If the sum of two numbers is 12 and their product is 35, what is the sum of their squares?
Correct!
Wrong!
The sum of the squares of two numbers is given by the formula: (a + b)^2 - 2ab. Substituting the values, we get (12)^2 - 2(35) = 144 - 70 = 74.
A train travels 60 miles in 1.5 hours. What is its average speed?
Correct!
Wrong!
Average speed is calculated as distance divided by time. 60 miles / 1.5 hours = 40 mph.
If the ratio of the ages of two people is 3:5, and the sum of their ages is 40, what is the age of the older person?
Correct!
Wrong!
Let the ages be 3x and 5x. Their sum is 8x = 40, so x = 5. The older person is 5x = 25 years old.
What is the next number in the sequence: 2, 6, 12, 20, ...?
Correct!
Wrong!
The differences between consecutive terms are 4, 6, 8, which increase by 2. The next difference is 10, so the next number is 20 + 10 = 30.
A person invests $1,000 at an annual simple interest rate of 5%. How much will the investment be worth after 3 years?
Correct!
Wrong!
Simple interest is calculated as principal × rate × time. $1,000 × 0.05 × 3 = $150. Total amount = $1,000 + $150 = $1,150.
What is the value of x in the equation 3x - 7 = 11?
Correct!
Wrong!
Add 7 to both sides to get 3x = 18. Divide both sides by 3 to find x = 6.