CAT 2008 — QA Question 14
Directions for next 2 questions:
The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.
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How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
Answer & solution
- A
499
- B
500
- C
375
376
- E
501
The minimum number that can be formed is 1000, hence the number is a 4-digit number,
The maximum number that can be formed is 4000.
As 4000 is the only number in which the first digit is 4, first let us calculate the numbers less than 4000 and then we will add 1 to it.
∴ First digit can be 1, 2 or 3.
Remaining 3 digits can be any of the 5 digits.
∴ Total numbers that can be formed, which are less than 4000 = 3 × 5 × 5 × 5 = 375
∴ Total numbers that satisfy the given condition = 375 + 1 = 376
Hence, option (d).