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

Question

Is x > y > z ?

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

GMATinsight · Answer

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

GinoRako · Answer

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!

Bunuel · Answer

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.

GinoRako · Answer

Bunuel

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

Thanks again!

SaquibHGMATWhiz · Answer

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 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

bumpbot · Answer

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

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