Set A = , If the median is x/2, what is x

Question

Set A =  ,
If the median is x/2, what is x?

GMATBLACKBELT · Answer

are these in order by value? or is it just random? I don't see how it could be in order by value b/c that would mean x/2=1 and x=2, which wouldnt make any sense at all.

I get 0=x

b/c if we have -1,-x... then x must be less than 1 so---> -1,-x,x,1,3 thus x=x/2 --> 2x=x Only way this can be is if x=0.

solaris1 · Answer

I am assuming x is an integer.

If the median of a set of 5 integers is x/2, then x/2 is the "middle" integer when all integers are arranged in increasing order.

so we have, -1, 1, x/2, 3, x. x must logically be the largest integer in the set if x/2 is the median.

Therefore, x must be 4.

Part of me thinks this was almost too easy, so please correct me if I made a mistake somewhere.

walker · Answer

Set A =

Set A have 5 numbers, Therefore, median is defined by one number: 1 or x (x<1)

1) x/2=1 ==> x=2
2) x/2=x ==> x=0

solaris1 · Answer

Wait, so Set A is already arranged in increasing order?

bmwhype2 · Answer

can you elaborate? if x=0, then 0/2 because median is is x/2

incognito1 · Answer

can you provide the answer choices?

0 and 2 both seem to work..

bmwhype2 · Answer

this is part of a DS question. both are correct. i just want to see how the answer came about.

walker · Answer

I guess choices are like I. 0 II 1 III 2 A only I B only II C I and III D II and III E I, II and III

GMATBLACKBELT · Answer

Ah yes, 2 can be an answer as well. -2,-1,1,2,3 And thus 2/2=1 is the median.

or -1,0,0,1,3. But in either case the original is not in the correct increasing order.

Haven't done a question quite like this before. whats the source?

incognito1 · Answer

lol didn't realize this was a DS question

pmenon · Answer

i just assumed that set was already in increasing order. since there are an odd number of terms, the median is equal to 1, and if 1=x/2, that leads to x=2 .... am i oversimplifying this q ?

bmwhype2 · Answer

thanks. finally figured out the logic... :-D

maratikus · Answer

x >= 0 because there are at least 3 numbers that are greater or equal than 0 and x/2 is the median.

1) x - median -> x = x/2 -> x = 0
2) 1 - median -> x/2 = 1 -> x = 2

there are no other options because the median is greater or equal than zero and it can't be equal to 3 because there are at least 3 numbers smaller than 3.

jimmyjamesdonkey · Answer

I assumed this set wasn't in order. and the value of x was the same integer. for -x equals -2 and x = 2. so I rearranged..

Set A = ( -2, -1, 1, 2, 3)

Median being 1.

Set A = , If the median is x/2, what is x

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