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# If x and y are prime numbers

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Joined: 31 Dec 1969
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If x and y are prime numbers [#permalink]  02 Jan 2011, 13:08
Hello,

Book: Kaplan GMAT Premier 2011
Pages: 457 and 458

For the data sufficiency problem "If x and y are prime numbers, is y(x-3) odd?" on page 457, explained answer on page 458 is D (Each statement alone is sufficient.)

2 statements are:
1. x > 10
2. y < 3

However, I feel that answer should be A (only 1 is sufficient).

Statement 2 is not sufficient, because:
1. If we pick y = 2 and x = 2, equation yields 2(-1) = -2 => Even number
2. If we pick y = 1 and x = 2, equation yields 1(-1) = -1 => Odd number

Thus depending on what we pick, the result can be even or odd...hence we cannot conclusively say if y(x-3) will be odd or not based on statement 2.

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Re: If x and y are prime numbers [#permalink]  02 Jan 2011, 13:32
Expert's post
bjshukla wrote:
Hello,

Book: Kaplan GMAT Premier 2011
Pages: 457 and 458

For the data sufficiency problem "If x and y are prime numbers, is y(x-3) odd?" on page 457, explained answer on page 458 is D (Each statement alone is sufficient.)

2 statements are:
1. x > 10
2. y < 3

However, I feel that answer should be A (only 1 is sufficient).

Statement 2 is not sufficient, because:
1. If we pick y = 2 and x = 2, equation yields 2(-1) = -2 => Even number
2. If we pick y = 1 and x = 2, equation yields 1(-1) = -1 => Odd number

Thus depending on what we pick, the result can be even or odd...hence we cannot conclusively say if y(x-3) will be odd or not based on statement 2.

If x and y are prime numbers, is y(x-3) odd?

Note that we are told that both x and y are prime numbers, also note that 1 is not a prime number.

Now, in order the product of 2 integers to be odd both must be odd, so y(x-3) to be odd y must be any odd prime and x must be the only even prime 2, so that x-3=even-odd=odd. In all other cases given product will be even.

(1) x > 10 --> x is not 2, so the product is even. Sufficient.

Or: x is a prime number more than 10, so it's odd --> x-3=odd-odd=even --> y(x-3)=y*even=even.

(2) y < 3 --> the only prime less than 3 is 2, so y(x-3)=even*(x-3)=even. Sufficient.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: If x and y are prime numbers [#permalink]  03 Nov 2011, 07:42
1. Only even prime is 2, so if x>10 then (x-3) is even. SUFFICIENT.
2. y<3 does not prove anything. NOT SUFFICIENT.
Hence ans is A
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Re: If x and y are prime numbers [#permalink]  03 Nov 2011, 07:47
Bunuel wrote:
bjshukla wrote:
Hello,

Book: Kaplan GMAT Premier 2011
Pages: 457 and 458

For the data sufficiency problem "If x and y are prime numbers, is y(x-3) odd?" on page 457, explained answer on page 458 is D (Each statement alone is sufficient.)

2 statements are:
1. x > 10
2. y < 3

However, I feel that answer should be A (only 1 is sufficient).

Statement 2 is not sufficient, because:
1. If we pick y = 2 and x = 2, equation yields 2(-1) = -2 => Even number
2. If we pick y = 1 and x = 2, equation yields 1(-1) = -1 => Odd number

Thus depending on what we pick, the result can be even or odd...hence we cannot conclusively say if y(x-3) will be odd or not based on statement 2.

If x and y are prime numbers, is y(x-3) odd?

Note that we are told that both x and y are prime numbers, also note that 1 is not a prime number.

Now, in order the product of 2 integers to be odd both must be odd, so y(x-3) to be odd y must be any odd prime and x must be the only even prime 2, so that x-3=even-odd=odd. In all other cases given product will be even.

(1) x > 10 --> x is not 2, so the product is even. Sufficient.

Or: x is a prime number more than 10, so it's odd --> x-3=odd-odd=even --> y(x-3)=y*even=even.

(2) y < 3 --> the only prime less than 3 is 2, so y(x-3)=even*(x-3)=even. Sufficient.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.

I have a question, Can we disregard -ve numbers here for part 2. (y<3) ?
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Re: If x and y are prime numbers [#permalink]  03 Nov 2011, 08:11
reatsaint wrote:
I have a question, Can we disregard -ve numbers here for part 2. (y<3) ?

Yes, because it is mentioned in the stem that "x and y are prime numbers". Prime numbers are never -ve;

Per GMATClub Math Book:
A Prime number is a natural number with exactly two distinct natural number divisors: 1 and itself.
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Re: If x and y are prime numbers   [#permalink] 03 Nov 2011, 08:11
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