How many numbers from 1 to 1000, both inclusive, have digits repeated

Question

How many numbers from 1 to 1000, both inclusive, have digits repeated ?

A. 9
B. 81
C. 262
D. 648
E. 738

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler  
  Reading Comprehension Butler  
  Data Insights Butler

GMATinsight · Answer

Single digit numbers without repetition of digits = 9 Two digit numbers without repetition of digits = 9*9 = 81 Three digit numbers without repetition of digits = 9*9*8 (9 for leftmost then second 9 for rightmost including zero excluding used digit and 8 for middle place) = 648 Total such numbers = 9+81+648 =738 Answer: Option E Related Video: https://www.youtube.com/watch?v=6AELi1S9gRA Please Like and Subscribe to YouTube channel if you like the video and access 1100+ more FREE videos . Every subscription matters!!! If you like to subscribe to modular courses on Quant and DI then please visit the following link: https://gmatinsight.com/gmat-2/

ManifestDreamMBA · Answer

With repeated digits, it should be atleast 2 digits
2 digits with repeated digits = 9 (11-99)

3 digits with repeated digits = 9*9*1 = 81
Fixing first digit to 9 (not considering 0)
Considering a different second digit and then repeating the third digit
This can be arranged in 3 ways = 3*81 = 243

Considering when all 3 digits are same = 9

Considering 1000, which has repeated 0 = 1

Adding all = 9+243+9+1 = 262

tgsankar10 · Answer

Numbers with unique digits can be calculated easily

Single digit numbers with unique digits are  9   (from 1 to 9)

Two digit numbers with unique digits are  9*9=81  (9 digits 1 to 9 for tens place, 9 digits for the units place with 0 replacing the first digit)

Three digit numbers with unique digits are  9*9*8=648

Numbers with unique digits =  9+81+648=738

Numbers with Repeated digits  = 1000-738=262

Answer: C

Gmat750aspirant · Answer

We need to determine how many numbers between 1 and 1000 (both inclusive) have at least one repeated digit.

Step 1: Total numbers from 1 to 1000 
- There are 1000 numbers.

Step 2: Count numbers with no repeated digits and subtract from 1000

(A) 1-digit numbers (1 to 9) 
- There are 9 numbers (1 to 9). All have unique digits.

(B) 2-digit numbers (10 to 99) 
- The tens digit can be any digit from 1 to 9 (9 choices). 
- The ones digit can be any digit from 0 to 9 except the tens digit (9 choices). 
- Total: 9 × 9 = 81 numbers.

(C) 3-digit numbers (100 to 999) 
- The hundreds digit can be any digit from 1 to 9 (9 choices). 
- The tens digit can be any digit from 0 to 9 except the hundreds digit (9 choices). 
- The ones digit can be any digit from 0 to 9 except the two already chosen (8 choices). 
- Total: 9 × 9 × 8 = 648 numbers.

(D) 4-digit number (1000) 
- Only one number, 1000, which has repeated digits (three 0's).

Total numbers with unique digits = 9 + 81 + 648 = 738.

Step 3: Count numbers with repeated digits 
- Numbers with repeated digits = Total numbers (1000) − Numbers with unique digits (738) = 262.

Conclusion 
Answer: C (262 numbers have at least one repeated digit).

NextstopISB · Answer

Total numbers from 1 to 1000 = 1000

Step 1: Count of numbers without repeated digits

(a) 1-digit numbers (1-9): 
 - All are unique → 9 numbers

(b) 2-digit numbers (10-99): 
 - First digit: 1-9 (9 choices) 
 - Second digit: 0-9, but not the first (9 choices) 
 - Total = 9 × 9 = 81

(c) 3-digit numbers (100-999): 
 - First digit: 1-9 (9 choices) 
 - Second digit: 0-9, but not the first (9 choices) 
 - Third digit: 0-9, but not first two (8 choices) 
 - Total = 9 × 9 × 8 = 648

(d) The number 1000: 
 - Has repeated digits ('0' appears three times), so it is not counted.

Total numbers without repeated digits = 9 + 81 + 648 = 738

Step 2: Count of numbers with repeated digits 
= Total numbers - Unique-digit numbers 
= 1000 - 738 
= 262

Final Answer: (C) 262

KDM91 · Answer

The question is about repeated digits. You have explained answer for non repeated digits. I would add the final explanation.

Total numbers without repetition= 738
Total numbers given= 1000
Total number with repetition = 1000-738 = 262

option C

How many numbers from 1 to 1000, both inclusive, have digits repeated

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

How many numbers from 1 to 1000, both inclusive, have digits repeated

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards