XYZ

[grandh01]

If x, y, and z are three integers, are
they consecutive integers?
(1) z - x = 2
(2) x < y < z

OA is C

[niketdoshi123]

If x, y, and z are three integers, are
they consecutive integers?
(1) z - x = 2
(2) x < y < z

OA is C

If x, y, and z are three integers, are
they consecutive integers?
(1) z - x = 2
(2) x < y < z

OA is C

statement 1:
z-x = 2
we don't know anything about y
let z = 4
since z - x = 2 , x = 2
y can be 5 , in which case 2,4 & 5 are not consecutive integers. NO
y can be 3 , in which case 2,3 & 4 are consecutive integers. YES

Hence the statement is insufficient

Statement 2:

x<y<z
2<4<6 Not consecutive integers but satisfy the equation. NO
2<3<4 Consecutive integers and satisfy the equation. YES

Hence the statement is insufficient

Combining both the statement

Since x,y&z are integers , z - x = 2 and x<y<z
therefore z - y (must be) = 1 to satisfy all the above conditions.

Hence x, y & z are consecutive integers.
Sufficient

The correct answer is C

[Anurag@Gurome]

If x, y, and z are three integers, are
they consecutive integers?
(1) z - x = 2
(2) x < y < z

OA is C

(1) z - x = 2 or z = x + 2
So, 3 integers are x, y, and x + 2, but we do not know the relation between x and y. So, it is difficult to answer whether x, y, and z are consecutive integers; NOT sufficient.

(2) x < y < z
There are many possibilities that satisfy this condition, viz., 2, 4, 6 (here the 3 integers are consecutive), OR, 1, 10, 40 (here the 3 integers are not consecutive).
No definite answer; NOT sufficient.

Combining (1) and (2), we get, x < y < x + 2
It is given that x, y, and z are integers, so the only possibility is that the 3 integers are: x , x + 1, x + 2.
Hence the 3 integers are consecutive; SUFFICIENT.

The correct answer is C.

[alex.gellatly]

If x, y, and z are three integers, are
they consecutive integers?
(1) z - x = 2
(2) x < y < z

Statement 1 is insufficient because it tells us nothing about y

Statement 2 is insufficient because z, y, and z could take on any values to satisfy the conditions.

Together it is a little tricky. One might want to say together they are still both insufficient. However, if you start plugging in values to satisfy the conditions you will quickly find that they are indeed consecutive. For example;

Take any number for z... say 4

(From 1) z=x+2, so x = 2. There is only 1 integer in between for y (3) to satisfy statement 2.

Another example say z = 10, so x=8... again only one integer in between for y (9)

Does this help? In my opinion its always a good idea to plug in values and see where you again. The GMAT loves to trick us!

[Scott@TargetTestPrep]

If x, y, and z are three integers, are
they consecutive integers?
(1) z - x = 2
(2) x < y < z

OA is C

Solution:

Question Stem Analysis:

We need to determine whether x, y, and z are consecutive integers.

Statement One Alone:

Since we don’t know anything about y, statement one alone is sufficient.

Statement Two Alone:

Even though we know the order of the three integers, we can’t determine whether x, y, and z are consecutive integers. Statement two alone is not sufficient.

Statements One and Two Together:

Since z - x = 2 and x < y < z, y = x +1 and z = x + 2. This makes the three integers consecutive integers. Both statements together are sufficient.

Answer: C