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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] New post 07 Jul 2013, 21:40
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

47% (01:49) correct 53% (00:40) wrong based on 112 sessions
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

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Jul 2013, 21:50, edited 1 time in total.
Renamed the topic, edited the question and moved to DS forum.
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Re: If x and y are prime numbers, is y(x-3) odd? [#permalink] New post 07 Jul 2013, 21:51
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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

[Reveal] Spoiler:
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] New post 07 Jul 2013, 21:59
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] New post 15 Oct 2013, 20:14
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] New post 15 Oct 2013, 22:58
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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] New post 16 Oct 2013, 20:30
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] New post 12 Nov 2013, 04:16
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] New post 12 Nov 2013, 06:21
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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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If x and y are prime numbers, is y(x-3) odd? [#permalink] New post 07 Jan 2014, 09:24
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

[Reveal] Spoiler:
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!
J :)
Re: If x and y are prime numbers, is y(x-3) odd?   [#permalink] 07 Jan 2014, 09:24
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