Problem Solving

If the ages of players in a cricket team vary between 17 and 37 inclusive, which of the following describes
all possible ages x in this cricket team?
A) |x - 17| ≤ 27
B) |x + 27| ≤ 10
C) |x - 27| ≤ 10
D) |x - 37| ≤ 17

Hmna wrote:If the ages of players in a cricket team vary between 17 and 37 inclusive, which of the following describes all possible ages x in this cricket team?
A) |x - 17| ≤ 27
B) |x + 27| ≤ 10
C) |x - 27| ≤ 10
D) |x - 37| ≤ 17

|a-b| = the DISTANCE between a and b.

The midpoint of the range = the average of 17 and 37 = (17+37)/2 = 27.
Plotted on a number line:
17----------27----------37

x can be any value on the number line above.
Implication:
x can be up to 10 PLACES TO THE LEFT OF 27 or up to 10 PLACES TO THE RIGHT OF 27.
In other words:
The distance between x and 27 must LESS THAN OR EQUAL TO 10.
In math terms:
|x-27|≤10.

The correct answer is C.

Hmna wrote:If the ages of players in a cricket team vary between 17 and 37 inclusive, which of the following describes
all possible ages x in this cricket team?
A) |x - 17| ≤ 27
B) |x + 27| ≤ 10
C) |x - 27| ≤ 10
D) |x - 37| ≤ 17

An alternate approach is to TEST THE ANSWER CHOICES.
The correct inequality must include every value between 17 and 37, inclusive, but must exclude every value outside this range.

Since 17 is a valid age, x=17 must work in the correct inequality.
Test x=17 in the answer choices:
A) |17 - 17| ≤ 27 --> 0≤27
B) |17 + 27| ≤ 10 --> 44≤10
C) |17 - 27| ≤ 10 --> 10≤10
D) |17 - 37| ≤ 17 --> 20≤17
Since x=17 does not work in B and D, eliminate B and D.

Since 16 is an INVALID age, x=16 must NOT work in the correct inequality.
Test x=16 in the remaining answer choices:
A) |16 - 17| ≤ 27 --> 1≤27
C) |16 - 27| ≤ 10 --> 11≤10
Since x=16 works in A -- and this value is NOT a valid age and thus must NOT work in the correct inequality -- eliminate A.

The correct answer is C.