?  [#permalink]

Show Tags

New post 25 Jan 2018, 23:45
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

GMAT Club Bot
Re: If a and b are prime numbers, is ab even? &nbs [#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  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.