If x is a positive, single-digit integer such that 2/3*x, 2x, x, and x + 2, and 3x – 2 form a non-...
If x is a positive, single-digit integer such that 2/3*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?
Answer/Solution
5
Steps/Work
The big hints are thatx is a 1-digit integerAND (2/3)x, 2x, x, and x + 2, and 3x – 2 are ALLintegers
For (2/3)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: (2/3)(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: 2, 4, 5, 6, 7. 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 (2/3)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: (2/3)(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: 2, 4, 5, 6, 7. 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