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If S is a set of four numbers x, y, z and w, is the range of the numbe

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If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]

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New post 17 Sep 2017, 03:14
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

44% (00:50) correct 56% (00:46) wrong based on 27 sessions

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Kudos [?]: 129035 [0], given: 12187

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Joined: 09 Mar 2017
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WE: Information Technology (Computer Software)
If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]

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New post 17 Sep 2017, 04:03
Bunuel wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S less than 4?

(1) x > w + 4
(2) y – 5 > z


statement 1 : x > w + 4
or x-w > 4 ------> difference of first number in the series and the last number is positive and > 4.This tells us that x>w
So this is a series arranged in descending order.
So range would be greatest number - smallest number i.e. (x-w)
So stem asks "is (x-w)<4"
So the answer is No with statement 1.
Sufficient

Statement 2:: y – 5 > z
or y - z> 5.
States that y>z ----> again implies that series is in descending order.
Secondly, if the difference between intermediate numbers in a set of four arranged in descending order, is greater than 4 then surely the difference between the largest and smallest number must be greater than 5. Even if the stem would have stated distinct integers, the range wouldn't have still been less than 4.
This provides an answer No, the range is not less than 4.
Sufficient

"D"
_________________

------------------------------
"Trust the timing of your life"


Last edited by TaN1213 on 17 Sep 2017, 05:53, edited 2 times in total.

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]

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New post 17 Sep 2017, 04:11
TaN1213 wrote:
Bunuel wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S less than 4?

(1) x > w + 4
(2) y – 5 > z


While our mind tends to assume that the series is arranged from lowest to largest value, there is no explicit mention of this in the question.

Statement 1 : x > w + 4
The essence of this question is the uncertainty whether the series is arranged in Ascending order or Descending order i.e
we have two cases
case 1:: x<w -- Series is arranged in Ascending order
Range is Greatest number - smallest number = w - x
then rephrase the stem as "Is (w-x < 4)?
statement 1--> x> w+ 4
or x-w >4
or w - x < -4
this provides us with a 'Yes' to the rephrased question.

But, for case2 ::x>w -- Series is arranged in Descending Order
Range is Greatest number - smallest number = x - w
the rephrased question becomes "is (x-w) < 4 ? "
statement 1---> x-w >4
We get an answer "No" to the rephrased question

Since we cannot determine from statement 1 which case to choose from, statement 1 is insufficient .


Statement 2:: y – 5 > z
or y > z+5.
Clearly insufficient as no information about the greatest and smallest number is given to find out the range.

Combining statement (1) & (2)
This tells us that 'y' is certainly greater than 'z'. This further tells us that the series is arranged in Descending order. So statement 1 & 2 together gives us the information to select case 2(previously explained) and hence come to a definite answer.

"C"

Hi tan1213,
Can you pls help me in understanding the Part 1 of statement 1..
I am unable to hold the case ... I mean can u pls take any number and then use it ..

Thanks in advance !!!!

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]

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New post 17 Sep 2017, 04:12
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X>w holds good for my understanding.. but unable to grasp the case when x<w...

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]

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New post 17 Sep 2017, 05:35
kumarparitosh123 wrote:
X>w holds good for my understanding.. but unable to grasp the case when x<w...

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app


hello kumarparitosh123,

Thanks a lot for pointing out the fault in my reasoning. Have edited my explanation and +1 to you for helping me learn through my mistake.
_________________

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"Trust the timing of your life"

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe [#permalink]

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New post 18 Sep 2017, 10:45
should not the answer will be "E" ?

As the range in a set is difference of smallest number and the highest number and by using both the statement we can not deduce which is highest and which one is smallest

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe   [#permalink] 18 Sep 2017, 10:45
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