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If x, y, and z are 3 different prime numbers, which of the

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If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 02:45
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D
E

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If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

A. x + y
B. y – z
C. xy + 1
D. xyz + 1
E. x^2 + y^2
[Reveal] Spoiler: OA

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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 02:51
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karishmatandon wrote:
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

A. x + y
B. y – z
C. xy + 1
D. xyz + 1
E. x^2 + y^2


xyz and xyx+1 are are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Since xyz is a multiple of each x, y, and z, then xyx+1 cannot be a multiple of any of them.

Answer: D.

Similar question to practice: if-x-and-y-are-two-different-prime-numbers-which-of-the-134177.html

Hope it helps.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 02:52
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If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

pick: 2,3,5

A) x + y, 3+5=8 multiple of 2
B) y-z, 5-2=2 multiple of 2
C) xy + 1, 3*5+1=16 multiple of 2
D) xyz + 1, CORRECT
E) x^2 + y^2 3^2+5^2=36 multiple of 2

Why D?
Every prime number except 2 is odd.
In case you pick 2, xyz + 1=E*O*O +1=Odd and an ODD number cannot be a multiple of 2
In case you DO NOT pick 2 (you have only odd numbers), xyz + 1=O*O*O +1=Even and en EVEN number cannot be a multiple of an ODD number.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 02:53
Expert's post
karishmatandon wrote:
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

A. x + y
B. y – z
C. xy + 1
D. xyz + 1
E. x^2 + y^2


To discard other options, consider z=2, x=3, and y=5, in this case A, B, C, and E will be a multiple of z=2.

Hope it helps.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 02:57
Expert's post
Zarrolou wrote:
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

pick: 2,3,5

A) x + y, 3+5=8 multiple of 2
B) y-z, 5-2=2 multiple of 2
C) xy + 1, 3*5+1=16 multiple of 2
D) xyz + 1, CORRECT
E) x^2 + y^2 3^2+5^2=36 multiple of 2

Why D?
Every prime number except 2 is odd.
In case you pick 2, xyz + 1=E*O*O +1=Odd and an ODD number cannot be a multiple of 2
In case you DO NOT pick 2 (you have only odd numbers), xyz + 1=O*O*O +1=Even and en EVEN number cannot be a multiple of an ODD number.


Your logic to discard D is not correct.

Yes, if one of the primes is 2, then xyz + 1=E*O*O +1=Odd and an odd number cannot be a multiple of an even number but it could be a multiple of remaining odd primes.

Hope it's clear.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 03:01
Zarrolou wrote:
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

pick: 2,3,5

A) x + y, 3+5=8 multiple of 2
B) y-z, 5-2=2 multiple of 2
C) xy + 1, 3*5+1=16 multiple of 2
D) xyz + 1, CORRECT
E) x^2 + y^2 3^2+5^2=36 multiple of 2


I used picking numbers strategy and was down to D and E..couldn't figure out a way from there!

Bunuel wrote:
xyz and xyx+1 are are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Since xyz is a multiple of each x, y, and z, then xyx+1 cannot be a multiple of any of them.

Answer: D.


This is a much easier way..Thanks for the explanation :-D
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 03:03
Expert's post
karishmatandon wrote:
Zarrolou wrote:

Why D?
Every prime number except 2 is odd.
In case you pick 2, xyz + 1=E*O*O +1=Odd and an ODD number cannot be a multiple of 2
In case you DO NOT pick 2 (you have only odd numbers), xyz + 1=O*O*O +1=Even and en EVEN number cannot be a multiple of an ODD number.


I used picking numbers strategy and was down to D and E..couldn't figure out a way from there! Thanks this helps..

Bunuel wrote:
xyz and xyx+1 are are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Since xyz is a multiple of each x, y, and z, then xyx+1 cannot be a multiple of any of them.

Answer: D.


This is a much easier way..Thanks for the explanation :-D


Note that Zarrolou's way to discard D is not 100% correct: if-x-y-and-z-are-3-different-prime-numbers-which-of-the-153338.html#p1229032
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 03:07
Bunuel wrote:
Your logic to discard D is not correct.

Yes, if one of the primes is 2, then xyz + 1=E*O*O +1=Odd and an odd number cannot be a multiple of an even number but it could be a multiple of remaining odd primes.

Hope it's clear.


Maybe I misunderstood the question...

If I pick E, O, O, I get as result of D an ODD number.
So an ODD number can be a multiple of the two odds (of course it can), but since the question asks CANNOT be a multiple of any, if one of the values is Even, then an odd number cannot a multiple of an even one.

Is this reasoning flawed?
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 25 May 2013, 03:11
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Zarrolou wrote:
Bunuel wrote:
Your logic to discard D is not correct.

Yes, if one of the primes is 2, then xyz + 1=E*O*O +1=Odd and an odd number cannot be a multiple of an even number but it could be a multiple of remaining odd primes.

Hope it's clear.


Maybe I misunderstood the question...

If I pick E, O, O, I get as result of D an ODD number.
So an ODD number can be a multiple of the two odds (of course it can), but since the question asks CANNOT be a multiple of any, if one of the values is Even, then an odd number cannot a multiple of an even one.

Is this reasoning flawed?


The correct option must not be a multiple of ANY of the three variables, so if it could be a multiple of some of them, then it's not the right choice.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 05 Sep 2013, 22:10
Bunuel wrote:
Zarrolou wrote:
Bunuel wrote:
Your logic to discard D is not correct.

Yes, if one of the primes is 2, then xyz + 1=E*O*O +1=Odd and an odd number cannot be a multiple of an even number but it could be a multiple of remaining odd primes.

Hope it's clear.


Maybe I misunderstood the question...

If I pick E, O, O, I get as result of D an ODD number.
So an ODD number can be a multiple of the two odds (of course it can), but since the question asks CANNOT be a multiple of any, if one of the values is Even, then an odd number cannot a multiple of an even one.

Is this reasoning flawed?


The correct option must not be a multiple of ANY of the three variables, so if it could be a multiple of some of them, then it's not the right choice.



Hi,

If i pick the numbers as x=3 y=5 z=7

then to discard
1) x+y = 3+5=8 this is not divisible by any of 3 numbers

Same applies for other options too.

Pls tell me where i am wrong.

Thanks in Advance,
Rrsnathan.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 05 Sep 2013, 22:33
Expert's post
rrsnathan wrote:
Bunuel wrote:
Zarrolou wrote:
Maybe I misunderstood the question...

If I pick E, O, O, I get as result of D an ODD number.
So an ODD number can be a multiple of the two odds (of course it can), but since the question asks CANNOT be a multiple of any, if one of the values is Even, then an odd number cannot a multiple of an even one.

Is this reasoning flawed?


The correct option must not be a multiple of ANY of the three variables, so if it could be a multiple of some of them, then it's not the right choice.



Hi,

If i pick the numbers as x=3 y=5 z=7

then to discard
1) x+y = 3+5=8 this is not divisible by any of 3 numbers

Same applies for other options too.

Pls tell me where i am wrong.

Thanks in Advance,
Rrsnathan.


The question asks which of the options CANNOT be a multiple of any of x, y, and z in ANY case. Four options will not be multiples in SOME cases (not all) and only one of the options CANNOT be a multiple in ANY case.

Does this make sense?
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 05 Sep 2013, 23:44
Quote:
The question asks which of the options CANNOT be a multiple of any of x, y, and z in ANY case. Four options will not be multiples in SOME cases (not all) and only one of the options CANNOT be a multiple in ANY case.

Does this make sense?



Yeah Bunuel i got it.
It CAN be a multiple of any of X,Y and Z but we need the option that is CANNOT be a multiple in ANY case(ANY Prime number).
Thanks a lot
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 11 Nov 2013, 01:35
A prime number cannot be a multiple of another prime number. How can i apply this logic in this case?
Odd number cannot be a multiple of an even number. Is it always true? 3 is multiple of 6...
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 11 Nov 2013, 01:42
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monirjewel wrote:
A prime number cannot be a multiple of another prime number. How can i apply this logic in this case?
Odd number cannot be a multiple of an even number. Is it always true? 3 is multiple of 6...


3 is a factor of 6, not a multiple.

An odd number is not divisible by 2, thus it cannot be a multiple of even number.
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If x, y, and z are 3 different prime numbers, which of [#permalink] New post 13 Jan 2014, 04:10
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?
x + y
y – z
xy + 1
xyz + 1
x^2 + y^2

Possible solution
[Reveal] Spoiler:
(e.g.) If x= 2, y = 3, z = 5
(E): If x = 2 & y = 5, → (x2 + y2) = (4 + 25) = 29 & z could be 29 → Wrong
(D): If x = 2 & y = 3 & z = 7, → (xyz + 1) = (2 x 3 x 7 + 1) = (42 + 1) = 43
Since used up all variables (x, y, z) to plug-in, cannot be a multiple of x, y or z. → Answer
(C): If x = 2 & y = 3, → (xy + 1) = (2 x 3 + 1) = (6 + 1) = 7, z can be 7. → Wrong
(B): If y = 5 & z = 2, → (y – z) = (5 – 2) = 3. x could be 3 → Wrong
(A): If x = 2 & y = 3, → (x + y) = (2 + 3) = 5. z could be 5 → Wrong

Hi,
Can we say, because only (D) has all 3 variables (x, y, z), this is the answer?
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Re: If x, y, and z are 3 different prime numbers, which of [#permalink] New post 13 Jan 2014, 05:19
Expert's post
goodyear2013 wrote:
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?
x + y
y – z
xy + 1
xyz + 1
x^2 + y^2

Possible solution
[Reveal] Spoiler:
(e.g.) If x= 2, y = 3, z = 5
(E): If x = 2 & y = 5, → (x2 + y2) = (4 + 25) = 29 & z could be 29 → Wrong
(D): If x = 2 & y = 3 & z = 7, → (xyz + 1) = (2 x 3 x 7 + 1) = (42 + 1) = 43
Since used up all variables (x, y, z) to plug-in, cannot be a multiple of x, y or z. → Answer
(C): If x = 2 & y = 3, → (xy + 1) = (2 x 3 + 1) = (6 + 1) = 7, z can be 7. → Wrong
(B): If y = 5 & z = 2, → (y – z) = (5 – 2) = 3. x could be 3 → Wrong
(A): If x = 2 & y = 3, → (x + y) = (2 + 3) = 5. z could be 5 → Wrong

Hi,
Can we say, because only (D) has all 3 variables (x, y, z), this is the answer?


Merging similar topics. Please refer to the solutions above.
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Re: If x, y, and z are 3 different prime numbers, which of the [#permalink] New post 15 Jan 2014, 22:41
karishmatandon wrote:
If x, y, and z are 3 different prime numbers, which of the following CANNOT be a multiple of any of x, y, and z?

A. x + y
B. y – z
C. xy + 1
D. xyz + 1
E. x^2 + y^2


Let us say x = 2, y = 3 and z = 5

A. 5 (ELIMINATED)
B. -2 (ELIMINATED)
C. 7
D. 31
E. 4 + 9 = 13

Let us say x = 7, y = 11 and z = 2
C. 77 + 1 = 78 (ELIMINATED)
D. 155
E. 49 + 121 = 170 (ELIMINATED)

Answer is D
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Re: If x, y, and z are 3 different prime numbers, which of the   [#permalink] 15 Jan 2014, 22:41
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