If x and y are prime integers, what is x + y?

Question

Competition Mode Question

(1) x - y is a prime integer
(2) y < x < 6

CareerGeek · Answer

(1) x - y is a prime integer
—> Many values of x and y are possible
Eg: 5 - 2 = 3 is a prime integer —> (x, y) = (5, 2)
7 - 2 = 5 is a prime integer —> (x, y) = (7, 2) so on
—> Insufficient

(2) y < x < 6
Possible prime integers less than 6 are 2, 3 & 5
—> Possible values of (x, y) = {(5, 2), (5, 3), (3, 2)} —> Insufficient

Combining (1) & (2),
x - y = 2 or 3 and x > y
—> (x, y) = (5, 3) or (5, 2)
—> x + y = 8 or 7 —> Insufficient

IMO Option E

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BelalHossain046 · Answer

My answer: E.

While doing the question, I looked at statement 2 first because it's easy to figure out the prime numbers smaller than 6. 
the primers smaller than 6 are 2,3, & 5.

Statement 2: INSUFFICIENT
if y=2, x=5 , x+y=7.
if y=3, x=5 , x+y=8.

Statement 1: INSUFFICIENT
if y=2, x=5 , 5-2=3 (Prime Number). So, x+y=7.
if y=3, x=5 , 5-3=2 (Prime Number). So, x+y=8.

Combining:
Since I took same numbers to check both statements, I dont need to combine. So the answer is E.
Even If I recheck both statements, (x=5 & y=2) and (x=5 & y=3) SUFFICE both statements. So, x+y can be 7 or 8. NO UNIQUE value. 
My answer is E.

kk47 · Answer

1) This will give following values-
x=5 and y=2,3
Or
x=7 and y=5
Or
x=19 and y=17
And so on.
Therefore statement 1 alone is not sufficient.

2) This will give following values -
x=5 and y=3,2
Or
x=3 and y=2
Since there can be multiple values for (x+y) therefore statement 2 alone is also not sufficient.

1&2) This will give following values -
x=5 and y=3, => x-y = 2, a prime number.
And,
x=5 and y=2, => x-y = 3, a prime number.

Since again we are getting more than 1 value for (x+y) therefore both statements together also are not sufficient enough.

Answer is (E).

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vg18 · Answer

If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
If x is 5, y is 3
If x is 7, y is 5

Not sufficient

but from above we get X and Y are consecutive odd integers.

(2) y < x < 6
if x is 3, y is 2,
if x is 5, y can be 3 or 2.

Not sufficient

Combining.only comibination that works is x as 5 and y as 3. hence sufficient to find x+y. Ans C

chetan2u · Answer

If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
5-2=3....x+y=5+2=7
7-2=5...x+y=7+2=9
Insuff

(2) y < x < 6
So, y and x prime numbers less than 6..
2<3<6......2+3=5
2<5<6.....2+5=7
3<5<6.....3+5=8
Insuff

Combined..
y=2 and x=5 is left..x+y=2+5=7
y=3 and x=5....x+y=8
Insuff

E

unraveled · Answer

If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
A number of possibilities exist when both x and y are prime numbers and their difference is a prime number. Since prime numbers are odd except 2 the possible difference would only be even i.e. difference can only be 2, a prime.
x = 5 y = 3; x - y = 2
x = 13 y = 11; x - y = 2
x = 31 y = 29; x - y = 2

All the possible cases result in various values of 'x + y'. Thus

INSUFFICIENT.

(2) y < x < 6
Case - I: y = 2 x = 3
Case - II: y = 3 x = 5

x + y get different values. Thus,

INSUFFICIENT.

Together 1 and 2
Only Case II of statement 2 is possible since as per Case I x - y = 1 which is not prime number.

SUFFICIENT.

Answer C.

Verbal33 · Answer

If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
 x and y can be any prime integers. Insufficient

(2) y < x < 6
 there are 3 primes below 6. 
2, 3, and 5.
but x and y can be anything.

Together:
 5 - 2 = 3 which is prime
5 - 3 = 2 which is prime.
y can be 2 or 3.
Insufficient.

Answer: E

sampriya · Answer

If x and y are prime integers, what is x + y?

evaluating 1)
(1) x - y is a prime integer
5-3=2 ; x=5 and y=3; x+y= 8
7-5=2; x=7 and y= 5; x+y=12

we don't have a unique value for x+y therefore option 1 is insufficient

(2) y < x < 6

prime integers less than 6 are : 2,3,5

a)y=2, x=3--->x+y= 5
b)y=3, x=5--->x+y=8

we do not have a unique value for x+y therefore option 2 is insufficient

examining both option 1 and option 2:

x-y= prime

therefore a) x=3, y=2; x-y=1---> not prime
therefore x=5 and y=3!! since, X-Y =2 and we have a unique value for X+Y= 8

C is the answer

madgmat2019 · Answer

1) x - y is a prime integer

There are many values Satisfying x,y....so insufficient

(2) y < x < 6

There are 3values for 2variables....2,3,5
So not sufficient

Combining both also we got three combinations ...so not sufficient

OA:E

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lacktutor · Answer

If x and y are prime integers, what is x + y?

evaluating 1)
(1) x - y is a prime integer
5-3=2 ; x=5 and y=3; x+y= 8
7-5=2; x=7 and y= 5; x+y=12

we don't have a unique value for x+y therefore option 1 is insufficient

(2) y < x < 6

prime integers less than 6 are : 2,3,5

a)y=2, x=3--->x+y= 5
b)y=3, x=5--->x+y=8

we do not have a unique value for x+y therefore option 2 is insufficient

examining both option 1 and option 2:

x-y= prime

therefore a) x=3, y=2; x-y=1---> not prime
therefore x=5 and y=3!! since, X-Y =2 and we have a unique value for X+Y= 8

C is the answer

JiddiHuMain · Answer

Answer is E.

Let's I am explaining it .

As per given information x and y are prime numbers. What is x + y

Info-1 : x -y is prime integer
let's simulate it . put x =7 , y =5 , then x-y = 7-5 = 2-----------> prime integer...
put x = 5 , y =2 , then x-y = 5-2 = 3 ----------> prime integer..

we are looking x +y = ???-----> if x =7 , y =5 , then x+ y = 12, if x = 5 , y =2 , then x+ y = 7
Hence multiple values possible...Insufficient.. Definitely answer is not A or D.

Info-2 : y < x < 6
let's simulate it . if x = 5 , then y = 3 or 2 -----> x+y = 8 or 7
if x = 3 then y = 2 ------------> x+y = 5
Hence multiple values are possible. ....Insufficient...Definitely answer is not B

let simulate info-1+info-2

x-y = prime integer and y<x<6
let's check - x=5, y=3---> x-y =2 prime
x=5. y=2---->x-y =3 prime

again multiple values are coming so x+y = 8 or 7.
hence ....insufficient information.....option C is also out.

Now, concluding -- Correct Answer is E. both data are not sufficient.

Archit3110 · Answer

If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
(2) y < x < 6

#1
x-y is a prime integer
x=5 and y=3 or 2
insufficient
#2
y<x<6
again insufficient as x=5,3 and y=3,2 insufficient
from 1 &2
no unique value
IMO E

chaitralirr · Answer

If x and y are prime integers, what is x + y? IS it even or ODD

(1) x - y is a prime integer
let X=5 and y=3, 5-3=2 yes even prime
Let X=7 and y=2, 7-2=5 No odd prime.

Statement 1 is not sufficient

2) Statement 2:
y < x < 6

so y and x can be either 2, 3, 5 still we cannot determine if x+y is even or odd.

Hence statement 2 is insufficient.

While combining both sentences it is observed that x and y are less than 6 so they can be 5, 3 or 2.

5-3=2 and 5-2= 3.

even when combined together they are not sufficient

IMO E

exc4libur · Answer

(x,y)=primes

(1) x - y is a prime integer   insufic. 
x-y=prime
5-2=3…5+2=7
5-3=2…5+3=8

(2) y < x < 6   insufic. 
(x,y)=(5,3;5,2;3,2)

(1 & 2)   insufic. 
5-2=3…5+2=7
5-3=2…5+3=8

Answer (E)

amalantony13 · Answer

TheNightKing · Answer

chetan2u 
OA is E here and I agree. For 2,3 and 5 -> Both 5-3 and 5-2 result in a prime and hence insufficient.

Tagging you just to make sure OA is E. 
Thank you!

chetan2u · Answer

Thanks. OA is E. A stupid error on my part.

Bunuel · Answer

If x and y are prime integers, what is x + y?

(1)  x-y  is a prime number. If  x=5  and  y=2  (notice that in this case  x-y=3=	ext{prime} ) then  x+y=7  but if  x=5  and  y=3  (notice that in this case  x-y=2=	ext{prime} ) then  x+y=8 . Not sufficient.
 
(2)  y \lt x \lt 6 . The same example as above is valid for this statement as well. Not sufficient.
 
(1)+(2) Again, the example from statement (1) is still valid and gives two different values for  x+y . Not sufficient.

Answer: E

If x and y are prime integers, what is x + y?

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If x and y are prime integers, what is x + y?

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