CAT Counting: Question with digits


This is an interesting question from Counting. Simple framework, but one needs to be very careful with the enumeration. One can get wrong answers in a number of ways.

Question
If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?
A.      3980
B.      3700
C.      3840
D.      3780

Correct Answer
Choice A

Explanatory Answer
We need to consider all three digit and all 4-digit numbers.

Three-digit numbers: A B C. 3 can be printed in the 100’s place or10’s place or units place.

Ø  100’s place:  3 B C. B can take values 0 to 9, C can take values 0 to 9. So, 3 gets printed in the 100’s place 100 times

Ø  10’s place:  A 3 C. A can take values 1 to 9, C can take values 0 to 9. So, 3 gets printed in the 10’s place 90 times

Ø  Unit’s place:  A B 3. A can take values 1 to 9, B can take values 0 to 9. So, 3 gets printed in the unit’s place 90 times

So, 3 gets printed 280 times in 3-digit numbers
Four-digit numbers: A B C D. 3 can be printed in the 1000’s place, 100’s place or10’s place or units place.

Ø  1000’s place:  3 B C D. B can take values 0 to 9, C can take values 0 to 9, D can take values 0 to 9. So, 3 gets printed in the 100’s place 1000 times.

Ø  100’s place:  A 3 C D. A can take values 1 to 9, C & D can take values 0 to 9. So, 3 gets printed in the 100’s place 900 times.

Ø  10’s place:  A B 3 D. A can take values 1 to 9, B & D can take values 0 to 9. So, 3 gets printed in the 10’s place 900 times.

Ø  Unit’s place:  A B C 3. A can take values 1 to 9, B & C can take values 0 to 9. So, 3 gets printed in the unit’s place 900 times.

3 gets printed 3700 times in 4-digit numbers.
So, there are totally 3700 + 280 = 3980 numbers

Answer Choice (A)


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IIM CAT Preparation Tips: CAT Counting: Question with digits

May 23, 2013

CAT Counting: Question with digits


This is an interesting question from Counting. Simple framework, but one needs to be very careful with the enumeration. One can get wrong answers in a number of ways.

Question
If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?
A.      3980
B.      3700
C.      3840
D.      3780

Correct Answer
Choice A

Explanatory Answer
We need to consider all three digit and all 4-digit numbers.

Three-digit numbers: A B C. 3 can be printed in the 100’s place or10’s place or units place.

Ø  100’s place:  3 B C. B can take values 0 to 9, C can take values 0 to 9. So, 3 gets printed in the 100’s place 100 times

Ø  10’s place:  A 3 C. A can take values 1 to 9, C can take values 0 to 9. So, 3 gets printed in the 10’s place 90 times

Ø  Unit’s place:  A B 3. A can take values 1 to 9, B can take values 0 to 9. So, 3 gets printed in the unit’s place 90 times

So, 3 gets printed 280 times in 3-digit numbers
Four-digit numbers: A B C D. 3 can be printed in the 1000’s place, 100’s place or10’s place or units place.

Ø  1000’s place:  3 B C D. B can take values 0 to 9, C can take values 0 to 9, D can take values 0 to 9. So, 3 gets printed in the 100’s place 1000 times.

Ø  100’s place:  A 3 C D. A can take values 1 to 9, C & D can take values 0 to 9. So, 3 gets printed in the 100’s place 900 times.

Ø  10’s place:  A B 3 D. A can take values 1 to 9, B & D can take values 0 to 9. So, 3 gets printed in the 10’s place 900 times.

Ø  Unit’s place:  A B C 3. A can take values 1 to 9, B & C can take values 0 to 9. So, 3 gets printed in the unit’s place 900 times.

3 gets printed 3700 times in 4-digit numbers.
So, there are totally 3700 + 280 = 3980 numbers

Answer Choice (A)


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1 Comments:

At 12:30 PM , Blogger Sam SID BID said...

A. 3980

 

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