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How many integers in the set - Quantitative Aptitude – Equation

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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Equation : How many integers in the set 

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills.

You may also find remaining question solution of CAT 2020, Slot 3 by searching the question in the search bar.

CAT 2020 - Slot 3 - Quantitative Aptitude - Equation – Question 16 - How many integers in the set

Q. 16: How many integers in the set {100, 101, 102, …, 999} have at least one digit repeated?

16. Correct Answer: 252

The total number of integers from 100 to 999 is 999 – 99 = 900.

Of these 900 integers, if we could find the number of integers which do not have repetitions in them, we can also find the number of integers that have repetitions.

Let’s find the number of integers that between 100 and 999, which do not have repetitions.

 

a

b

c

Possibilities

1 to 9

0 to 9
   except a

0 to 9
except a and b

Number of
Possibilities

9

9

8

The number of integers that between 100 and 999, which do not have repetitions = 9 × 9 × 8

Therefore, the number of integers that have repetitions = 900 – 9 × 9 × 8

= 9 (100 – 9 × 8)

= 9 (28)

= 180 + 72 = 200 + 52 = 252

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