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

Question

Competition Mode Question

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

(1) x - y = prime
(2) y is not prime

Are You Up For the Challenge: 700 Level Questions

Is the product of two numbers x and y a prime number?
1) x - y = prime
2) y is not prime

ArunSharma12 · Answer

Given: x,y are integers > 0.
is x*y = prime?
prime number = 1*prime.

statement 1:
x = prime + y
possible values of x,y:  (3,1): product is a prime
(4,1):product is not a prime 
not sufficient

statement 2:
y  
e  prime
nothing is specified about x.
not sufficient

combining both statements,
possible values of x,y:  (3,1): product is a prime
(4,1):product is not a prime 
Ans: E

exc4libur · Answer

(x,y)=posintegers

xy=prime when (x,y)=(1,prime)

(1) insufic
6-1=5, 6*1=6 not prime
3-1=2, 3*1=3 prime

(2) insufic
nothing x

(1/2) insufic
6-1=5, 6*1=6 not prime
3-1=2, 3*1=3 prime

Ans (E)

bidskamikaze · Answer

IMO E
Product of two positive integers can be prime ONLY if one of them is a prime and other is 1.

1) x-y= prime
for x=3, y=1 >> x-y=2 (i.e,prime), 3X1= prime
for x=7, y=4 >> x-y=3 (i.e, prime), 7X4 not a prime
So 1 is not sufficient.

2) y is not prime
Doesn't say anything about product of x and y>>> not sufficient.

Combine 1) and 2) 
Both cases of option 1 still exist; not sufficient.

Therefore, answer E.

debjit1990 · Answer

ns:E

Is the product of two positive integers x and y a prime number?
(1) x - y = prime
(2) y is not prime

x,y=+ve int
(1) x - y = prime
3-1=2..x=3 & y=1..so xy=3 prime yes
4-2=2..x=4 & y=2..so xy=8 prime no
so both possible..not sufficient

(2) y is not prime
very less info..Not sufficient

1+2
we know 1 is not a prime number.
3-1=2..x=3,y=1...xy=3 prime yes
8-1=7..x=8,y=1..xy=8 prime no
not sufficient

MayankSingh · Answer

IMO E

(1) x - y = prime
x= 5, y=3 , xy=10 (Not prime)
x=3, y=1 , xy=3 (Prime)
Not sufficient

(2) y is not prime
x can be anything
Not sufficient.

Together,
x - y = prime, y is not prime
x=3, y=1 , xy=3 (Prime)
x=8, y=1 , xy=8 (Not Prime)
Not sufficient.

HoneyLemon · Answer

Good one . 
 Is it B ? 
Below is my reasoning . 
 
Q > 
 Is the product of two positive integers x and y a prime number?
 
 X and y > 0 and integers . 
product of 2 int will only give a prime number if one number is 1 and another number is a prime number. 
So basically the ques is asking us whether out of X and Y one is 1 and other is a prime ?

Statement (1) : 
 x - y = prime 
 Case 1 : 
 X and Y both greater than 1 . e.g. X = 8 , Y = 3 , X - Y = 5 (Prime ). But product of X and Y is not prime . 
Case 2: 
 Y = 1 . X = 3 . X-Y = 2 (Prime) . but xy = 2 = Prime.

So we cannot conclusively tell the ans. SO statement 1 is insufficient .

Statement (2):
 y is not prime

If y is not prime , irrespective of value of x , xy will not be prime . So statement 2 is sufficient .

Ans B , IMO.

madgmat2019 · Answer

the product of two positive integers x and y a prime number

(1) x - y = prime....... 
(4,2) - x is non-prime, y is prime
(3,1) - x is prime, y is non-prime
(6,1) - x is non-prime, y is non-prime
(5,3) - x is prime, y is prime

INSUFFICIENT

(2) y is not prime

(3,1) - x is prime, y is non-prime
(6,1) - x is non-prime, y is non-prime

INSUFFFICIENT

even after combining both we have above two cases for which product of x and y can be prime/non-prime

OA:E

naveenban · Answer

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

For the product of X and Y to be prime, either X has to be 1 or Y has to be 1.

(1) x - y = prime -  Insufficient  -
  Let X = 3, Y = 1.
So, 3 - 1 = 2. Product of X and Y = 3 - Prime
Let X = 5, Y = 2.
5 - 2 = 3. Product of X and Y = 10 - Non Prime
So, we have 2 cases.

(2) y is not prime -  Sufficient - If Y isn't prime irrespective of the value of X, the product wouldn't be Prime.
Example X = 1...9 Y = 4.
Product will never be Prime

HoneyLemon · Answer

Agreed Ans should be E . 
From statement 2 : Y can be 1 or any non prime . X can be again 1 , prime and non -prime . so insuff.

So combining also we have same scenario. Not suffi.
So E .

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

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