Entrance Exams
Govt. Exams
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
A+B rate = 1/6 + 1/8 = 7/24.
Work in 2 days = 14/24 = 7/12.
Remaining = 5/12.
All three rate = 1/6 + 1/8 + 1/12 = 9/24 = 3/8.
Days = (5/12)/(3/8) = 40/36 ≈ 1.11, recalculating: remaining work done in 2 days
Let A's rate = 1/x, B's rate = 1/y.
From equations: 3/x + 2/y = 1/4 and 2/x + 3/y = 1/3.
Solving: x = 30 days
Combined rate = 1/8, A's rate = 1/12. B's rate = 1/8 - 1/12 = 3/24 - 2/24 = 1/24. B takes 24 days
A completes 1/3 work in 5 days, so rate = 1/15 per day.
Remaining work = 2/3.
Days needed = (2/3)/(1/15) = (2/3) × 15 = 10 days
Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5.
Time = 5 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.
A's rate = 1/12, B's rate = 1/18.
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36.
Time = 36/5 = 7.2 days