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If x and y are prime integers, what is x + y?
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29 Oct 2019, 21:11
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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?
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Updated on: 12 Nov 2019, 23:05
(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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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?
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29 Oct 2019, 21:54
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 , 52=3 (Prime Number). So, x+y=7. if y=3, x=5 , 53=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.



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Re: If x and y are prime integers, what is x + y?
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29 Oct 2019, 22:07
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, => xy = 2, a prime number. And, x=5 and y=2, => xy = 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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Re: If x and y are prime integers, what is x + y?
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29 Oct 2019, 22:19
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



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If x and y are prime integers, what is x + y?
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29 Oct 2019, 22:40
If x and y are prime integers, what is x + y? (1) x  y is a prime integer 52=3....x+y=5+2=7 72=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?
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29 Oct 2019, 23:00
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.
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Re: If x and y are prime integers, what is x + y?
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29 Oct 2019, 23:14
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
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Re: If x and y are prime integers, what is x + y?
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30 Oct 2019, 00:24
If x and y are prime integers, what is x + y? evaluating 1) (1) x  y is a prime integer 53=2 ; x=5 and y=3; x+y= 8 75=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: xy= prime therefore a) x=3, y=2; xy=1> not prime therefore x=5 and y=3!! since, XY =2 and we have a unique value for X+Y= 8 C is the answer
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Re: If x and y are prime integers, what is x + y?
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30 Oct 2019, 00:30
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?
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30 Oct 2019, 01:36
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
The answer is E
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Re: If x and y are prime integers, what is x + y?
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30 Oct 2019, 01:47
Answer is E.
Let's I am explaining it .
As per given information x and y are prime numbers. What is x + y
Info1 : x y is prime integer let's simulate it . put x =7 , y =5 , then xy = 75 = 2> prime integer... put x = 5 , y =2 , then xy = 52 = 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.
Info2 : 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 info1+info2
xy = prime integer and y<x<6 let's check  x=5, y=3> xy =2 prime x=5. y=2>xy =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?
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30 Oct 2019, 02:51
If x and y are prime integers, what is x + y?
(1) x  y is a prime integer (2) y < x < 6
#1 xy 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?
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30 Oct 2019, 11:31
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, 53=2 yes even prime Let X=7 and y=2, 72=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.
53=2 and 52= 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?
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04 Nov 2019, 05:33
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.xy=prime 52=3…5+2=7 53=2…5+3=8 (2) y < x < 6 insufic.(x,y)=(5,3;5,2;3,2) (1 & 2) insufic.52=3…5+2=7 53=2…5+3=8 Answer (E)



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Re: If x and y are prime integers, what is x + y?
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05 Nov 2019, 07:47
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.. 52=3....x+y=5+2=7 72=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?
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12 Nov 2019, 17:34
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.. 52=3....x+y=5+2=7 72=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 chetan2uOA is E here and I agree. For 2,3 and 5 > Both 53 and 52 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?
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12 Nov 2019, 18:44
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.. 52=3....x+y=5+2=7 72=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 chetan2uOA is E here and I agree. For 2,3 and 5 > Both 53 and 52 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.
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Re: If x and y are prime integers, what is x + y?
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