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For the list of numbers above, what is the range?

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For the list of numbers above, what is the range?  [#permalink]

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New post 20 May 2017, 04:25
2
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (00:56) correct 41% (00:45) wrong based on 167 sessions

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Re: For the list of numbers above, what is the range?  [#permalink]

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New post 20 May 2017, 04:50
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1
Bunuel wrote:
-10, 3, 5, x, y

For the list of numbers above, what is the range?


(1) The list of numbers has exactly two modes.

(2) x does not equal y


Target question: What is the range?

Given: Set = {-10, 3, 5, x, y}

Statement 1: The list of numbers has exactly two modes.
This tells us that x must equal one of -10, 3, 5, and y must also equal one of -10, 3, 5, BUT X AND Y ARE DIFFERENT VALUES
For example, it COULD be that x = -10 and y = 3, in which case the set = {-10, 3, 5, -10, 3}. In this case, the modes are -10 and 3, and the range = 5 - (-10) =15
Or it COULD be that x = 5 and y = -10, in which case the set = {-10, 3, 5, 5, -10}. In this case, the modes are 5 and -10, and the range = 5 - (-10) =15
Or it COULD be that x = 3 and y = 5, in which case the set = {-10, 3, 5, 3, 5}. In this case, the modes are 3 and 5, and the range = 5 - (-10) =15
etc.
Since x and y are equal to the values -10, 3, and 5, the range will ALWAYS equal 5 - (-10) =15
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x does not equal y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = -10 and y = 3, in which case the set = {-10, 3, 5, -10, 3}. In this case, the range = 5 - (-10) =15
Case b: x = -100 and y = 200, in which case the set = {-10, 3, 5, -100, 200}. In this case, the range = 200 - (-100) =300
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

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Re: For the list of numbers above, what is the range?  [#permalink]

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New post 29 May 2017, 22:55
Bunuel wrote:
-10, 3, 5, x, y

For the list of numbers above, what is the range?


(1) The list of numbers has exactly two modes.

(2) x does not equal y



Stmt 1 : There are exactly 2 modes. As there are a total of 5 numbers, 2 of those are repeated twice and 1 of them is present once.

Range is basically the diff. between the max and min. value. Min. out of the 3 mentioned is -10 and max. is 5.
Whatever be the mode, range would be the same as the values are fixed.


Lets take a few scenarios-

Case 1 : Let -10 and 3 be the modes.
Set = {-10, -10, 3, 3, 5} --> Range = 15

Case 2 : Let -10 and 5 be the modes.
Set = {-10, -10, 3, 5, 5} --> Range = 15

Case 3 : Let 3 and 5 be the modes.
Set = { -10, 3, 3, 5, 5} --> Range = 15

Sufficient.


Stmt 2 : x != y
Clearly insufficient as doesnt give any data points on the values of x and y.

Option A.
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Re: For the list of numbers above, what is the range?  [#permalink]

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New post 05 Jun 2017, 21:38
My approach is bit simple.

given -10, 3, 5, x, y.
St 1: the list has two modes that means X and Y can take any of the three values from the list but not an outside number. In any case the least no will remain -10 and highest number will remain 5. So, range will be the same. Hence, Sufficient. Possible Ans A or D
St 2: X !=Y Clearly insufficient.
So Answer is A
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Re: -10, 3, 5, x, y - For the list of numbers above, what is the range?  [#permalink]

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New post 09 Jul 2017, 07:58
could some one provide me an explanation for the answer ? i got the answer as E.
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Re: -10, 3, 5, x, y - For the list of numbers above, what is the range?  [#permalink]

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New post 09 Jul 2017, 08:02
OFFICIAL EXPLANATION By Veritas

The correct answer is A. In order for this list of numbers to have exactly two modes (as statement 1 states), when the given information includes three, unique, known values and two variables, x and y must each match a different known number. That would mean that each of two known values appears exactly twice, making those two values the modes.

If x and y were each unique values that did not match a value already known, there would be no mode to the set. If x equaled y but neither matched a value already known, then that x and y would form the single mode, and there would not be a second.

So in order for statement 1 to be true, x and y must match already known values. Bringing that back to the exact question, that would mean that the list only includes the values -10, 3, and 5 (with duplicates of two of those three), so the range would have to be 5 - (-10) = 15.

Statement 2 is not sufficient: leaving out the information from statement 1, statement 2 still allows x and y to be any value (as long as they don't match each other), so you cannot put a limit on the least or greatest value, and the range still has infinite potential values.
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Re: -10, 3, 5, x, y - For the list of numbers above, what is the range?  [#permalink]

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For the list of numbers above, what is the range?  [#permalink]

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New post 26 Sep 2018, 09:01
The correct answer is A. In order for this list of numbers to have exactly two modes (as statement 1 states), when the given information includes three, unique, known values and two variables, x and y must each match a different known number. That would mean that each of two known values appears exactly twice, making those two values the modes.

If x and y were each unique values that did not match a value already known, there would be no mode to the set. If x equaled y but neither matched a value already known, then that x and y would form the single mode, and there would not be a second.

Quote:
So in order for statement 1 to be true, x and y must match already known values. Bringing that back to the exact question, that would mean that the list only includes the values -10, 3, and 5 (with duplicates of two of those three), so the range would have to be 5 - (-10) = 15.


Quote:
Statement 2 is not sufficient: leaving out the information from statement 1, statement 2 still allows x and y to be any value (as long as they don't match each other), so you cannot put a limit on the least or greatest value, and the range still has infinite potential values.

Quote:
Take Away: Adding the same value to the set never changes the range

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For the list of numbers above, what is the range? &nbs [#permalink] 26 Sep 2018, 09:01
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