Data Sufficiency

Brent@GMATPrepNow wrote:

If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y

Target question: Is z between x and y?

Statement 1: x < 2z < y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 3, y = 10, and z = 2, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2x < z < 2y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 1, y = 2, and z = 3, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: x < 2z < y
Statement 2: 2x < z < 2y
Since the two inequalities are facing the same direction, we can add them to get:
3x < 3z < 3y
Divide all three parts by 3 to get: x < z < y
As we can see, z IS definitely between x and y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent@GMATPrepNow wrote:

a_new_start wrote:
Dear Brent,

What if we are unable to think of the values of x, y and z under exam pressure.

Any other way to tackle this question.

When statements are not sufficient, it can often be difficult to show that they are not sufficient using means other than PLUGGING IN.
Here, each statement contains very little information, so I can't see any options other than plugging in.

Fortunately, with the statements combined, we have something to work with.

Cheers,
Brent

a_new_start wrote:

If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y

What if we are unable to think of the values of x, y and z under exam pressure.

Any other way to tackle this question.

GMATGuruNY wrote:

a_new_start wrote:

If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y

What if we are unable to think of the values of x, y and z under exam pressure.

Any other way to tackle this question.

One suggestion:
Since the question stem asks whether z is between x and y, test values for x and y that are SPREAD OUT.
Let x=10 and y=100.

Statement 1: x < 2z < y
Substituting x=10 and y=100, we get:
10 < 2z < 100
5 < z < 50.
If z=20, then z is between x and y.
If z=6, then z is NOT between x and y.
INSUFFICIENT.

Statement 2: 2x < z < 2y
Substituting x=10 and y=100, we get:
2*10 < z < 2*100
20 < z < 200.
If z=30, then z is between x and y.
If z=150, then z is NOT between x and y.
INSUFFICIENT.

Statements combined:
Adding together x < 2z < y and 2x < z < 2y, we get:
x+2x < 2z+z < y+2y
3x < 3z < 3y
x < z < y.
SUFFICIENT.

The correct answer is C.