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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.

May you please advise if I am not approaching this correctly?

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.

May you please advise if I am not approaching this correctly?

Thank you for your help in advance!

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 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.

May you please advise if I am not approaching this correctly?

Thank you for your help in advance!

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.

Re: If x and y are prime numbers, is y(x-3) odd? [#permalink]

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08 May 2015, 07:30

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This is a great Number Property question; even if you don't immediately recognize the Number Properties involved, you can still discover the patterns (although it might take a little work).

We're told that X and Y are PRIME NUMBERS. We're asked if Y(X-3) is ODD. This is a YES/NO question.

Fact 1: X > 10

Since we know that X is PRIME, this Fact tells us that X must also be ODD. Y can be ANY PRIME number....

IF.... X = 11 then (X-3) = (11-3) = 8 (any prime)(8) will be EVEN, so the answer to the question is NO.

IF.... X = 13 then (X-3) = (13-3) = 10 (any prime)(10) will be EVEN, so the answer to the question is NO.

IF.... X = 17 then (X-3) = (17-3) = 14 (any prime)(14) will be EVEN, so the answer to the question is NO.

This pattern continues on; the answer to the question is ALWAYS NO. Fact 1 is SUFFICIENT

Fact 2: Y < 3

Since Y is PRIME, we know that Y MUST be 2. X can be ANY PRIME number....

IF.... Y = 2 and X = ANY PRIME then (X-3) = an integer (2)(any integer) will be EVEN, so the answer to the question is ALWAYS NO. Fact 2 is SUFFICIENT

So is this question telling me that Prime numbers cannot be -ve numbers??

Is that also true for the GMAT

That's true in all of math, GMAT or otherwise - prime numbers are never negative. The smallest prime is 2.
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