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.
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