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19 May 2020, 02:23
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C
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Difficulty:
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Question Stats:
53% (02:29) correct
47%
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wrong
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The students of a class are to be arranged in rows, starting from number 1, such that a row can have a maximum of x students, where x is a number to be determined that is greater than 1. If the minimum number of rows required to accommodate all the students is 10, what is the number of students in the class?
(1) If 3 students are shifted from row number 9 to row number 10, both the rows would have an equal number of students.
(2) Had there been 1 student less in the class, the minimum number of rows required would have been 9.
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19 May 2020, 03:42
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IMO is E.
Statement 1: no information regarding students sitting in row 1 to 8 (insufficient)
Statement 2: one less student. Nothing given regarding how many students are allowed to sit in a row. Maximum could be 100 or 2 (insufficient)
Statement 1&2: no common inference to use to determine no. of students.
So, will go with E
Posted from my mobile device
Statement 1: no information regarding students sitting in row 1 to 8 (insufficient)
Statement 2: one less student. Nothing given regarding how many students are allowed to sit in a row. Maximum could be 100 or 2 (insufficient)
Statement 1&2: no common inference to use to determine no. of students.
So, will go with E
Posted from my mobile device
19 May 2020, 03:54
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Max. no. of students in a row = x
Min. no. of rows required to accommodate all students = 10
2 possible cases:
(A) No. of students when all 10 rows have x students each = 10x
(B) No. of students when last (10th) row is partially occupied = 9x + j, where j is no. of students in the last (10th) row.
1) If 3 students are shifted from row number 9 to row number 10, both the rows would have an equal number of students.
Shifting of students is required to equalize no. of students in Rows 9 and 10. This means that only case (B) is applicable.
No of students in row #9 = x
No of students in row #10 = j
x - 3 = j + 3 --> x = j + 6.
We cannot deduce unique value of both x and j.
NOT SUFFICIENT
2) Had there been 1 student less in the class, the minimum number of rows required would have been 9.
This means that there is only one student in last (10th) row. Case (B) is thus applicable and j = 1. However, we cannot deduce unique value of x.
NOT SUFFICIENT
Combined
x = j + 6; and j = 1
So, x = 7
No. of students when last (10th) row is partially occupied = 9x + j = 64
SUFFICIENT
FINAL ANSWER IS (C)
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Min. no. of rows required to accommodate all students = 10
2 possible cases:
(A) No. of students when all 10 rows have x students each = 10x
(B) No. of students when last (10th) row is partially occupied = 9x + j, where j is no. of students in the last (10th) row.
1) If 3 students are shifted from row number 9 to row number 10, both the rows would have an equal number of students.
Shifting of students is required to equalize no. of students in Rows 9 and 10. This means that only case (B) is applicable.
No of students in row #9 = x
No of students in row #10 = j
x - 3 = j + 3 --> x = j + 6.
We cannot deduce unique value of both x and j.
NOT SUFFICIENT
2) Had there been 1 student less in the class, the minimum number of rows required would have been 9.
This means that there is only one student in last (10th) row. Case (B) is thus applicable and j = 1. However, we cannot deduce unique value of x.
NOT SUFFICIENT
Combined
x = j + 6; and j = 1
So, x = 7
No. of students when last (10th) row is partially occupied = 9x + j = 64
SUFFICIENT
FINAL ANSWER IS (C)
Posted from my mobile device
