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

Question

-10, 3, 5, x, y

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

(2) x does not equal y

BrentGMATPrepNow · Answer

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:  A

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Shruti0805 · Answer

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.

ShreyansJ · Answer

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

Kritesh · Answer

could some one provide me an explanation for the answer ? i got the answer as E.

ydmuley · Answer

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.

Leo8 · Answer

FullSizeRender (10).jpg A

GMATYoda · Answer

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.

sdas80923 · Answer

Is it a given fact that x and y cannot be equal here? Since the answer won't be A without this assumption.

Bunuel · Answer

x = y is not possible under statement (1), because in that case the list cannot have exactly two modes. If x = y, the list would have only one mode, not two.

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

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

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