GATE Electrical 2020 | GA Question: 8

Question

In four-digit integer numbers from $1001$ to $9999$, the digit group $\text{“37”}$ (in the same sequence) appears ________ times.

• A. $270$
• B. $279$
• C. $280$
• D. $299$

Answer 1

Ans C

Number of four digit numbers from $1001$ to $9999 =  8999.$ Number of times digit group $“37”$ appears is given by:

• $\_ \;\;\_\;\;3 \;\;7 \to \text{(1 to 9) (0 to 9)} \to 9 \cdot 10 = 90$
• $\_\;\;3 \;\;7\; \_  \to \text{(1 to 9) (0 to 9)} \to 9 \cdot 10 = 90$
• $3 \;\;7\;\_\;\; \_ \to \text{(0 to 9) (0 to 9)} \to 10\cdot 10 = 100$

Total count $=90+90+100 = 280.$

Correct option: C

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If the question was for finding the number of integers in which $“37”$ appeared then answer would be $279$ because in the above counting we double counted for $3737$, first in  $\_ \;\;\_\;\; 3\; \;7$ and second in $3\; \; 7\; \_ \;\;\_ .$

Comments

What’s the use to write 4^th line (3737 is counted twicw ….)

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Edited now.