If the range of the set containing the numbers x, y, and z

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, \(\frac{x+y+z+8}{4}=12.5\) --> \(x+y+z+8=4*12.5=50\) --> \(x+y+z=42\).

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.

Hope it's clear.

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.

Bunuel VeritasKarishma

If the question statement would have specified to find the least possible value of the smallest number then the answer would be choice 'A', right ?

And the value of the smallest number in that case would be 0.

Please correct me if I am wrong.

Thanks
Saurabh

Saurabh,

Note that minimum/maximum values of variables may not make sense in DS questions.
Say the question is what is the smallest value of integer x?
Stmnt 1: x is a positive integer.
Smallest value of x is 1.
Stmtn 2: x > 10
Smallest value of x is 11. As you get more information, your answer may be different.
Hence, the DS question may not make a lot of sense.


Additionally, in our original question, using stmnt 1 alone, the smallest possible value of x is not 0.

Range of x, y, z = 8
Say z is the greatest number and x the smallest.
x = z - 8 and y must lie between x and z.

Mean of x, y, z, 8 = 12.5
Note that 8 is already 4.5 less than 12.5. So there needs to be atleast one number greater than 12.5
If x needs the smallest value, z needs to be greatest but z cannot be 8 more than x. We need to maximise positive deviation so y = z

x + (x + 8) + (x + 8) = 42
x = 8.667

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