Data Sufficiency

In a certain class, boys'heights range is 10 inches, and girls' height range is 8 inches. What is heights' range for all of the students?

1) The shortest boy is 2 inches taller than the tallest girl.
2) The tallest girl in the class is 72 inches in height.

The OA is A.

Please, can anyone assist me with this question? I need help to solve it. Thanks in advance.

BTGmoderatorLU wrote:In a certain class, boys' heights range is 10 inches, and girls' height range is 8 inches. What is heights' range for all of the students?

1) The shortest boy is 2 inches taller than the tallest girl.
2) The tallest girl in the class is 72 inches in height.

Since the range for the boys = 10, we get:
tallest boy - shortest boy = 10
tallest boy = 10 + shortest boy.

Since the range for the girls = 8, we get:
tallest girl - shortest girl = 8
shortest girl = tallest girl - 8.

Statement 1:
Case 1: tallest girl = 10, shortest boy = 12
Substituting tallest girl = 10 into the blue equation, we get:
shortest girl = 10-8 = 2.
Substituting shortest boy = 12 into the red equation, we get:
tallest boy = 10 + shortest boy = 10+12 = 22.
Resulting range:
tallest boy - shortest girl = 22-2 = 20.

Case 2: Case 1: tallest girl = 20, shortest boy = 22
Substituting tallest girl = 20 into the blue equation, we get:
shortest girl = 20-8 = 12.
Substituting shortest boy = 22 into the red equation, we get:
tallest boy = 10 + shortest boy = 10+22 = 32.
Resulting range:
tallest boy - shortest girl = 32-12 = 20.

Since the range in each case is the same value -- 20 -- Statement 1 is SUFFICIENT.

Statement 2:
Substituting tallest girl = 72 into the blue equation, we get:
shortest girl = 72-8 = 64.
If the tallest boy = 100, then the range = tallest boy - shortest girl = 100-64 = 36.
If the tallest boy = 110, then the range = tallest boy - shortest girl = 110-64 = 46.
Thus, the range can be different values, INSUFFICIENT.

The correct answer is A.