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Joined: 31 Dec 1969
Location: Russian Federation
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If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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Question Stats: 59% (01:20) correct 41% (01:17) wrong based on 237 sessions

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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.

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

Thank you for your help in advance!

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55173
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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.

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.

Answer: D.

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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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
Manager  Joined: 06 Feb 2011
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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.

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.

Answer: D.

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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Posts: 1779
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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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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

The answer is D

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55173
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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

The answer is D

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.

Answer: D.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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Ok, i'll follow rules next time, srry new to forum.

anyways i understand now, feel dumb lol
Intern  Joined: 07 Mar 2013
Posts: 24
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55173
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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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Thanx Bunuel. I suddenly feel stupid. odd-odd=even, how silly of me.
Intern  Joined: 08 Oct 2011
Posts: 36
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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Are there no negative prime numbers? Because if there are negative prime numbers, the answer to this question would be A.
Math Expert V
Joined: 02 Sep 2009
Posts: 55173
Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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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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

The answer is D

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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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

Final Answer:

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GMAT 1: 690 Q48 V36 Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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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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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GMAT 1: 690 Q48 V36 Re: If x and y are prime numbers, is y(x-3) odd?  [#permalink]

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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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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
Hence, the answer is A
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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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
Hence, the answer is A
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.

Check for more below threads:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

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

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