TARGET730 wrote:
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 70.
(2) The number of students is a two-digit number greater than 50.
We are given that when we divide the total students by 4, we have a remainder of 3, so the total could be values such as:
7, 11, 15, 19, 23, 27, 31, 35, 39, ...
We are given that when we divide the total students by 9, we have a remainder of 4, so the total could be values such as:
13, 22, 31, 40, 49, 58, ...
The first value common to our lists is 31; we can keep adding the LCM of 4 and 9, which is 36, to 31 to generate succeeding values. Thus, the total number of students could be:
31, 67, 103, ...
We need to determine the exact total number of students.
Statement One Alone:
The number of students is a two-digit number less than 70.
Since the total number of students could be 31 or 67, statement one alone is not sufficient to answer the question.
Statement Two Alone:
The number of students is a two-digit number greater than 50.
Of the numbers 31, 67, 103, ... there is only one number that is both a 2-digit number and greater than 50. Thus, statement two is sufficient.
Answer: B
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