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Math Expert V
Joined: 02 Sep 2009
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If x and y are prime integers, what is x + y?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 53% (01:31) correct 47% (01:20) wrong based on 103 sessions

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Competition Mode Question

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

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

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If x and y are prime integers, what is x + y?  [#permalink]

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(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

Posted from my mobile device

Originally posted by Dillesh4096 on 29 Oct 2019, 21:28.
Last edited by Dillesh4096 on 12 Nov 2019, 23:05, edited 1 time in total.
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1

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.
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1
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.

Posted from my mobile device
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GMAT 1: 690 Q49 V35 Re: If x and y are prime integers, what is x + y?  [#permalink]

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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
Math Expert V
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If x and y are prime integers, what is x + y?  [#permalink]

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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
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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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.

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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1
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.

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Re: If x and y are prime integers, what is x + y?  [#permalink]

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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

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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1
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[(5,),(),()]...so not sufficient

OA:E

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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1
If x and y are prime integers, what is x +y ???

(Statement1): x—y is a prime number

—> 7–2= 5 —> x+y= 9
—> 5–3= 2 —> x+y= 8
Insufficient

(Statement2): y< x< 6

2<3 < 6 —> x+y = 5
3< 5 < 6 —> 5+3= 8
Insufficient

Taken together 1&2,

3< 5< 6 —> x—y= 2 (prime)
2< 5< 6 —> x—y= 3( prime )

x+y= 3+5= 8
x+y= 2+5= 7
Insufficient

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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1

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.
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1
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
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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1
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
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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Bunuel wrote:

Competition Mode Question

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

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

(x,y)=primes[2,3,5,7,…]

(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

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Re: If x and y are prime integers, what is x + y?  [#permalink]

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chetan2u wrote:
If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
the difference of two prime numbers will be prime ONLY when y is 2, but x can be aything..
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 is 2 and x<6. y=2 and x=5 is left..x+y=2+5=7
y=3 and x=5 ( difference is a prime number 2)... x+y=3+5=8

not sufficient
ANS E

C
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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chetan2u wrote:
If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
the difference of two prime numbers will be prime ONLY when y is 2, but x can be aything..
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 is 2 and x<6.
Only y=2 and x=5 is left..x+y=2+5=7
Suff

C

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!
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Re: If x and y are prime integers, what is x + y?  [#permalink]

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TheNightKing wrote:
chetan2u wrote:
If x and y are prime integers, what is x + y?

(1) x - y is a prime integer
the difference of two prime numbers will be prime ONLY when y is 2, but x can be aything..
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 is 2 and x<6.
Only y=2 and x=5 is left..x+y=2+5=7
Suff

C

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!

Thanks. OA is E. A stupid error on my part.
_________________ Re: If x and y are prime integers, what is x + y?   [#permalink] 12 Nov 2019, 18:44
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