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16 Mar 2026, 19:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
45% (02:47) correct
55%
(03:01)
wrong
based on 84
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The average weight of students in a class of 25 was 30 kilograms. Four new students joined and the weight increased to 31 kilograms. If the weights of the new students are in integers, the weight of no two students is the same, and the heaviest student weighs 42 kilograms, what is the highest possible weight of the lightest new student?
A. 33
B. 34
C. 35
D. 36
E. 41
A. 33
B. 34
C. 35
D. 36
E. 41
16 Mar 2026, 23:03
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In my opinion, the fastest way to approach this question would be to test the option choices, one by one.
The total weight of new students = Average weight * Number of students = 31*29 = 149 kgs
Now, let's test the options, starting from the highest value:
Option D - 36:
Smallest 4 distinct weights >= 36 are 36 + 37 + 38 + 39 = 150 > 149, which is incorrect.
So, 36 is not possible.
Now, let's check Option C - 35:
Smallest 4 distinct weights >= 35 are 35 + 36 + 37 + 38 = 146
We need +3 more -> add it to the largest:
35 + 36 + 37 + 41 = 149, which is correct.
Since these are all distinct and max <= 42 kgs, this is the correct choice.
Hence, the correct answer is Option C - 35.
Hope this helps!
The total weight of new students = Average weight * Number of students = 31*29 = 149 kgs
Now, let's test the options, starting from the highest value:
Option D - 36:
Smallest 4 distinct weights >= 36 are 36 + 37 + 38 + 39 = 150 > 149, which is incorrect.
So, 36 is not possible.
Now, let's check Option C - 35:
Smallest 4 distinct weights >= 35 are 35 + 36 + 37 + 38 = 146
We need +3 more -> add it to the largest:
35 + 36 + 37 + 41 = 149, which is correct.
Since these are all distinct and max <= 42 kgs, this is the correct choice.
Hence, the correct answer is Option C - 35.
Hope this helps!
17 Mar 2026, 00:01
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I think there is a small mistake in your evaluation.
It is stated that among the new students the heaviest weighs 42Kgs.
In your case the heaviest guy is 41Kgs:
"35 + 36 + 37 + 41 = 149, which is correct"
The heaviest guy is 42Kgs, and the total weight of the 25 students is 750 so that becomes 792Kgs.
Let the 3 remaining new students' weights be x, y and z, where x<y<z<42
Now the equation becomes x+y+z+792 = 31*29
=> x+y+z = 107
Remember that no 2 new students have the same weight.
Now take the options and subtract the option from 107, which will give us the sum of (y+z). [as the option is the value of x]
Then we try to split the remainder into 2 integers such that no integer is higher than 42 or equal to or less than the option. They shouldn't be equal to each other as well.
So,
107 - 33 = 74 => 34 + 40
107 - 34 = 73 => 36 + 37
107 - 35 = 72 => here either one has to be 35 or less or greater than 42, or both have to be 36.
107 - 36 = 71 => Similarly, one has to be 35[which is less than the option of 36]
107 - 41 => This is not possible as there are no integers between 41 and 42.
So the answer is 34, which is option B
Hope this helps
It is stated that among the new students the heaviest weighs 42Kgs.
In your case the heaviest guy is 41Kgs:
"35 + 36 + 37 + 41 = 149, which is correct"
The heaviest guy is 42Kgs, and the total weight of the 25 students is 750 so that becomes 792Kgs.
Let the 3 remaining new students' weights be x, y and z, where x<y<z<42
Now the equation becomes x+y+z+792 = 31*29
=> x+y+z = 107
Remember that no 2 new students have the same weight.
Now take the options and subtract the option from 107, which will give us the sum of (y+z). [as the option is the value of x]
Then we try to split the remainder into 2 integers such that no integer is higher than 42 or equal to or less than the option. They shouldn't be equal to each other as well.
So,
107 - 33 = 74 => 34 + 40
107 - 34 = 73 => 36 + 37
107 - 35 = 72 => here either one has to be 35 or less or greater than 42, or both have to be 36.
107 - 36 = 71 => Similarly, one has to be 35[which is less than the option of 36]
107 - 41 => This is not possible as there are no integers between 41 and 42.
So the answer is 34, which is option B
Hope this helps
shivani1351
