Using the digits 1, 2, 3, 4, 5 and 6 with no digit repeated, how many even four-digit numbers greater than 3000 can be formed?

Answer and explanation

Correct answer: D. 120

  1. Step 1: The thousands digit must be 3, 4, 5 or 6. Split by whether it is even (4 or 6) or odd (3 or 5).
  2. Step 2: Even first digit: 2 choices, then the last digit must be one of the 2 remaining even digits, then the middle two digits come from 4 left: 4 x 3 = 12. Count = 2 x 2 x 12 = 48.
  3. Step 3: Odd first digit: 2 choices, last digit 3 even choices, middle 12. Count = 2 x 3 x 12 = 72.
  4. Step 4: Total = 48 + 72 = 120.
Answer
120.
Why not the others: 144 counts three even last digits for every first digit; 108 and 96 drop one of the two cases.

Practise more Analytical, Inductive and Deductive Reasoning.

Free questions with an explanation for every one, and full timed Jubilee Institute Admission Test mock tests.

All Analytical, Inductive and Deductive Reasoning questionsTake a mock test

More Analytical, Inductive and Deductive Reasoning questions