Join WhatsApp Icon CAT WhatsApp Group
Question 10

How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?


Correct Answer: 252

Solution

Share

Total number of numbers from 100 to 999 = 900

The number of three digits numbers with unique digits:

_ _ _

The hundredth's place can be filled in 9 ways ( Number 0 cannot be selected)

Ten's place can be filled in 9 ways

One's place can be filled in 8 ways

Total number of numbers = 9*9*8 = 648

Number of integers in the set {100, 101, 102, ..., 999} have at least one digit repeated = 900 - 648 = 252

Get AI Help

Video Solution

video
View More Questions From Number Systems

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 35+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Quadratic Equations QuestionsCAT Geometry QuestionsCAT Averages, Ratio and Proportion QuestionsCAT Miscellaneous QuestionsCAT Number Systems Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Charts QuestionsCAT Quant Based LR QuestionsCAT DI Miscellaneous QuestionsCAT Data Interpretation QuestionsCAT Selection With Condition Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Reading Comprehension QuestionsCAT Para Summary QuestionsCAT Vocabulary QuestionsCAT Grammar and Sentence Correction QuestionsCAT Odd One Out Questions

Free CAT Quant Questions

CAT Logarithms, Surds and IndicesCAT Venn DiagramsCAT InequalitiesCAT Number SystemsCAT ArithmeticCAT MensurationCAT LogarithmsCAT Quadratic EquationsCAT Time, Speed and DistanceCAT GeometryCAT Data SufficiencyCAT Functions, Graphs and StatisticsCAT Profit And LossCAT Time And WorkCAT Number SeriesCAT Simple Interest Compound InterestCAT AlgebraCAT Profit and LossCAT MiscellaneousCAT Averages Mixtures AlligationsCAT PercentagesCAT Averages, Ratio and ProportionCAT AveragesCAT Coordinate GeometryCAT Time Speed DistanceCAT Linear EquationsCAT Progressions and SeriesCAT Probability, CombinatoricsCAT Remainders

Related Formulas With Tests

Arrangement, permutation and combination formulas

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI