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

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

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02 Jan 2011, 14:08
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If x and y are prime numbers, is y(x-3) odd?

(1) x > 10

(2) y < 3

[Reveal] Spoiler:
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.

[Reveal] Spoiler: OA

Last edited by Bunuel on 08 May 2015, 08:29, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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

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02 Jan 2011, 14:32
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, is y(x-3) odd? [#permalink]

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03 Nov 2011, 08:42
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, is y(x-3) odd? [#permalink]

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03 Nov 2011, 08:47
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, is y(x-3) odd? [#permalink]

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03 Nov 2011, 09:11
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, is y(x-3) odd? [#permalink]

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08 May 2015, 08:30
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Re: If x and y are prime numbers, is y(x-3) odd? [#permalink]

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09 May 2015, 11:20
Hi All,

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

[Reveal] Spoiler:
D

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

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10 May 2015, 05:30
Hi Rich,

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

Is that also true for the GMAT

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

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10 May 2015, 06:38
Tmoni26 wrote:
Hi Rich,

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

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10 May 2015, 07:36
Hi IanStewart,

Thanks a lot for that clarification....

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Re: If x and y are prime numbers, is y(x-3) odd?   [#permalink] 10 May 2015, 07:36
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