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08 May 2024, 01:30
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Students in a class are arranged to form groups of 4 members each. After forming the groups, 3 students are left. If the students had been arranged in groups of 9 members each, however, 4 students would be left. What is the total number of students in the class?
(1) The number of students is a two-digit number less than 65.
(2) The number of students is a two-digit number greater than 30.
(1) The number of students is a two-digit number less than 65.
(2) The number of students is a two-digit number greater than 30.
08 May 2024, 04:38
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Let the total number of students in the class = \(x\)
Students in a class are arranged to form groups of 4 members each, with 3 students left: \(4a + 3 = x\)
If the students had been arranged in groups of 9 members each, however, 4 students would be left: \(9b + 4 = x\)
The process to find the possible values of x is:
1- Find the first value which both equations have in common.
2- Find the lowest common multiple of the divisors.
3- Adding the lowest common multiple to the first value and then to each proceeding value will generate a list of all possible answers from the lowest value right through to infinity.
1- As 9 is bigger than 4, I'll start with \(9b + 4 = x\).
\(9b + 4 = x\): 13, 22, 31, 40, 49.
\(4a + 3 = x\): 7, 11, 15, 19, 23, 27, 31.
The lowest value that could be the answer 31.
2- The lowest common multiple of 4 and 9 is 36.
3- Therefore the possible values for the number of students in the classroom will be: 31, 67, 103, 139....
(1) The number of students is a two-digit number less than 65.
The only value which fits this statement is 31.
SUFFICIENT
(2) The number of students is a two-digit number greater than 30.
This incompasses all the possible values. Without further information it is impossible is narrow it down to a single answer choice.
INSUFFICIENT
ANSWER A
Students in a class are arranged to form groups of 4 members each, with 3 students left: \(4a + 3 = x\)
If the students had been arranged in groups of 9 members each, however, 4 students would be left: \(9b + 4 = x\)
The process to find the possible values of x is:
1- Find the first value which both equations have in common.
2- Find the lowest common multiple of the divisors.
3- Adding the lowest common multiple to the first value and then to each proceeding value will generate a list of all possible answers from the lowest value right through to infinity.
1- As 9 is bigger than 4, I'll start with \(9b + 4 = x\).
\(9b + 4 = x\): 13, 22, 31, 40, 49.
\(4a + 3 = x\): 7, 11, 15, 19, 23, 27, 31.
The lowest value that could be the answer 31.
2- The lowest common multiple of 4 and 9 is 36.
3- Therefore the possible values for the number of students in the classroom will be: 31, 67, 103, 139....
(1) The number of students is a two-digit number less than 65.
The only value which fits this statement is 31.
SUFFICIENT
(2) The number of students is a two-digit number greater than 30.
This incompasses all the possible values. Without further information it is impossible is narrow it down to a single answer choice.
INSUFFICIENT
ANSWER A
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01 Jun 2024, 07:30
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