# If x is a positive, single-digit integer such that 4/3*x, 3x, x, and x + 2, and 3x – 2 form a non-...

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

## Answer/Solution

5

### Steps/Work

The big hints are thatx is a 1-digit integerAND (4/3)x, 3x, x, and x + 2, and 3x – 2 are ALLintegers

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 ofconsecutive integers

When x =3, we get the following terms: (4/3)(3), 3(3),3,3+ 2, and 3(3) – 2.

When we evaluate these terms we get: 4, 9, 3, 5 and 7

Rearrange to get: 3, 4, 5, 7, 9. So, when x = 3, we getconsecutive 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

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 ofconsecutive integers

When x =3, we get the following terms: (4/3)(3), 3(3),3,3+ 2, and 3(3) – 2.

When we evaluate these terms we get: 4, 9, 3, 5 and 7

Rearrange to get: 3, 4, 5, 7, 9. So, when x = 3, we getconsecutive 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