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Is 1 considered a prime number? I selected C but was wrong. According to the answer: S2 is not sufficient. Consider X = 5 , Y = 3 and X = 3 , Y = 2 which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

Is 1 considered a prime number? I selected C but was wrong. According to the answer: S2 is not sufficient. Consider X = 5 , Y = 3 and X = 3 , Y = 2 which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

1) X - Y is prime case 1: 5 - 2 = 3 5 + 2 = 7

case 2: 7 - 5 = 2 7 + 5 = 13

Two answers. Insufficient.

2) Y < X < 6 Possible value for Y = {2, 3} Possible value for X = {3, 5}

More than one answer. Insufficient.

1) & 2) Case 1: 2 < 3 < 6 3 - 2 = 1 ----- Not Prime Drop this case

Is 1 considered a prime number? I selected C but was wrong. According to the answer: S2 is not sufficient. Consider X = 5 , Y = 3 and X = 3 , Y = 2 which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

If x and y are prime numbers, what is the value of x+y ?

(1) x-y is a prime number --> if x=5 and y=2 (notice that in this case x-y=3=prime) then x+y=7 but if x=5 and y=3 (notice that in this case x-y=2=prime) then x+y=8. Not sufficient.

(2) y<x<6 --> the same example as above is valid for this statement also. 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.

Can we also consider negative cases of these integers, since the question did not explicitly state that the integers were positive?

No, we cannot. "If x and y are prime numbers..." Only positive numbers can be primes.

Is 1 considered a prime number? I selected C but was wrong. According to the answer: S2 is not sufficient. Consider X = 5 , Y = 3 and X = 3 , Y = 2 which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

If x and y are prime numbers, what is the value of x+y ?

(1) x-y is a prime number --> if x=5 and y=2 (notice that in this case x-y=3=prime) then x+y=7 but if x=5 and y=3 (notice that in this case x-y=2=prime) then x+y=8. Not sufficient.

(2) y<x<6 --> the same example as above is valid for this statement also. Not sufficient.

(1)+(2) Again, the example from statement (1) is still valid and gives two different values for x+y. Not sufficient.

Good question. I am particularly happy that I did end up solving this one is about a min and half.

Followed the plugging in of values approach with values as 5,2,3 for statement (ii) and for statement (i) there are a whole number of possible options.

Both statements together as well fail to give a concrete answer for the values 2,3,5. Hence chose E.
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My attempt to capture my B-School Journey in a Blog : tranquilnomadgmat.blogspot.com

Picking up on bunnels statement re: 1 being a prime....

If you have trouble remembering in the heat of battle, think: a prime number has 2 factors, 1 and itself. Although 1 has factors of 1 and iteslf, these are one and the same and therefore it doesn't have 2 (intiger) factors.
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Is 1 considered a prime number? I selected C but was wrong. According to the answer: S2 is not sufficient. Consider X = 5 , Y = 3 and X = 3 , Y = 2 which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

If x and y are prime numbers, what is the value of x+y ?

(1) x-y is a prime number --> if x=5 and y=2 (notice that in this case x-y=3=prime) then x+y=7 but if x=5 and y=3 (notice that in this case x-y=2=prime) then x+y=8. Not sufficient.

(2) y<x<6 --> the same example as above is valid for this statement also. 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.

Can we also consider negative cases of these integers, since the question did not explicitly state that the integers were positive?
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Natural numbers that have EXACTLY two factors are called prime numbers. Obviously, the number "1" has exactly 1 factor, so it is neither prime nor composite.. Yeah, this number is a different breed !!
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Natural numbers that have EXACTLY two factors are called prime numbers. Obviously, the number "1" has exactly 1 factor, so it is neither prime nor composite.. Yeah, this number is a different breed !!

Right. So if I see "different breed" on a GMAT DS, I should think "1" right?
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Natural numbers that have EXACTLY two factors are called prime numbers. Obviously, the number "1" has exactly 1 factor, so it is neither prime nor composite.. Yeah, this number is a different breed !!

Right. So if I see "different breed" on a GMAT DS, I should think "1" right?

1 is NOT a prime number. The smallest prime is 2. And this is not only for the GMAT but generally.