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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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Updated on: 17 Sep 2017, 05:53
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"
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe
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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 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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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe
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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
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe
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14 Jan 2019, 11:21
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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
Target question:Is the range of the numbers in S less than 4? ASIDE: Range = (greatest value) - (least value)
KEY CONCEPT: If the range of a set containing 2 values = k, then adding additional values to the set cannot decrease the range. For example, the set {3, 10} has a range of 7 If we add more values to the set, we cannot make the range less than 7
Statement 1: x > w + 4 Subtract w from both sides to get: x - w > 4 This us tells us that the range of the set {x, w} is already greater than 4 So, if we add y and z, the range of the set {w, x, y, z} MUST be greater than 4 So, the answer to the target question is NO, the range is NOT less than 4 Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: y – 5 > z Add 5 to both sides to get: y > z + 5 Subtract z from both sides to get: y - z > 5 This us tells us that the range of the set {y, z} is already greater than 5 So, if we add w and x, the range of the set {w, x, y, z} MUST be greater than 5 So, the answer to the target question is NO, the range is NOT less than 4 Since we can answer the target question with certainty, statement 2 is SUFFICIENT