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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?

\(X\) and \(Y\) are prime integers. What is \(X + Y\) ?

1. \(X - Y\) is a prime integer 2. \(Y \lt X \lt 6\)

(C) 2008 GMAT Club - m25#29

* 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.

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.

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. _________________

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. _________________

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? _________________

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 !! _________________

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? _________________

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.