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02 Oct 2024, 04:38
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S represent a set in which the smallest 500 positive integers that have atleast one digit as 5 are arranged in an ascending order. What is 97th integer listed in S?
A. 495
B. 500
C. 501
D. 502
E. 503
A. 495
B. 500
C. 501
D. 502
E. 503
02 Oct 2024, 05:21
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MalachiKeti
We can count the number of digits to arrive at the answer
Between 0 and 99
The smallest digit = 5
5, 15, 25, 35, 45 ➾ 5 numbers
50 to 50 ➾ 10 numbers
65, 75, 85, 95 ➾ 4 numbers
Hence, between 0 and 99, we have 19 numbers that have atleast one digit as 5.
The same pattern will repeat between 100 and 199; 200 and 299; 300 and 399; 400 and 499
Hence, number of digits between 0 and 499 that have atleast one digit as 5 ➾ 19 * 5 = 95
The 96th number ➾ 500
The 97th number ➾ 501
Option C
11 Feb 2025, 12:32
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Looking at the options, looks like we need to count numbers less than 500 which has atleast one digit as 5,
Numbers with only second digit as 5 = 5*1*9 (First digit can be 0 to 4, Second digit would be 5, Third digit cannot be 5)
Similarly numbers with only third digit as 5 = 5*9*1 (First digit can be 0 to 4, Second digit cannot be 5, Third digit would be 5)
Numbers with both second and third digits as 5 = 5*1*1
Total numbers less than 500 with atleast one digit as 5 = 45 + 45 + 5 = 95
96th digit => 500
97th digit => 501
Ans: C
Numbers with only second digit as 5 = 5*1*9 (First digit can be 0 to 4, Second digit would be 5, Third digit cannot be 5)
Similarly numbers with only third digit as 5 = 5*9*1 (First digit can be 0 to 4, Second digit cannot be 5, Third digit would be 5)
Numbers with both second and third digits as 5 = 5*1*1
Total numbers less than 500 with atleast one digit as 5 = 45 + 45 + 5 = 95
96th digit => 500
97th digit => 501
Ans: C
