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

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If a and b are prime numbers, is ab even?  [#permalink]

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29 Sep 2016, 04:42
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58% (01:24) correct 42% (01:28) wrong based on 143 sessions

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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

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If a and b are prime numbers, is ab even?  [#permalink]

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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.
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Re: If a and b are prime numbers, is ab even?  [#permalink]

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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
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If a and b are prime numbers, is ab even?  [#permalink]

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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.
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Re: If a and b are prime numbers, is ab even?  [#permalink]

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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.

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Re: If a and b are prime numbers, is ab even?  [#permalink]

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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
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Re: If a and b are prime numbers, is ab even?  [#permalink]

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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

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Re: If a and b are prime numbers, is ab even?  [#permalink]

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25 Jan 2018, 23:45
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Re: If a and b are prime numbers, is ab even?   [#permalink] 25 Jan 2018, 23:45
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