If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x

Question

If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?

A. 3
B. 4
C. 5
D. 6
E. 8

BrentGMATPrepNow · Accepted Answer

The big hints are that  x is a 1-digit integer  AND (4/3)x, 2x, x, and x + 2, and 3x – 2 are ALL  integers  
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9. 
Now let's plug each possible value of x into the terms and see which one yields a list of  consecutive integers

When x =  3 , we get the following terms: (4/3)( 3 ), 2( 3 ),  3 ,  3  + 2, and 3( 3 ) – 2. 
When we evaluate these terms we get: 4, 6, 3, 5 and 7
Rearrange to get: 3, 4, 5, 6, 7. So, when x = 3, we get  consecutive integers . 
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)

Answer:  C

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Senthil1981 · Answer

given that x is positive and single digit and based on 4/3*x being one of them, assume x as 3
this gives the list as 4, 6, 3, 5, 7 and when ordered, 3,4,5,6,7 and hence median is 5
Answer is C

ScottTargetTestPrep · Answer

Since all the values of the expressions in x are integers, we see that x must be a multiple of 3 so that 4/3*x is an integer. Therefore, if x = 3, the values of the expressions are 4, 6, 3, 5, and 7, respectively.

Arranging them in ascending order, we have:

3, 4, 5, 6, 7

We see that the median could be 5.

Answer: C

Kinshook · Answer

If x = 3 
4/3x=4
2x = 6
x+2=5
3x-2=7

The ordered list of consecutive integers = {3,4,5,6,7}

Median = 5

IMO C

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If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x

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If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x

Prep Toolkit

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