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Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny

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Bunuel
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Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   29 Jan 2020, 02:00
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Is x > y > z ?

(1) x, y, and z are consecutive integers.
(2) nx > ny > nz, where n is an integer.
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E
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   29 Jan 2020, 05:34
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Bunuel wrote:
Is x > y > z ?

(1) x, y, and z are consecutive integers.
(2) nx > ny > nz, where n is an integer.


Question: Is x > y > z ?

Statement 1: x, y, and z are consecutive integers.

It doesn't ensure the order of their magnitude hence

NOT SUFFICIENT

Statement 2: nx > ny > nz, where n is an integer

Case 1: @n = 1, x = 3, y = 2, z = 1 i.e. x > y > z
Case 2: @n = -1, x = -3, y = -2, z = -1 i.e. x < y < z

NOT SUFFICIENT

Combining the two statements

Case 1: @n = 1, x = 3, y = 2, z = 1 i.e. x > y > z
Case 2: @n = -1, x = -3, y = -2, z = -1 i.e. x < y < z

NOT SUFFICIENT

Answer: Option E
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   04 Jan 2023, 02:32
Why is statement 1 not sufficient?

If X,Y,and Z are consecutive integers, then they could be 1,2,3 or -1,0,1 or -3,-2,-1?

What does consecutive integers otherwise mean than the above sets?

What do you mean when you say: It doesn't ensure the order of their magnitude hence Can you please elaborate on the meaning of ensuring the order of magnitude?

Thanks in advance!
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   04 Jan 2023, 03:09
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GinoRako wrote:
Why is statement 1 not sufficient?

If X,Y,and Z are consecutive integers, then they could be 1,2,3 or -1,0,1 or -3,-2,-1?

What does consecutive integers otherwise mean than the above sets?

What do you mean when you say: It doesn't ensure the order of their magnitude hence Can you please elaborate on the meaning of ensuring the order of magnitude?

Thanks in advance!


The point here is that x, y, and z are consecutive integers does not necessarily mean that x < y < z. They can be in any order:

x < y < z;
x < z < y;
y < x < z;
y < z < y;
z < x < y;
z < y < x.

Hope it's clear.
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   04 Jan 2023, 03:40
Bunuel

I got it! Thank you for your detailed explanation. To be honest, i overlooked that part.

Thanks again!
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   04 Jan 2023, 07:53
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Bunuel wrote:
Is x > y > z ?

(1) x, y, and z are consecutive integers.
(2) nx > ny > nz, where n is an integer.


Solution:
Pre Analysis:
  • We are asked if \(x>y>z\)

Statement 1: x, y, and z are consecutive integers
  • According to this statement, let us take 2 cases into consideration:
  • Case 1:x = 3, y = 2, z = 1
    • In this case, we can say \(x>y>z\)
  • Case 2:x = 1, y = 2, z = 3
    • In this case, we can say \(x<y<z\)
  • This statement is a TRAP!! Consecutive integers don't mean in any order
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: \(nx > ny > nz\), where n is an integer
  • This statement is again a TRAP!!
  • You might want to cancel the n in the inequality and write it as \(x>y>z\)
  • However, that would be incorrect
  • Becasue if n is negative, then the sign would change
  • Thus, statement 2 alone is also not sufficient

Combining:
  • Even after combining, we cannot say if \(x>y>z\) or \(x<y<z\)
  • Because we do not know the positive negative nature of n

Hence the right answer is Option E
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink] New post   17 Jan 2024, 03:33
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Re: Is x > y > z ? (1) x, y, and z are consecutive integers. (2) nx > ny [#permalink]
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