Q45·CSAT · Prelims 2024
Determining the final percentage change after multiple sequential operations
NumericalPercentagesFactual single● Medium
Question
What is the number of fives used in numbering a 260-page book? [cite: 1832, 1833]
Options
a
55
bAnswer
56
c
57
d
60
Explanation
To count the occurrences of the digit 5 up to 260, track them systematically across hundreds blocks:
1From 1 to 99:
5 in the units place: {5, 15, 25, 35, 45, 55, 65, 75, 85, 95} \rightarrow 10 times.
5 in the tens place: {50, 51, 52, 53, 54, 55, 56, 57, 58, 59} \rightarrow 10 times.
(Note: 55 is counted in both lines, matching its 2 actual digits). Total for 1-99 = 10 + 10 = 20.
2From 100 to 199:
Repeats the exact same pattern for units and tens places = 20.
3From 200 to 260:
Units place 5s: {205, 215, 225, 235, 245, 255} \rightarrow 6 times.
Tens place 5s: {250, 251, 252, 253, 254, 255, 256, 257, 258, 259} \rightarrow 10 times.
Total for 200-260 = 6 + 10 = 16.
Summing all blocks together: 20 + 20 + 16 = 56.
In a standard 100-number block (0-99), any single digit appears exactly 20 times across the units and tens dimensions.
Answer: (b).
Question details
Year
2024
Paper
CSAT
Question
Q45
Section
Numerical Ability
Sub-topic
Percentages
Type
Factual single
Difficulty
Medium
Source hint
Percentage application
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