The radius of a circle is increased

The radius of a circle is increased by 100%. Find the percentage increase in
the area?
(2)
Three committees meet today. Of these three committees, one meets every 11
days, a second meets every 15 days, and the third meets every 21 days. What
is the number of days before they all meet on the same day again?
(3)
A nonzero number is halved and the result is squared. This yields a number
which is twice the original number. What is the original number?
(4)
The hypotenuse of a right triangle has length 10 cm, and the other two sides
have lengths *y *and 3*y *respectively. Find the area of the triangle, in cm
2
.
(5)
In the diagram below, *ABC *is an equilateral triangle of side length 7 cm.
The
arcs *AB*, *BC *and *CA *are drawn with centres *C*, *A *and *B *respectively.
Find the
total length, in cm, of the three arcs. (Using
22
7
π
=
)
(6)
Carmen selects four different numbers from the set {1, 2, 3, 4, 5, 6, 7}
whose
sum is 11. If
*l*
is the
*largest*
of these four numbers, what is the value of
*l*
?
(7)
When my age is divided by 2, 3, 4 or 6 there is always a remainder of 1, but
when divided by 7 there is no remainder. How old am I if my age is under
100?
(8)
If 7 is subtracted from a three-digit number
*x*
, the result is a multiple of 7. If 8
is subtracted from
*x*
, the result is a multiple of 8. If 9 is subtracted from
*x*
, the
result is a multiple of 9. When
*x*
is divided by 10, what is the remainder?
(9)
In a class of 25 children, 12 wear glasses and 11 wear braces. If 7 wear
both
glasses and braces, what is the number of those who wear neither?
(10)
*IMSO*
,
*MOSI*
and
*SMIO*
are some arrangements of the letters
*I*
,
*M*
,
*S*
and
*O*
.
How many different arrangements are there such that the letter
*I*
is not next to
the letter
*O*
?
(11) A boy saved 1 dollar in the first week, 4 dollars in the second week,
he saved
3 dollars more than he did the previous week. What was the total number of
dollars that the boy had in the first ten weeks?
*A*
*C*
*B*
------------------------------
*Page 3*
(12) A two-digit odd number is a multiple of 9. The product of its digits
is also a
multiple of 9. What is this number?
(13) The product of two positive integers is 1 000 000. Neither of the two
numbers
contains the digit 0. What is their sum?
(14) In triangle
△
*ABC*,
*A *=50° and the external bisector of *B *and *C *meet
in *O*. find the measure of *BOC *, in degrees?
(15) In the diagram below, each of the small squares in the 4×4 grid
measures 1 cm
by 1 cm. Find the area of the 11-sided polygon, in cm
2
.
(16) The teacher gave ten tests during the year, each carrying the same
weight. If
Mary had got 10 more marks on the last test, her average would have become
92. What was her actual average?
(17) The faces of a cube contain the numbers 1, 2, 3, 4, 5, 6 such that
the sum of the numbers on each pair of opposite faces is 7. For
each of the cube’s eight corners, we multiply the three numbers
on the faces incident to that corner, and write down its value. (In
the diagram, the value of the indicated corner is 1 × 2 × 3 = 6.)
What is the sum of the eight values assigned to the cube’s corners?
(18) In a certain province, there are twelve highways, each joining a pair
of cities.
Each city is situated at the termination of three highways. What is the
number
of cities in this province?
(19) A positive integer *n *is divisible by four of 2, 3, 4, 5, 6 and 7,
but not by the
other two. If the two numbers that do not divide *n *are consecutive, what
is the
smallest value of *n*?
(20) The positive integers *a *and *b *are such that
5
9
7
11
*a*
*b*
< <
.
Find the value of *a *+ *b *when *b *takes the smallest possible value.
*B*
*C*
*D*
*E*
*O*
50°
*A*
2
1
3
------------------------------
*Page 4*
(21) In the diagram below, *ABCD *is a square, *E *is a point on *AD *and *F
*a point on
*AB *such that *DE*=2*AE *and *AF*=2*BF*. What is the ratio of the area of
triangle
*CEF *to that of square *ABCD*?
(22) Consider the following pattern:
● ● ● ●
● ●