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02 Jun 2022, 02:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (02:27) correct
18%
(01:56)
wrong
based on 44
sessions
History
Date
Time
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Not Attempted Yet
Hundred and twenty chocolates were equally distributed among the students present in the class. If there were 4 more students, each of them would have received one chocolate less. How many students were present in the class?
(A) 16
(B) 20
(C) 24
(D) 32
(E) 36
(A) 16
(B) 20
(C) 24
(D) 32
(E) 36
02 Jun 2022, 11:11
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Number of chocolates distributed = 120.
These chocolates were equally distributed among the students present; this means every student got the same number of chocolates.
Therefore, the number of students should be a divisor of 120.
Out of the answer options given, 16, 32 and 36 are not divisors of 120. Therefore, answer options A, D and E can be eliminated.
Answer options B and C remain.
If there were 4 more students, each of them would have received one chocolate less. This means that the revised number of students should also be a divisor of 120, since the difference between the two quotients is an integer.
With this evidence, answer option C can be ruled out; if 24 were to be the original number of students, revised number of students = 24 + 4 = 28, which is not a divisor of 120.
The correct answer option is B
Let’s review answer option B.
If number of students = 20, chocolates received by each child = \(\frac{120 }{ 20}\) = 6
If there were 4 more students, number of students = 24; chocolates received by each child = \(\frac{120 }{ 24}\) = 5.
Clearly, in the second case, each child received 1 chocolate less.
These chocolates were equally distributed among the students present; this means every student got the same number of chocolates.
Therefore, the number of students should be a divisor of 120.
Out of the answer options given, 16, 32 and 36 are not divisors of 120. Therefore, answer options A, D and E can be eliminated.
Answer options B and C remain.
If there were 4 more students, each of them would have received one chocolate less. This means that the revised number of students should also be a divisor of 120, since the difference between the two quotients is an integer.
With this evidence, answer option C can be ruled out; if 24 were to be the original number of students, revised number of students = 24 + 4 = 28, which is not a divisor of 120.
The correct answer option is B
Let’s review answer option B.
If number of students = 20, chocolates received by each child = \(\frac{120 }{ 20}\) = 6
If there were 4 more students, number of students = 24; chocolates received by each child = \(\frac{120 }{ 24}\) = 5.
Clearly, in the second case, each child received 1 chocolate less.
03 Jul 2022, 05:53
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Let
Total students = n
Chocolates per student = c
Case 1 : nc = 120
Case 2: (n+4)(c-1) = 120
Hence, (n+4)(c-1) = nc
nc -n+4c-4 = nc
so, 4c -n = 4
Note :- We have to look for value of n and c such that nc = 120
Let's check the possibilties :-
c n
1 0
2 4
3 8
4 12
5 16
6 20
7 24
Clearly n=20 and c =6 satisfies the requirement.
So, Number of students = 20
(B) is the correct answer
Hope this helps..
Total students = n
Chocolates per student = c
Case 1 : nc = 120
Case 2: (n+4)(c-1) = 120
Hence, (n+4)(c-1) = nc
nc -n+4c-4 = nc
so, 4c -n = 4
Note :- We have to look for value of n and c such that nc = 120
Let's check the possibilties :-
c n
1 0
2 4
3 8
4 12
5 16
6 20
7 24
Clearly n=20 and c =6 satisfies the requirement.
So, Number of students = 20
(B) is the correct answer
Hope this helps..
