Is the product of two numbers x and y a prime number?

Question

(1) x + y = even
(2) x is even

Harsh9676 · Answer

The questions is asking whether XY = 2,3,5,7,11,.....

We know all primes are integers and have only 2 factors (1 being one of the factors). So either one of X or Y should be 1 and the other should be the prime number itself.

St1: X + Y = even >> possible when

i) Even + Even = Even >> 0 + 2 = 2 (prime ) and 2+4 = 6 not a prime ; Insufficient
ii) Odd + Odd = Even >> 1+3 = 4 (not prime)

St2 : X is even. Insufficient since we do not know anything about Y (Y could either be 1 or something else)

Combined: Scenario i) satisfies and it still is insufficient to answer.

Ans E

kntombat · Answer

Bunuel ,  chetan2u ,  nick1816 , could you post the official explanation please, I guess I have figured out where I went wrong but would love for an expert to give their take on the same.

firas92 · Answer

(1) x + y = even
If x=2, y=2, xy=4 which is not prime
If x=1, y=3, xy=3 which is prime

1 is not sufficient

(2) x is even
If x=2, y=2, xy=4 which is not prime
If x=2, y=1, xy=2 which is prime

2 is not sufficient

(1)+(2)
x+y=even and x=even
So y=even

xy=even*even which must be divisible by 4 and so xy is not prime

(1)+(2) is sufficient

Answer is (C)

Posted from my mobile device

kntombat · Answer

Thank you firas92 .

chetan2u · Answer

kntombat 
For xy to be a prime number, one of the two should be a prime number and other 1.
So let us check each of the statement.

1) x+y=even
Either both x and y are even, in which case none of x and y is 1, and xy is NOT a prime
Or both x and y are odd, in which case the numbers could be 3 and 1, and xy is prime
Insuff

2) x is even 
Nothing about y, and even x can be 0 or 2.
Insufficient

Combined. 
x+y is even and x is even, so y is also even. 
None of x and y is 1, so answer is always NO, xy is not prime.

kntombat · Answer

Thank you for the prompt reply  chetan2u .

Basshead · Answer

Is the product of two numbers x and y a prime number?

(1) x + y = even
If x = y = 1; xy = not prime
if x = 3, y = 1; xy = prime

NOT SUFFICIENT.

(2) x is even
if x = y = 2; not prime
if x = 2, y = 1; prime

NOT SUFFICIENT.

(1&2) x = even, y must be even. We can't have a prime number from 2 even integers. SUFFICIENT.

aamani02 · Answer

Product of two numbers can be prime only if one of the numbe is 1 and other is some prime number ( 2,3,5,7, 11,13...)

Options 
1. X+y is even, if y =1 , x+y is even for all prime number except 2, but we don't know what is y

2.x is even i.e. so y is even too,

So combining both, x and y is not prime,

Posted from my mobile device

Is the product of two numbers x and y a prime number?

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