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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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M47-186
11 Jun 2026, 01:15
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GMAT Club Official Solution:
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?
The total weight of all 7 people was:
7 * 55 = 385 kilograms
The question asks whether the total weight of the 4 junior climbers was less than:
4 * 53 = 212 kilograms
(1) The average weight of the other two instructors was 56 kilograms.
So the total weight of those two instructors was:
2 * 56 = 112 kilograms
The heaviest instructor weighed 80 kilograms, so the total weight of the 3 instructors was:
80 + 112 = 192 kilograms
Therefore, the total weight of the 4 junior climbers was:
385 - 192 = 193 kilograms
Since 193 < 212, the average weight of the junior climbers was less than 53 kilograms.
Sufficient.
(2) The three lightest people in the group were junior climbers, each weighing 47 kilograms.
Let x be the weight of the fourth junior climber, and let y and z be the weights of the other two instructors.
Then:
47 + 47 + 47 + x + y + z + 80 = 385
x + y + z = 164
If the average weight of the 4 junior climbers were not less than 53 kilograms, then their total weight would be at least 212 kilograms:
47 + 47 + 47 + x >= 212
x >= 71
Then:
y + z <= 164 - 71 = 93
But since the three 47-kilogram junior climbers were the lightest people, each of the other two instructors must weigh at least 47 kilograms. So:
y + z >= 47 + 47 = 94
This is impossible.
Therefore, the average weight of the junior climbers must be less than 53 kilograms.
Sufficient.
Answer: D.
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?
The total weight of all 7 people was:
7 * 55 = 385 kilograms
The question asks whether the total weight of the 4 junior climbers was less than:
4 * 53 = 212 kilograms
(1) The average weight of the other two instructors was 56 kilograms.
So the total weight of those two instructors was:
2 * 56 = 112 kilograms
The heaviest instructor weighed 80 kilograms, so the total weight of the 3 instructors was:
80 + 112 = 192 kilograms
Therefore, the total weight of the 4 junior climbers was:
385 - 192 = 193 kilograms
Since 193 < 212, the average weight of the junior climbers was less than 53 kilograms.
Sufficient.
(2) The three lightest people in the group were junior climbers, each weighing 47 kilograms.
Let x be the weight of the fourth junior climber, and let y and z be the weights of the other two instructors.
Then:
47 + 47 + 47 + x + y + z + 80 = 385
x + y + z = 164
If the average weight of the 4 junior climbers were not less than 53 kilograms, then their total weight would be at least 212 kilograms:
47 + 47 + 47 + x >= 212
x >= 71
Then:
y + z <= 164 - 71 = 93
But since the three 47-kilogram junior climbers were the lightest people, each of the other two instructors must weigh at least 47 kilograms. So:
y + z >= 47 + 47 = 94
This is impossible.
Therefore, the average weight of the junior climbers must be less than 53 kilograms.
Sufficient.
Answer: D.
General Discussion
ankushsambare
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04 Jun 2026, 22:02
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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.
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.
