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Individual Test
Team test
Soal Individual Contest WIZMIC 2007
Problem
1.
If the result of 
is written in expanded
form, then what is the sum of the digits in that number ?
is written in expanded
form, then what is the sum of the digits in that number ?
Problem
2.
The figure below is an unfolded
cube. The faces of the cube are numbered from 1 to 6. Each vertex of the cube
is the intersection of the faces. Add
the numbers that appears on each face and place the sum in each vertex
respectively. Find the biggest sum in the eight vertices.
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Problem
3.
There are two sizes of metal balls. Each large ball
weighs 
times as much as a small
ball. Currently the left pan of the balance contains 12 small balls while the
right pan has 4 large balls. You are to add a number of balls of either type to
the right pan in order the two sides will be balanced. How many balls of each
type must be added?
times as much as a small
ball. Currently the left pan of the balance contains 12 small balls while the
right pan has 4 large balls. You are to add a number of balls of either type to
the right pan in order the two sides will be balanced. How many balls of each
type must be added? |
Problem 4.
Two 6-digit integers 
and 
satisfy
the equation:
and satisfy
the equation:
Find 
.
.
Problem
5.
If the area of three squares in the figure below
are 360 cm2, 40 cm2 and 40 cm2, respectively,
then what is the area of triangle ABC ?
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Problem
6.
What is the largest sum that can be obtained in the
expression BAD+MADD+DAM, when substitute the four numbers 2, 5, 9 and 8,
in the letters of the above addition problem (different letters
represent different numbers) ?
Problem
7.
Eleven different positive integers have average 12. If all
these numbers are arranged in increasing order on a line, then what is the
greatest possible median number in these group of positive integers?
Problem
8.
Find
the value of N in the equation below.
Problem
9.
In
the figure below some pattern of circles with the largest circle has radius 10
cm. Find the area of the shaded part. (Use 
= 3.14)
= 3.14) |
Problem
10.
If S =
(x + 87) + (x + 89) + (x + 91) + ....
+ (x + 2007), where x is a positive integer; then what is the
smallest value of x such that S is a perfect square number ?
Problem
11.
In the multiplication equation 
, where a, b, c are digits from 0 to 9 with 
. How many possible three-digit numbers 
are there in all that
satisfy the above given condition?
, where a, b, c are digits from 0 to 9 with . How many possible three-digit numbers are there in all that
satisfy the above given condition?
Problem
12.
Maria is about to travel on a bus, and she knows she must
prepare the exact fare. She is not sure how much will be the bus fare, but she
knows it is more than $2.00 and less than $4.00. What is the minimum number of
coins she must carry to be sure of canying the correct fare? (Assume that the
available coins are lc, 2c, 5c, 10c, 20c, 50c, $1 and $2.)
Problem
13.
P(n) is the product of the multiplication
of the digits of n and Q(n) is the sum of the digits of n,
where n is a natural number. For
example, P(23) = 2 x 3 = 6, Q(23) =
2 + 3 = 5. There is a property for n, that is : n = 3
x P(n) + Q(n). How many two-digit numbers have this
property?
Problem
14.
In
triangle ABC, points D, E, F are on sides AB, BC, CA respectively, with AD =
DB, CE = 3BE and AF = 2CF. If the area of triangle ABC is 480 cm2,
then what is the area of triangle DEF?
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Problem
15.
In a race of 200 m, Andy finishes 20 m ahead of Marry, and
29 m ahead of Betty. If Marry and Betty continue to run at their
previous average speeds, by how many meters will Marry finish ahead of Betty?