Carloselopez wrote:The average height of a group of 5 people is 70 inches. What is the height of the shortest person in the group?
1) If the shortest person left the group, the average height of the group would be 72.5 inches.
2) The ratio of height of the tallest person in the group to the height of the shortest person in the group is 5:4.
Target question: What is the height of the shortest person in the group?
Given: The average height of a group of 5 people is 70 inches.
So, the sum of all 5 heights = (5)(70) =
350 inches
Statement 1: If the shortest person left the group, the average height of the group would be 72.5 inches
If the average height of 4 people is 72.5 inches, then the sum of the 4 heights = (4)(72.5) =
290 inches
The total height went from
350 inches to
290 inches (a 60-inch difference), so
the shortest person in the group must be 60 inches tall
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The ratio of height of the tallest person in the group to the height of the shortest person in the group is 5:4
As vinay1983 and Java_85 noted, this statement is not sufficient. To show this, consider these two conflicting cases:
Case a: the heights are {60, 71, 72, 72, 75} in which case
the shortest person in the group is 60 inches tall
Case b: the heights are {64, 68, 68, 70, 80} in which case
the shortest person in the group is 64 inches tall
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
