If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value

How can I more quickly translate all of these fractions to see which ones qualify?

Hi All,

In certain Quant questions, the ability to convert information from one 'format' to another can be quite helpful (and sometimes it's even required!). This is meant to say that knowing your fraction-to-decimal conversions (from 1/2 to 1/11) will make answering a handful of questions considerably easier on the Official GMAT.

In this prompt, we're told that Z is equal to one of the numbers 3/5, 5/8 or 2/3. This means that Z is one of the following: .6, .625 or .66666666. We're asked for the value of Z.

1) 1/2 < Z < 2/3

This Fact now tells us that .5 < Z < .6666666

With the range provided by this Fact, we know that Z can be EITHER .6 or .625
Fact 1 is INSUFFICIENT

2) 5/9 < z < 5/6

The interesting thing about this Fact is that it provides us with an interesting Number Property 'shortcut.' If you want to do the math, then you'll get a range of .5555555 < Z < .8333333

However, you don't actually have to do all of that work. The largest of the 3 possible values of Z is 2/3, which equals 4/6. Since 5/6 is GREATER than 4/6, we know that the upper-end of this range is bigger than ALL 3 possible values of Z.

With the range provided by this Fact, we know that Z can be ANY of the three values (.6, .625 or .66666)
Fact 2 is INSUFFICIENT

Combined, we have two values that "overlap" (.6 and .625).
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

If struggling with fraction then,
STEP1- Take LCM of 9,8,6,5 i.e. 360
STEP2- Convert fractions into integers by multiplying all of them with 360
3/5 becomes 216, 5/8 becomes 225 similarily
2/3-- 240
1/2-- 180
5/9--200
5/6--300
Statement 1
180<z<240
so z can be 216 or 225 insuff

Satement 2-

200<z<300
so z can be 216, 240, 225
Insuff

Togther
180< z< 300
Still insuff