# 1. Joshua buys two CD's at \$14.95 each and three tapes at \$3.99

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```							Seventh Grade Test - Excellence in Mathematics Contest - 2000
1.   Joshua buys two CD's at \$14.95 each, three tapes at \$3.99 each, and pays 6% state sales tax.
How much change does he receive from a \$50 bill? (Round to the nearest cent.)

A.     \$5.24             B.        \$5.62                 C.   \$6.28

D.     \$8.13             E.        None, he owes more than \$50

5    2
2.                     equals
12   3

13                  7                     1                1                 1
A.                 B.                    C.                D.              E.
12                 12                     3                4                 3

3.    A basketball team has won seven of its first fifteen games. How many wins in their next ten
games will raise their winning percentage for the season to 60%?

A. 2               B.   6                 C.   7             D.      8            E.       9

4.                   A                                                     B

The length of line segment AB is approximately

A. 6 mm            B.   25 mm             C.   3 cm          D.      8 cm         E.       0.5 m

5.   The amount of state income tax that a Missouri family must pay is

" \$315 plus 6% of any Adjusted Gross Income over \$9,000 ".

If a Missouri family's Adjusted Gross Income is \$36,400,
the amount of Missouri state income tax they must pay is

A.     \$1644        B.   \$1959             C.   \$2184         D.      \$2499        E.       \$16,755

6.   If these five numbers were placed in a list from smallest to largest, the middle number would be

13
A.     0.8          B.   0.78              C.                 D.      0.93         E.           0.62
17

7.   The peel of a banana weighs 1/8 of the total weight of the banana. If you buy 3.5 kg of bananas
at one kg for \$1.10, how much are you paying for the peels?      (Round to the nearest cent.)

A.     \$0.14        B.   \$0.35             C.   \$0.41         D.      \$0.48        E.       \$0.51

1
Seventh Grade Test - Excellence in Mathematics Contest - 2000

8.    Which one of these five lengths of time is NOT EQUAL to the other four?

A.    1.45 hours              B.      1.75 hours          C.     6300 seconds

D.    1 hour, 45 minutes      E.      105 minutes

9.    Make a correct addition problem by replacing                    43A2
each of the variables: A, B, and C with a digit.                 35B
+C627
--------------------
The sum A+B+C equals                                             8293

A.    7             B.   8            C.    9             D.     10              E.   11

10.                   A                                          B

-4 -3      -2 -1       0     1     2      3     4
A and B represent points on this number line. B - A equals

2                                                            2                   5
A.    4             B.   -1           C.    4             D.      1             E.   3
3                                                            3                   6

11.   A graduate of Washington School earns her living by planning meals and buying groceries for
ladies who do not like to do it themselves. From one family, she receives \$8.00 a month plus 1/3
of every dollar less than \$80 per month that the family has to spend for food. How much does
this family pay her for a month when the food costs them \$62.00?       (Round to the nearest cent.)
(The Thorndike Arithmetics, Edward Lee Thorndike, 1917, page 57)

A.    \$6.00         B.   \$14.00       C.    \$16.33        D.     \$28.67               E.       \$34.67

12.   GIVEN:                3.141592654        Which one of these five numbers is closest to ?

355                22
A.                  B.                C.        10        D.       2 +      3         E.       3.14
113                 7

13.   A painter has finished painting 2/3 of a room by 2:00 PM and 3/4 of the same room by 2:30 PM.
At this rate, when does he finish painting the room?

A.    3:30 PM       B.   4:00 PM      C.    4:30 PM       D.     5:00 PM         E.   5:30 PM

14.   Angle ABC is a right angle.                           A
2
D
Seventh Grade Test - Excellence in Mathematics Contest - 2000
The measure of angle ABD is closest to

A.    20o          B.     45o             C.     60o

D.    75o          E.     90o

15.   Shannon and Suzanne average 68 miles per hour on a 390 mile automobile drive.
If they start at 8:40 AM, when do they complete their drive? (Round to the nearest minute.)

A.    2:14 PM           B. 2:24 PM               C.    2:40 PM        D.   2:41 PM          E. 3:14 PM

16.   The largest of the following five numbers is

1 2                                 1 3                             1   3
A.    2     x                   B.        2     x                 C.       2     
3 3                                 3 4                             3   4

1   2                               1   2
D.    2                        E.        2      
3   3                               3   3

17.   If it takes Jeremy 18 hours to dig a 2 meter by 2 meter by 2 meter hole, how many hours would it
take three men (each working at the same rate as Jeremy) to dig a 4 meter by 4 meter by 4 meter
hole?

A.    12           B.     18              C.     24         D.    36             E.    48

18.   9 - 9 x 9 + 92         9 equals

A.    -66          B.     -45             C.     -18        D.    3              E.    27

19.   (The figure is not drawn to scale.)                                        24 cm
The area, in square centimeters,
of the shaded region is                                                                       5 cm
18 cm
A.    288          B.     306        C.        314                                     9 cm
10 cm
D.    320          E.     336
6 cm

20.   The date of the second Thursday of a month is a square number.
3
Seventh Grade Test - Excellence in Mathematics Contest - 2000
The last Monday of the month is on the

A.    26th           B.   27th        C.    28th         D. 30th          E.   Cannot be determined

21.   In a school district, 32% of the students are enrolled in high school. The ratio of girls to boys in
the high school is 4:5 . What per cent of the district's students are high school males?
(Round to the nearest tenth of a per cent.)

A.    14.2%          B.   17.8%        C.     21.1%         D.     25.6%       E.    44.4%

22.   Frank bought a dog one day for \$2.50 and spent one hour per day for nine days trying to sell it.
Food for the dog cost him 25 cents, and he spent a total of four hours in cleaning and caring for
the dog. He sold the dog for \$3.75. How much did he profit per hour for the time spent on the
whole transaction? (Round to the nearest cent.)
(Thorndike Arithmetics - Book Three, Edward Lee Thorndike, 1917, page 51)

A.    8 cents/hour               B.    10 cents/hour               C.     11 cents/hour

D.    14 cents/hour              E.    29 cents/hour

23.   A city park is rectangular with a length of 3/4 mile and a width of 330 yards. The area of the
park is what fraction of one square mile?     (1 mile = 1760 yards)

9                   3                  15                   1                 7
A.                   B.                C.                   D.                 E.
64                  16                  16                   8                 8

24.   For HOW MANY of these five values for x is             x3 < x ?
-5            -1/2        1/2                 0.8                  5

A.    One            B.   Two          C.     Three         D.     Four        E.    Five

25.   A backpacking group plans to leave the Rock at 11:00 AM, walk past Heartbreak Hill, and finish
at Taum Sauk Peak. The total hiking distance will be 12 km. Hiking at an average rate of 3
km/hr, they arrive at Heartbreak Hill at 12:45 PM. In order to reach Taum Sauk Peak by 2:00
PM, how fast, in kilometers per hour, will they have to walk from Heartbreak Hill to Taum Sauk
Peak?

A.    3.5            B.   4.2          C.     4.5           D.     5.1         E.    5.4

26.   A number x is doubled, the result is increased by 6, then that result is halved.
4
Seventh Grade Test - Excellence in Mathematics Contest - 2000
A number y is divided by 3, the result is decreased by 6, then that result is tripled.
The sum x + y equals

A.    52          B.     57          C.     66          D.     82          E.     87

27.   A package of 20 plastic forks costs \$0.39 . A package of 24 plastic knives costs \$0.45 .
If you wish to purchase the same number of forks and knives,
what is the least amount that you could spend?

A.    \$3.36       B.     \$4.20       C.     \$4.59       D.     \$5.34       E.     \$9.18

28.   You have eight United States coins worth exactly \$0.92 .
(Consider only the current coins: penny, nickel, dime, quarter, and half-dollar.)
HOW MANY different combinations of coins are possible?

A.    One         B.     Two         C.     Three       D.     Four        E.     More than four

29.   The three circles are tangent to the rectangle and to each other.
The length of the rectangle is 24 cm.

The area, in square centimeters, of the shaded region is
(Round to the nearest tenth.)                                            24 cm

A.    41.2        B.     56.6        C.     84.6

D.    116.6       E.     Cannot be determined

5
Seventh Grade Test - Excellence in Mathematics Contest - 2000
30.   2000 is the sum of 40 consecutive odd integers. The smallest of these is

A.    9           B.     11           C.        27             D.    29             E.   31

D
31.   MATH is a rectangle. DH = HT.
The area of triangle DHT is 8 .
The area of triangle AHT is 3 .

The area of triangle MAD is                                     M                                   A

A.    4.5         B.     5            C.        5.5
H                              T
D.    6.5         E.     11

32.                                  -10,        -7,           -4,    0,     2,       5
From these five numbers select three different numbers for x, y, and z, in order to make this
expression, x(y - z), as large as possible

What is the largest possible value of x(y       - z)?
A.    60          B.     85           C.        90             D.    105            E.   120

33.   Example: The "sum of digits" of 1656 is 1+6+5+6 = 18 .
HOW MANY whole numbers from 1 to 2000 have their "sum of digits" equal to 25?

A.    10            B.    12               C.     13           D.    15             E.   16

34.   Suzanne's birthday is tomorrow (March 19). Suzanne's father, Rick, has his birthday on April 1
(no fooling!). On March 18, 1999, Rick was three times as old as Suzanne. Today (March 18,
2000), Rick is 32 years older than Suzanne. (In this problem, all "ages" are whole numbers.)

What will be the sum of their ages on April 2, 2000?

A.    64 years    B.     65 years     C.        66 years       D.    67 years       E.   68 years

35.   The number 9 has been placed into one of the small
triangles. Place the digits 1 through 8, inclusive,
into the other eight small triangles so that the sum of the
four numbers in each of these three triangles:

6
A

Seventh Grade Test - Excellence in Mathematics Contest - 2000
B           C
ADE, BFH, and CGI, is equal to 21.
D      x       y
E
x + y equals
D
9
A.   8          B.    9          C.   11
F          G   9   H           I
G
D.   12         E.    13

7
Seventh Grade Test - Excellence in Mathematics Contest - 2000
36.   ABCD was a square sheet of paper, 6 cm
on a side. As shown, corner D was folded                          A                                 B
to point F on the diagonal BD. The area of
triangle EFG equals the area of the shaded                     E                              F
L-shaped polygon: ABCGFE.

The length of BF, in centimeters, is
(Round to the nearest tenth.)
D                       G         C
A.    1.4 cm      B.      1.6 cm        C.     1.8 cm

D.    2.0 cm      E.      2.2 cm

37.   Let N = 1234567898765432AB , where A and B are digits, possibly equal.

Of the many different possible values of N, HOW MANY are divisible by 18?

A.    Two B.      Three        C.       Four            D.   Five               E.   Ten

38.
1              3                   5                  7                  9

2                4                    6                  8

Always following the direction of the arrows, the number of distinct paths from                      1 to 9   is

A.    32          B.      34            C.     36            D.       38             E.       40

1
39.           120 equals
of 9                 3 N . What does N equal?
3

A.    40          B.      80            C.     119           D.       239            E.       359

40.   In this multiplication problem, replace each letter                             MEGSL
with a digit chosen from 0 through 9, inclusive. M  0 .                           x 4
Replace identical letters with the same number.                                      -------------
Different letters represent different numbers.                                  LSGEM

8
Seventh Grade Test - Excellence in Mathematics Contest - 2000
The sum M+E+G+S+L          equals

A.   20         B.    22            C.   23       D.   26   E.   27

9

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