CAT 2006QA Question 23

Number TheoryEasy

The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

Answer & solution

Correct answer: 97 : 84

  • A

    101 : 88

  • B

    87 : 100

  • C

    110 : 111

  • D

    85 : 98

  • 97 : 84

Solution

Consider options. As the number of employees is prime we can add the numerator and denominator of ratios directly to find the number of employees.

Option (a): Number of employees = 101 + 88 = 189
Number of employees = 189, which is not a prime number.
∴ Option (a) is eliminated.

Option (b): Number of employees = 87 + 100 = 187
Number of employees = 187, which is not a prime number.
∴ Option (b) is eliminated.

Option (c): Number of employees = 110 + 111 = 221
Number of employees = 221, which is not a prime number.
∴ Option (c) is eliminated.

Option (d): Number of employees = 85 + 98 = 183
Number of employees = 183, which is not a prime number.
∴ Option (d) is eliminated.

Option (e): Number of employees = 97 + 84 = 181
Number of employees = 181, which is a prime number.
∴ The ratio of employees = 97 : 84

Hence, option (e).

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CAT 2006 QA Q23: The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number o — Solution | TheCATExam