MBApyq

Five Digit Code Criteria

CMAT 2022 · Logical Reasoning · Medium · Logical Conditions

All CMAT 2022 questionsMore Logical Conditions questionsAll CMAT LR

A device classifies numbers according to the following criteria. The number must have: (A) Five digits (B) First and last digits are perfect squares. (C) The middle digit is an odd number and it is an addition of first and last digits. (D) Second and fourth digits are the difference between first and third digits, third and fifth digits.

Which of the following numbers could be correct according to the conditions given above?

  1. A.

    14514

  2. B.

    94514

  3. C.

    44949

  4. D.

    93524

Answer

A

Explanation

Let the 5-digit number be d1d2d3d4d5d_1 d_2 d_3 d_4 d_5.

Let's test option 14514:

  • Condition A: 5 digits (Yes)
  • Condition B: d1=1d_1 = 1 (perfect square), d5=4d_5 = 4 (perfect square). (Yes)
  • Condition C: Middle digit d3=d1+d5=1+4=5d_3 = d_1 + d_5 = 1 + 4 = 5, which is an odd number. (Yes)
  • Condition D:
    • Second digit d2=∣d3−d1∣=∣5−1∣=4d_2 = |d_3 - d_1| = |5 - 1| = 4.
    • Fourth digit d4=∣d3−d5∣=∣5−4∣=1d_4 = |d_3 - d_5| = |5 - 4| = 1.
    • So d2=4d_2 = 4 and d4=1d_4 = 1, matching 14514! (Yes)

Hence, 14514 satisfies all criteria.

Related Logical Conditions questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace