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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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Updated on: 08 May 2015, 08:29
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If x and y are prime numbers, is y(x-3) odd?

(1) x > 10

(2) y < 3

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.

Originally posted by bjshukla on 02 Jan 2011, 14:08.
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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If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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Updated on: 07 Jul 2013, 22:50
If x and y are prime numbers, is y(x-3) odd?

(1) x > 10
(2) y < 3

This is from the Kaplan 2013 book, page 562 #11

I put B. I don't understand how (1) alone can be sufficient. Because when you plug in any prime number for x>10 using (1) guidelines, you will get an ODD number for (x-3) however we don't know the value of y, what if its 2 or 3, that can change the yes/no answer to the question. Please help the explanation is not thorough and its been bugging me for so long.

Originally posted by laserglare on 07 Jul 2013, 22:40.
Last edited by Bunuel on 07 Jul 2013, 22:50, edited 1 time in total.
Renamed the topic, edited the question and moved to DS forum.
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Posts: 55173
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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07 Jul 2013, 22:51
2
laserglare wrote:
If x and y are prime numbers, is y(x-3) odd?

(1) x > 10
(2) y < 3

This is from the Kaplan 2013 book, page 562 #11

I put B. I don't understand how (1) alone can be sufficient. Because when you plug in any prime number for x>10 using (1) guidelines, you will get an ODD number for (x-3) however we don't know the value of y, what if its 2 or 3, that can change the yes/no answer to the question. Please help the explanation is not thorough and its been bugging me for so long.

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

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.

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

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07 Jul 2013, 22:59
Ok, i'll follow rules next time, srry new to forum.

anyways i understand now, feel dumb lol
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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15 Oct 2013, 21:14
Hi Banuel,

why are we presuming one of x and y to be 2 ?
for statement 1 : x is odd, so x-3 will be odd. y can also be odd, why do we presume it to be 2 ?

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

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15 Oct 2013, 23:58
1
vishalrastogi wrote:
Hi Banuel,

why are we presuming one of x and y to be 2 ?
for statement 1 : x is odd, so x-3 will be odd. y can also be odd, why do we presume it to be 2 ?

pl help.

We are not doing that.

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.

Also, if x is odd, then x-3=odd-odd=even.
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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16 Oct 2013, 21:30
Thanx Bunuel. I suddenly feel stupid. odd-odd=even, how silly of me.
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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12 Nov 2013, 05:16
Are there no negative prime numbers? Because if there are negative prime numbers, the answer to this question would be A.
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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12 Nov 2013, 07:21
aakrity wrote:
Are there no negative prime numbers? Because if there are negative prime numbers, the answer to this question would be A.

No, only positive integers can be primes. The smallest prime (and the only even prime) is 2. For more check here: 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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07 Jan 2014, 10:24
laserglare wrote:
If x and y are prime numbers, is y(x-3) odd?

(1) x > 10
(2) y < 3

This is from the Kaplan 2013 book, page 562 #11

I put B. I don't understand how (1) alone can be sufficient. Because when you plug in any prime number for x>10 using (1) guidelines, you will get an ODD number for (x-3) however we don't know the value of y, what if its 2 or 3, that can change the yes/no answer to the question. Please help the explanation is not thorough and its been bugging me for so long.

Take a look at the question is y(x-3) odd?

Now, x,y both primes right? So x-3 will always be even except when x = 2, only even prime

(1) x>10 so x is not 2
Suff

(2) y<3 so 'y' has to be 2 cause is the smallest prime number

Remember negatives can't be prime numbers
1 is of course not prime either

Hence D here

Cheers!
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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

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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]

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08 Jun 2018, 12:42
Hi,
Maybe somebody can explain me, whi we can't take x=3 in the (2)? In this case it would be 2(3-3) = 0 => insufficient
Why it's not like that?
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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08 Jun 2018, 13:11
anna3565 wrote:
Hi,
Maybe somebody can explain me, whi we can't take x=3 in the (2)? In this case it would be 2(3-3) = 0 => insufficient
Why it's not like that?

ZERO.

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: If x and y are prime numbers, is y(x-3) odd?   [#permalink] 08 Jun 2018, 13:11

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