CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 19

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 19 : A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is


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Explanatory Answer

Let the number of students in the school be N.
N < 5000
N leaves a remainder of 4 when divided by 9, 10, 12, or 25.
Since 4 is less than 9, 10, 12 and 25
N leaves a remainder of 4 when divided by LCM(9, 10, 12, 25).
N leaves a remainder of 4 when divided by 900.
N = 900(x) + 4
Since N < 5000
x can range from 0 to 5
But 900(x) + 4 is a multiple of 11 only when x = 2
N = 900(2) + 4 = 1804
When we divide these 1804 students into groups of 12, we get, 150 groups.
Because, 1804 = 12(150) + 4


The answer is '150'

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