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If the range of the set containing the numbers x, y, and z [#permalink]
05 Feb 2012, 15:31

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Difficulty:

65% (hard)

Question Stats:

59% (02:48) correct
41% (01:44) wrong based on 107 sessions

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

Let the numbers in ascending order be {x, y, z} (it really doesn't matter how we group them).

The range of a set is the difference between the largest and smallest elements in the set. Given: \(z-x=8\). Question: \(x=?\)

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5 --> \(x+y+z+8=4*12.5=50\) --> \(x+y+z=42\): 2 distinct linear equations 3 with unknowns. Not sufficient.

(2) The mean and the median of the set containing the numbers x, y, and z are equal --> \(mean=\frac{x+y+z}{3}=y=median\) --> \(x+z=2y\): 2 distinct linear equations with 3 unknowns. Not sufficient.

(1)+(2) 3 distinct linear equations with 3 unknowns --> we can solve for \(x\). Sufficient.

Re: If the range of the set containing the numbers x, y, and z [#permalink]
14 Jul 2012, 02:45

Expert's post

mohan514 wrote:

hello sir..

here when you have calculated the mean .. as per the data in 1st option mean should include 8 in the set and its value is 12.5

but you have excluded it... can you just let me know where i am goin wrong

please explain me about the relation between mean and median.....

I don't understand what you mean.

(1) says: The average of the set containing the numbers x, y, z, and 8 is 12.5. So, \(\frac{x+y+z+8}{4}=12.5\) --> \(x+y+z+8=4*12.5=50\) --> \(x+y+z=42\). _________________

if the range of the set containing the numbers x, y, and z [#permalink]
15 Sep 2012, 06:47

if the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

Re: if the range of the set containing the numbers x, y, and z [#permalink]
15 Sep 2012, 07:00

Expert's post

adineo wrote:

if the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

Merging similar topics. Please refer to the solution above. _________________

Re: If the range of the set containing the numbers x, y, and z [#permalink]
15 Sep 2012, 07:10

I had a doubt regarding option A:

In that we are given that x + y+ z = 42 and also that range is 8.

Now lets say smallest number is x and largest is z then equation is (x) + (x+n) + (x+8). Where 0<n<8 .

isnt this constraint enough to give us the required answer? Since we are just looking for the smallest number, for finding the middle number we will need another equation.

Re: If the range of the set containing the numbers x, y, and z [#permalink]
15 Sep 2012, 07:20

1

This post received KUDOS

Expert's post

adineo wrote:

I had a doubt regarding option A:

In that we are given that x + y+ z = 42 and also that range is 8.

Now lets say smallest number is x and largest is z then equation is (x) + (x+n) + (x+8). Where 0<n<8 .

isnt this constraint enough to give us the required answer? Since we are just looking for the smallest number, for finding the middle number we will need another equation.

From (1) we can have many options, for example: {10, 14, 18} or {11, 12, 19}, therefore this statement is not sufficient.

Re: If the range of the set containing the numbers x, y, and z [#permalink]
21 Sep 2014, 17:41

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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If the range of the set containing the numbers x, y, and z [#permalink]
22 Sep 2014, 08:26

calreg11 wrote:

If the range of the set containing the numbers x, y, and z is 8, what is the value of the smallest number in the set?

(1) The average of the set containing the numbers x, y, z, and 8 is 12.5. (2) The mean and the median of the set containing the numbers x, y, and z are equal.

C.

did it like this

1) x+y+z+8 = 50 => x+y+z = 42 and |x-z| = 8 so, sets can be: {8,16,16}, {9,15,17}, {10,14,18}, {11,13,19}, and {12,12,20} A is insufficient.

2) (x+y+z)/3 = y => x+z = 2y and |x-z| = 8 B is insufficient.

(1)+(2) among the sets in (1) the sets which have x+z = 2y is {10,14,18} hence C. _________________

Illegitimi non carborundum.

gmatclubot

If the range of the set containing the numbers x, y, and z
[#permalink]
22 Sep 2014, 08:26

Good news for globetrotting MBAs: travel can make you a better leader. A recent article I read espoused the benefits of traveling from a managerial perspective, stating that it...