A circle of radius 3 crosses the center of a square of side length 2. Find the positive difference between the areas of the non overlapping portions of the figures.
If the area of the square is s, the area of the circle is c, and the area of the overlapping portion is x. Then the area of the circle not overlapped by the square is c − x and the area of the square not overlapped by the circle is s − x, so the difference between these two is (c − x) − (s − x) = c − s= 9π² – 4
Place the digits 1 through 8 in the circles below such that no two adjacent circles contain consecutive digits.
Find the least value of x² + 4y² + 9z² , if x + y + z = 14.
A sales representative plans to visit each of six companies – A, B , C , D , E and F – exactly once during the course of a day. She is setting up her schedule for the day according to the following conditions:
She must visit B before D.
She must visit A before B and E.
The third company she visit must be C.
1. Which of the following must be true about the sales representative’s schedule ?
1. She visits A before D.
2. She visits B before E.
3. She visits C before A.
4. She visits C before F.
2. Which of the following could be the order in which the sales representative visits the six companies ?
1. C, E , A , B , D , F
2. C, F, A , E , D , B
3. A ,F, C, B , E, D
4. F, A , C, D, B, E
Find the number of integer solutions of the equation x² + 12 = y⁴.
Task – Make three pancakes in the least amount of time possible.
Conditions: One side of a pancake takes exactly three minutes to cook on a pan. You need to cook both sides. This means that a pancake takes exactly six minutes to cook.
Anything else: Yes. You’ve got two pans and two gas burners. Use them as you please.
Have I got gas? Of course. Assume what you’ve got to assume.
Get started!
Which of the following statements are always correct :-
I. If p and p² + 8 are prime numbers, then p³ + 8p + 2 is also prime.
II. a4 + 4 is prime for some a > 1.
a) Only I
b) Only II
c) Both
d) None
6 men, R, S, T, U, V and W sat around a circular table playing cards. It was noticed that no two men , the initial letters of whose names are adjacent in English alphabet, sat next to each other .U was opposite to R. V was not to immediate right of R.
1. Who sat to the immediate left of R ?
a. U
b. T
c. V
d. W
