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13 Dec 2014, 04:02
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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:
95%
(hard)
Question Stats:
33% (02:34) correct
67%
(02:43)
wrong
based on 566
sessions
History
Date
Time
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Not Attempted Yet
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.
I got the answer to this question, but is there any easy way to find the answer other than by listing all the numbers?
(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.
I got the answer to this question, but is there any easy way to find the answer other than by listing all the numbers?
17 Dec 2014, 06:43
Kudos
Bookmarks
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?
If the students had been arranged in groups of 4 members each, however, 3 students would be left --> x = 4q + 3 --> x could be 3, 7, 11, 15, 19, 23, 27, 31, ...
If the students had been arranged in groups of 9 members each, however, 4 students would be left --> x = 9p + 4 --> x could be 4, 13, 22, 31, ...
From above general formula would be: x = 36n + 31 --> x could be 31, 67, 103, 139, ... (for more about deriving general formula check: manhattan-remainder-problem-93752.html#p721341)
(1) The number of students is a two-digit number less than 70 --> x could be 31 or 67. Not sufficient,
(2) The number of students is a two-digit number greater than 50 --> x could only be 67. Sufficient.
Answer: B.
If the students had been arranged in groups of 4 members each, however, 3 students would be left --> x = 4q + 3 --> x could be 3, 7, 11, 15, 19, 23, 27, 31, ...
If the students had been arranged in groups of 9 members each, however, 4 students would be left --> x = 9p + 4 --> x could be 4, 13, 22, 31, ...
From above general formula would be: x = 36n + 31 --> x could be 31, 67, 103, 139, ... (for more about deriving general formula check: manhattan-remainder-problem-93752.html#p721341)
(1) The number of students is a two-digit number less than 70 --> x could be 31 or 67. Not sufficient,
(2) The number of students is a two-digit number greater than 50 --> x could only be 67. Sufficient.
Answer: B.
General Discussion
24 Dec 2014, 10:26
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Hi TARGET730,
For this DS question, you really do have to list out a certain number of the possibilities (until you have enough information that you know that you can stop working).
The reason why is because the algebra equations that you could form from the information in the prompt do not provide enough information for you to solve.
Z = Total number of students
If students are formed into groups of 4 members each, then 3 students would be left...
4X + 3 = Z
If students are formed into groups of 9 members each, then 4 students would be left..
9Y + 4 = Z
Here, we have 3 variables, but only 2 equations, so while we can establish a relationship between Y and X (by combining the 2 equations), we can't figure out the exact value of either one until we "map out" the possibilities.
We'd end up with
4X + 3 = 9Y + 4
4X = 9Y + 1
Knowing that X and Y have to be integers limits the possibilities, but we'd still have to list them out.
GMAT assassins aren't born, they're made,
Rich
For this DS question, you really do have to list out a certain number of the possibilities (until you have enough information that you know that you can stop working).
The reason why is because the algebra equations that you could form from the information in the prompt do not provide enough information for you to solve.
Z = Total number of students
If students are formed into groups of 4 members each, then 3 students would be left...
4X + 3 = Z
If students are formed into groups of 9 members each, then 4 students would be left..
9Y + 4 = Z
Here, we have 3 variables, but only 2 equations, so while we can establish a relationship between Y and X (by combining the 2 equations), we can't figure out the exact value of either one until we "map out" the possibilities.
We'd end up with
4X + 3 = 9Y + 4
4X = 9Y + 1
Knowing that X and Y have to be integers limits the possibilities, but we'd still have to list them out.
GMAT assassins aren't born, they're made,
Rich
