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
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
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
60% work is done in 9 days.
Rate = 0.6/9 = 1/15 per day.
Total days = 1/(1/15) = 15 days
First five prime numbers are 2, 3, 5, 7, 11.
Product = 2 × 3 × 5 × 7 × 11 = 2310
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).
Largest 3-digit number = 999, Smallest 3-digit number = 100.
Difference = 999 - 100 = 899
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).
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 the remainder when 527 is divided by 15 using the division algorithm.
We need to divide 527 by 15 and find what's left over.
Determine how many times 15 goes into 527 completely.
Subtract the product from the original number to find the remainder.
The remainder when 527 is divided by 15 is 2, so the answer is (A).