Comprehension
Players are selected for Judo based on their body weights from the following 10 weight groups:
1. (48 kg - 52 kg)
2. (52 kg - 56 kg)
3. (56 kg - 60 kg)
4. (60 kg - 64 kg)
5. (64 kg - 68 kg)
6. (68 kg - 72 kg)
7. (72 kg - 76 kg)
8. (76 kg - 80 kg)
9. (80 kg - 84 kg)
10. (84 kg - 88 kg)
The average weight of the players after selecting one player from each group is 68 kg. If one of the players (named S) leaves the team, their average weight comes down to 66.5 kg
1. (48 kg - 52 kg)
2. (52 kg - 56 kg)
3. (56 kg - 60 kg)
4. (60 kg - 64 kg)
5. (64 kg - 68 kg)
6. (68 kg - 72 kg)
7. (72 kg - 76 kg)
8. (76 kg - 80 kg)
9. (80 kg - 84 kg)
10. (84 kg - 88 kg)
The average weight of the players after selecting one player from each group is 68 kg. If one of the players (named S) leaves the team, their average weight comes down to 66.5 kg
Question: 1
Player S is from the weight group:
Player S is from the weight group:
Updated On: Jul 14, 2026
- 1
- 9
- 5
- 10
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The Correct Option is B
Approach Solution - 1
The correct option is (B): 9.
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Approach Solution -2
Ten players, one from each weight group, have an average weight of 68 kg, so their total weight is:
\[ 68 \times 10 = 680 \text{ kg} \]When player S leaves, the remaining 9 players have an average of 66.5 kg, so their total weight is:
\[ 66.5 \times 9 = 598.5 \text{ kg} \]S's weight is the difference:
\[ 680 - 598.5 = 81.5 \text{ kg} \]- Group 1 (48-52 kg): 81.5 kg is far outside this range.
- Group 9 (80-84 kg): 81.5 kg falls squarely within this range.
- Group 5 (64-68 kg): 81.5 kg is well above this range.
- Group 10 (84-88 kg): 81.5 kg is below the lower bound of this range.
Therefore, the correct answer is Group 9.
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Question: 2
If S leaves the group and two new players join the group, their average weight increases to 68 kg. These players can NOT be from groups:
If S leaves the group and two new players join the group, their average weight increases to 68 kg. These players can NOT be from groups:
Updated On: Jul 14, 2026
- 1 and 3
- Both from group 7
- 4 and 10
- 5 and 9
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The Correct Option is A
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The correct option is (A): 1 and 3.
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Approach Solution -2
After S (81.5 kg) leaves, the remaining 9 players total 598.5 kg. Two new players join and the average of all 11 players rises to 68 kg, so the new total is:
\[ 68 \times 11 = 748 \text{ kg} \]The combined weight of the two new players is:
\[ 748 - 598.5 = 149.5 \text{ kg} \]We need to check which pair of groups CANNOT jointly produce a combined weight of 149.5 kg, using each group's weight range.
- 1 and 3 (48-52 kg and 56-60 kg): the maximum possible combined weight is \( 52 + 60 = 112 \) kg, which falls well short of 149.5 kg, so this pairing is impossible.
- Both from group 7 (72-76 kg each): combined weight ranges from 144 to 152 kg, which comfortably includes 149.5 kg, so this pairing is possible.
- 4 and 10 (60-64 kg and 84-88 kg): combined weight ranges from 144 to 152 kg, which includes 149.5 kg, so this pairing is possible.
- 5 and 9 (64-68 kg and 80-84 kg): combined weight ranges from 144 to 152 kg, which includes 149.5 kg, so this pairing is possible.
Only the pairing of groups 1 and 3 falls short of the required 149.5 kg combined weight.
Therefore, the correct answer is 1 and 3.
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Question: 3
What is the average weight of all the players taken together?
What is the average weight of all the players taken together?
Updated On: Jul 14, 2026
- 68 kg
- 66 kg
- 69 kg
- Cannot be determined
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The Correct Option is D
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The correct option is (D): Cannot be determined.
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This question asks for the average weight of "all the players taken together." Let's check what we actually know versus what's needed to answer this precisely.
- 68 kg: this is the average of the 11 players after the two new players join, not necessarily the average of every player who has been part of the team across the whole scenario (which would also include S, and depends on exactly how many players and which roster is meant by "all").
- 66 kg: this figure doesn't correspond to any of the computed totals (68 kg for the original ten, 66.5 kg for the nine after S left, or 68 kg for the eleven after two joined).
- 69 kg: this also does not match any of the group averages established from the given data.
- Cannot be determined: "all the players taken together" is ambiguous between the original ten, the nine remaining, or the eleven after replacements, and since only the group ranges (not each player's exact weight) are known for most players, a single definitive combined average cannot be pinned down.
Since the exact composition of "all the players" isn't uniquely fixed by the passage, and individual weights within a range aren't pinned to single values, no one figure can be stated with certainty.
Therefore, the correct answer is Cannot be determined.
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Question: 4
In the average of all the groups together, which group contributes most in overall average?
In the average of all the groups together, which group contributes most in overall average?
Updated On: Jul 14, 2026
- 10
- 8
- 1
- Cannot be determined
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The Correct Option is D
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The correct option is (D):Cannot be determined .
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This question asks which group "contributes most" to the overall average weight. Let's examine what's actually knowable here.
- Group 10: having the highest weight range (84-88 kg) doesn't guarantee the largest contribution to the average, since we don't know each player's exact weight within their range, only S's exact weight is known.
- Group 8: similarly, its range (76-80 kg) is high but not confirmed as the largest actual contributor without exact individual weights.
- Group 1: having the lowest range (48-52 kg) makes it an unlikely top contributor, but ruling it out doesn't tell us which group IS the top contributor.
- Cannot be determined: since only weight ranges (not exact values) are known for most players, we cannot say with certainty which single group's player pulls the average up the most; several different combinations of exact weights within the given ranges remain equally possible.
Without exact individual weights, the specific group contributing most to the average cannot be identified with certainty.
Therefore, the correct answer is Cannot be determined.
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Question: 5
If one of the new two players is from group 4, which group the other player is from?
If one of the new two players is from group 4, which group the other player is from?
Updated On: Jul 14, 2026
- 5
- 7
- 10
- None of the above
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The Correct Option is C
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The correct option is (C): 10.
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The two new players' combined weight is 149.5 kg (established earlier). If one of them is from group 4 (weight range 60-64 kg), the other player's weight must fall in the range:
\[ 149.5 - 64 = 85.5 \text{ kg (minimum)} \quad \text{to} \quad 149.5 - 60 = 89.5 \text{ kg (maximum)} \]So the other player's weight lies somewhere between 85.5 kg and 89.5 kg. Let's check which group this fits.
- Group 5 (64-68 kg): nowhere near the required 85.5-89.5 kg range.
- Group 7 (72-76 kg): also well short of the required range.
- Group 10 (84-88 kg): overlaps the required range between 85.5 kg and 88 kg, the only group whose range reaches into the 85.5-89.5 kg band.
- None of the above: not applicable, since group 10 does provide a valid overlap.
Therefore, the correct answer is Group 10.
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