Govt Exams
This question asks us to find the average value of the numbers 1 through 15.
The first 15 natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
Use the formula for sum of first n natural numbers: \[\text{Sum} = \frac{n(n+1)}{2}\]
Average is the sum divided by the count of numbers.
The average of the first 15 natural numbers is 8.
This question asks us to find an unknown number based on a sequence of arithmetic operations performed on it.
Let the unknown number be x. According to the problem, when x is multiplied by 8 and then 15 is subtracted, the result is 49.
Add 15 to both sides of the equation to move the constant to the right side.
Divide both sides by 8 to find the value of x.
The number is 8, which corresponds to answer choice (B).
Largest 3-digit number = 999, Smallest 3-digit number = 100.
Difference = 999 - 100 = 899
This question asks us to identify which number is a perfect square (a number that equals an integer multiplied by itself).
A perfect square is a number that can be expressed as n × n where n is an integer.
Test each option by finding if its square root is a whole number.
Only 169 has a whole number square root.
169 is a perfect square because 13 × 13 = 169, making the correct answer (B).
First five prime numbers are 2, 3, 5, 7, 11.
Product = 2 × 3 × 5 × 7 × 11 = 2310
60% work is done in 9 days.
Rate = 0.6/9 = 1/15 per day.
Total days = 1/(1/15) = 15 days
This question tests the concept of inverse proportionality between the number of workers and the time required to complete a fixed task.
Work is constant regardless of the number of workers, so we multiply workers by days.
With 10 workers, the same 40 worker-days of work must be completed.
Divide total work by the number of workers to find days required.
When 10 workers work together, they will build the same wall in 4 days.
This question asks us to find B's daily work rate when the total job can be completed in 15 days.
Work rate is the fraction of total work completed per day.
Since B completes the entire job, the total work equals 1.
B completes the job in 15 days, so divide the work by the number of days.
B's work rate is 1/15 of the job per day, which means B completes one-fifteenth of the job each day for 15 days to finish it completely.
This question tests the concept of work rate and how much work is completed in a given time period.
A completes the entire work in 20 days, so the work rate is 1 part per day.
Multiply the daily work rate by the number of days.
Reduce the fraction to its simplest form by dividing both numerator and denominator by 5.
A will complete 1/4 of the work in 5 days.
This question asks us to find the Least Common Multiple (LCM) of two numbers using prime factorization.
Break 15 into its prime factors.
Break 25 into its prime factors.
The LCM is found by taking the highest power of each prime that appears in either factorization: 3¹ and 5².
The LCM of 15 and 25 is 75.