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XAT 2015 — QA & DI Question 18

LCM & HCFEasy

An ascending series of numbers satisfies the following conditions:

  1. When divided by 3, 4, 5 or 6, the numbers leave a remainder of 2.
  2. When divided by 11, the numbers leave no remainder.

The 6th number in this series will be:

Answer & solution

  • A

    242

  • B

    2882

  • 3542

  • D

    4202

  • E

    None of the above

Solution

LCM (3, 4, 5, 6) = 60
From (i), numbers are of the form 60k + 2.
From (ii), numbers are of the form 11m.
11m = 60k + 2 = 55k + (5k + 2)
11 divides (5k + 2)
Units digit of (5k + 2) is 2 or 7
So, values of (5k + 2) are 11 × 2, 11 × 7, 11 × 12, 11 × 17, 11 × 22, 11 × 27, … and so on.
We need to find the 6th number of the ascending series.
∴ 5k + 2 = 11 × 27 ⇒ k = 59
The required number = 60 × 59 + 2 = 3542
Hence, option (c).

XAT 2015 QA & DI Q18: An ascending series of numbers satisfies the following conditions: When divided by 3, 4, 5 or 6, the numbers l — Solution | TheCATExam