Circle and Square I

The diameter of a circle is the same length as the side of a square. How much greater is the area of the square?

A. It isn't greater; the circle and square have the same area.

B. The area of the square is 25% greater.

C. The area of the square is 27.3% greater.

D. The area of the square is 50% greater.

E. The area of the square is 54.6% greater.

Explain your answer.

More Odd Numbers

The sum of a sequence of odd numbers is always divisible by half of the sum of the first and last odd numbers in the sequence. For example, 7 + 9 + 11 + 13 is divisible by ½(7 + 13), and 3 + 5 + 7 + 9 + 11 is divisible by ½(3 + 11). Why?

Odd Numbers

It's been a hectic month. I am now employed again, and have had little time for word problems. However, here's a good brain teaser.

A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."

Stock Up

Walter buys shares of a stock for $1000 on Monday. On Tuesday, the stock gains 10%. On Wednesday it loses 10%. What is the value of the stock at the end of trading on Wednesday?

Twice and Thrice

The sum of two integers is twice their difference. Their product is three times their difference. What are the two integers?

Easy Does It

The ratio of two numbers is twice their sum, and their difference is zero. What are the two numbers?

Equilateral Perimeter

The perimeter of an equilateral triangle is twice the area. What is the length of a side?