Expected CAT question – PnC

CAT 2016 expected question: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? A] 499 B] 500 C] 375 D] 376 E] 501 We will be posting hand picked questions every day… CAT expected questions is a special compilation of typical CAT-level questions from Cetking to help test takers gain an edge in the final lap of their CAT preparation. Note: all these questions are based on Cetking’s experience of last few years of taking CAT.. Solution: The smallest number in the series is 1000, a 4-digit number. The largest number in the series is 4000, the only 4-digit number to start with 4. The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3. The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4. Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999. Including 4000, there will be 376 such numbers. Method 2 numbers starting with 1= 5*5*5 ( fixing 1 on thousand digit and then we have 5 choices for filling three places of 4 digit no. ) numbers starting with 2= 5*5*5 ( fixing 2) numbers starting with 3=5*5*5 (fixing 3) finally the no. 4000 total nos. = (125*3)+1 =376