At a climbing gym, 4 junior climbers and 3 instructors were weighed

Question

At a climbing gym, 4 junior climbers and 3 instructors were weighed for harness fitting. If the average (arithmetic mean) weight of all 7 people was 55 kilograms and the heaviest instructor weighed 80 kilograms, was the average (arithmetic mean) weight of the 4 junior climbers less than 53 kilograms?

(1) The average (arithmetic mean) weight of the other two instructors was 56 kilograms.

(2) The three lightest people in the group were junior climbers, each weighing 47 kilograms.

ankushsambare · Answer

Total weight of all 7 people:
7 × 55 = 385 kg
We need to know whether the average weight of the 4 junior climbers is less than 53.
That means we need to know whether their total weight is less than:
4 × 53 = 212 kg
 
Statement (1):
The other two instructors average 56 kg.
Their total weight = 2 × 56 = 112 kg
Heaviest instructor = 80 kg
Total instructor weight = 112 + 80 = 192 kg
So junior climbers' total weight =
385 − 192 = 193 kg
Average junior weight =
193 / 4 = 48.25 kg
This is less than 53.
Answer is definitely YES.
 Statement (1) is sufficient. 
Statement (2):
The three lightest people are junior climbers weighing 47 kg each.
So three juniors weigh:
3 × 47 = 141 kg
Let the fourth junior weigh x.
Junior total = 141 + x
We need to know if:
141 + x < 212
x < 71
But we don't know x.
The heaviest instructor is 80, and x could be anywhere between 47 and 80.
If x = 60, junior average = 201/4 = 50.25 (< 53).
If x = 75, junior average = 216/4 = 54 (> 53).
Both are possible.
 Statement (2) is not sufficient. 
Therefore, Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.
 Answer: A.

SS990 · Answer

Given:
    
 J 
 I 
 Tot 
 
  no. 
 4 
 3 
 7 
 
  wt A 
 ? 
 ? 
 55 
 
  wt total 
 ? 
 ? 
 385

Heaviest instructor=80kg

Deduction wt of 4J+2I = 385-80=305

To find: if Aj<53 or total wt of 4J< 212

1) Wt of 2 other instructors = 2I= 56x 2...we would know 4J from this nd cna find Aj..so thsi is sufficient

2) wt of 3lower wt ppl = 47x 3 ... this is less than the Aj of 53 to find, hence we would need 4th weight to get the answer which can be any number. hence insufficient

So the asnwer is A

At a climbing gym, 4 junior climbers and 3 instructors were weighed

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