17th
Annual J. W. Andrushkiw
Mathematics
Competition
This exam is provided without any claims of accuracy
1.
Tom is 10 years older than Jim. Five years ago the sum of their ages was 34
years. How old is Tom now?
2.
The original price of an item was lowered 32% to obtain a sales price of
$27.20. By what percent should the original price be lowered to obtain a sales
price of $22.00?
3.
The sum of the supplement and the complement of an angle A is 
less than 14 times the degree measure of angle A. Find
the degree measure of angle A.
4.
Evaluate 
given that a = 
, b = 
and c = 5.
5.
Two bottles, A and B, contain mixtures of acid and water. A
contains 15 liters and the mixture is 60% acid; the mixture in B is 80%
acid. When the contents of bottles A and B are combined, a
mixture containing 74% acid is obtained. How many liters of acid should be
added to the combined mixture to obtain a mixture that is 80% acid?
6. Find the coefficient of 
in the expansion of 
7. Four couples have reserved
8 seats for a concert, 4 in one row and 4 directly behind those in the first
row. How many different seating arrangements are possible if Al and Beth sit in
adjacent seats in the first row, Carl and Doris sit in nonadjacent seats in the
second row, Ed sits in the second row, Freda sits in the first row, Greg sits
in the second row directly behind Beth, and Helen sits in the remaining seat?
8. Let N be a 3-digit
number with two digits the same and no digit 0. The sum of the digits of N
is odd, and the product of the digits of N is even and exceeds the sum
of its digits by M, where M is a 3-digit number with no digit 0.
The number formed by reversing the digits of N is 297 less than N.
Find N.
9. A rectangle and a rhombus
have a side AB ,of length 34, inches in common.
The sides opposite AB (in the rectangle and the rhombus, respectively)
lie on a line l, and the rectangle and the rhombus have equal areas ,of 544 square inches. Let trapezoid ABSR have AB
and RS as its two parallel sides with RS on line l and shorter than AB, AR a side of the
given rhombus and SB a side of the given rectangle. If trapezoid ABSR
has area 304 square inches, find the sum of the perimeters of the rectangle,
the rhombus and trapezoid ABSR.
10. A deck of 32 cards
includes 8 red, 8 green, 8 yellow and 8 blue cards; the 8 cards of each color
are numbered from 1 to 8, respectively. Four cards from the deck of 32 cards
are chosen, without replacement. Find the probability that cards of at most two
different colors are chosen given that four even-numbered cards are chosen.
11. Let 
. Let 
. Find the product of v and w.
12. Jane walks on a moving
walkway in an airport from a waiting area to a boarding area in 5 minutes at a
fixed rate; the rate at which the walkway moves is also constant. She realizes
that she left something in the waiting area and so walks back on the walkway,
in the direction opposite to which the walkway is moving, from the boarding
area to the waiting area in 8 minutes at double the rate she walked earlier.
Find the rate of the moving walkway, in yards per minute if the distance from
the waiting area to the boarding area on the walkway is 80 yards.
13. Lines l1: 2x
+ 2y = 3, l2: x
= y and l3: x
= 7y lie on a coordinate plane. Find the area of the smallest circle
such that all three lines are tangent to this circle.
14. A fenced pasture is in the shape of a tr
15. Let r, s, t,
u be integers such that 
for all real values of
x larger than 2. Find the product rstu.
16.
Let 
and 
, where 
=-1. The sum w + v is equal
to 
where t is a
positive integer. Find t.
Last Modified: Aug 2012
Maintained by: Math/CS @ SHU.edu (bgw)