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

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value  [#permalink]

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20 Dec 2015, 03:54
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Difficulty:

25% (medium)

Question Stats:

84% (02:09) correct 16% (02:00) wrong based on 76 sessions

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

(1) 1/2 < z < 2/3
(2) 5/9 < z < 5/6

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Posts: 7106
Re: If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value  [#permalink]

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21 Dec 2015, 03:04
Bunuel wrote:
If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value of z?

(1) 1/2 < z < 2/3
(2) 5/9 < z < 5/6

hi ,
in these we should equalize the denominator to check the relative values,,..
z is equal to one of the numbers 3/5, 5/8 or 2/3
(1) 1/2 < z < 2/3
z can be 3/5, 5/8 insuff
(2) 5/9 < z < 5/6
z can be any of the three .. insuff

combined two values 3/5, 5/8 possible.. insuff
ans E
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Re: If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value  [#permalink]

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21 Dec 2015, 07:36
3/5, 5/8 or 2/3, what is the value of z?

(1) 1/2 < z < 2/3
z cannot be 2 value 3/5 or 5/8...Insuff
(2) 5/9 < z < 5/6
z cannot be 3 values 3/5, 5/8 or 2/3...Insuff

combining both ...Insuff

Ans: E
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Re: If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value  [#permalink]

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15 Jan 2016, 11:09
How can I more quickly translate all of these fractions to see which ones qualify?
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Re: If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value  [#permalink]

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23 Jan 2016, 19:06
1
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

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Re: If z is equal to one of the numbers 3/5, 5/8 or 2/3, what is the value &nbs [#permalink] 23 Jan 2016, 19:06
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