Sixth Grade Contest – 2016 Pellissippi State Math Competition
Pellissippi State
Middle School Mathematics Competition
6th Grade Exam
Scoring Format: 3 points per correct response
-1 each wrong response
0 for blank answers
Directions:
For each multiple-choice problem there are 5 possible answers listed. You are to work the
problems, determine the correct answer, and indicate your choice on the separate answer
sheet provided.
Please use only CAPITAL letters on the answer sheet (A, B, C, D, E) and print neatly. This
will enable us to correctly grade your paper. If there is any question as to what letter an
answer is, it will be marked wrong.
If you change your mind about your answer, be sure to erase completely. Avoid wild
guessing, as wrong answers count against you. Do not make more than one answer for any
problem. Make no stray marks of any kind on your answer sheet. Additional room for you
to work out problems is on the back of each test page. You may take the test packet with you
after you complete it. Only the answer sheet must be turned in. We will discard any test
packets left in testing room so please take your packet with you if you want it.
When told to do so, open your test packet and begin. There are 50 questions in all. All
questions are multiple choice. The working time for the entire test is 65 minutes, so you
should work quickly to finish all problems.
1
Sixth Grade Contest – 2016 Pellissippi State Math Competition
1.
2.
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
D.
$8.13
E.
None, he owes more than $50

A.
3.
5
2

12
3

13
B.
12
C.
$6.28
equals

7
C.
12

1
3
1
4
D.
1
3
E.
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.
A
4.
8
E.
9
E.
0.5 m
B
The length of line segment AB is approximately
A. 6 mm
5.
B.
25 mm
C.
3 cm
D.
8 cm
The amount of income tax that a family must pay is
" $315 plus 6% of any Adjusted Gross Income over $9,000 ".
If a family's Adjusted Gross Income is $36,400, the amount of income tax they must pay is
A.
6.
B.
$1959
C.
$2184
D.
$2499
E.
$16,755
If these five numbers were placed in a list from smallest to largest, the middle number would be
A.
7.
$1644
0.8
B.
0.78
C.
13
17
D.
0.93
E.
0.62
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
2
D.
$0.48
E.
$0.51
Sixth Grade Contest – 2016 Pellissippi State Math Competition
8.
9.
Which one of these five lengths of time is NOT EQUAL to the other four?
A.
1.45 hours
B.
1.75 hours
D.
1 hour, 45 minutes
E.
105 minutes
C.
6300 seconds
43A2
35B
+C627
Make a correct addition problem by replacing
each of the variables: A, B, and C with a digit.
-------------------The sum A+B+C equals
A.
7
B.
10.
8
8293
C.
9
D.
A
10
E.
11
E.
3
B
-4 -3
-2 -1
0
1
2
3
4
A and B represent points on this number line. B - A equals
A.
11.
$6.00
GIVEN:
A.
13.
2
3
B.
-1
C.
4
D.
1
2
3
5
6
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.)
A.
12.
4
355
113
B.
$14.00
C.
  3.141592654
B.
22
7
$16.33
D.
$28.67
E.
$34.67
Which one of these five numbers is closest to ?
C.
10
D.
2 +
3 E.
3.14
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
3
D.
5:00 PM
E.
5:30 PM
Sixth Grade Contest – 2016 Pellissippi State Math Competition
14.
15.
Angle ABC is a right angle.
The measure of angle ABD is closest to
A.
20o
B.
45o
D.
75o
E.
90o
17.
B
2:14 PM
B. 2:24 PM
C.
2:40 PM
A.
2
1 2
x
3 3
B.
2
1 3
x
3 4
D.
2
1
2

3
3
E.
2
1
2

3
3
C
D.
2:41 PM
E. 3:14 PM
C.
2
1
3

3
4
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?
12
B.
9 - 9 x 9 + 92 
A.
19.
D
The largest of the following five numbers is
A.
18.
60o
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.
16.
C.
A
-66
18
C.
24
D.
36
E.
48
C.
-18
D.
3
E.
27
9 equals
B.
-45
24 cm
(The figure is not drawn to scale.)
The area, in square centimeters,
of the shaded region is
A.
288
B.
306
D.
320
E.
336
C.
5 cm
18 cm
314
10 cm
6 cm
4
9 cm
Sixth Grade Contest – 2016 Pellissippi State Math Competition
20.
The date of the second Thursday of a month is a square number.
The last Monday of the month is on the
A.
21.
23.
14.2%
C.
28th
D. 30th
B.
17.8%
C.
21.1%
A.
8 cents/hour
B.
10 cents/hour
D.
14 cents/hour
E.
29 cents/hour
E.
Cannot be determined
D.
25.6%
E.
44.4%
C.
11 cents/hour
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
64
B.
3
16
C.
15
16
D.
For HOW MANY of these five values for x is
-5
A.
25.
27th
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.)
A.
24.
B.
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.
22.
26th
-1/2
One
1/2
B.
Two
Three
E.
7
8
E.
Five
x3 < x ?
0.8
C.
1
8
5
D.
Four
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
5.1
E.
5.4
Sixth Grade Contest – 2016 Pellissippi State Math Competition
26.
A number x is doubled, the result is increased by 6, then that result is halved.
The final answer is 36.
A number y is divided by 3, the result is decreased by 6, then that result is tripled.
The final answer is 36.
The sum x + y equals
A.
27.
57
C.
66
D.
82
$3.36
B.
$4.20
C.
$4.59
D.
$5.34
One
B.
Two
C.
Three
D.
Four
87
E.
$9.18
E.
More than four
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.)
30.
E.
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.
29.
B.
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.
28.
52
A.
41.2
B.
56.6
C.
D.
116.6
E.
Cannot be determined
24 cm
84.6
2000 is the sum of 40 consecutive odd integers. The smallest of these is
A.
9
B.
11
C.
27
D.
6
29
E.
31
Sixth Grade Contest – 2016 Pellissippi State Math Competition
31.
MATH is a rectangle. DH = HT.
The area of triangle DHT is 8 .
The area of triangle AHT is 3 .
D
The area of triangle MAD is
A.
4.5
B.
5
D.
6.5
E.
11
M
C. 5.5
H
-10,
32.
A
-7,
-4,
0,
T
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
A.
33.
B.
85
C.
90
D.
105
E.
120
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.
34.
60
- z)?
10
B.
12
C.
13
D.
15
E.
16
Last year Suzanne's father, Rick, was three times as old as Suzanne. Today, Rick is 32 years
older than Suzanne. (In this problem, all "ages" are whole numbers.)
What will be the sum of their ages next year?
A.
35.
64 years
B.
65 years
C.
66 years
D.
67 years
E.
68 years
D.
137
E.
220
A circle with radius 16 cm is inscribed in a square.
Rounded to the nearest square centimeter,
the area of the shaded region is
A. 3
B.
55
C.
74
7
Sixth Grade Contest – 2016 Pellissippi State Math Competition
36.
ABCD was a square sheet of paper, 6 cm
on a side. As shown, corner D was folded
to point F on the diagonal BD. The area of
triangle EFG equals the area of the shaded
L-shaped polygon: ABCGFE.
A
B
E
F
The length of BF, in centimeters, is
(Round to the nearest tenth.)
37.
A.
1.4 cm
B.
1.6 cm
D.
2.0 cm
E.
2.2 cm
C.
G
D
1.8 cm
C
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.
38.
Three
1
C.
Four
3
2
D.
Five
5
E.
9
7
6
4
Ten
8
Always following the direction of the arrows, the number of distinct paths from
A.
39.
1
3
A.
32
B.
of 9 120 equals
40
B.
34
C.
36
D.
38
E.
40
D.
239
E.
359
3 N . What does N equal?
80
C.
119
8
1 to 9
is
Sixth Grade Contest – 2016 Pellissippi State Math Competition
40.
The sum
A.
41.
20
B.
22
$0.24
B.
23
D.
26
E.
27
C.
$0.36
D.
$0.40
E.
$0.42
A clock chimes on the hour once at 1 o'clock, twice at 2 o'clock, three times at 3 o'clock, and
so on, up to a maximum of twelve times at 12 o'clock. How many total times does this clock
chime between 10:15 AM one day and 6:50 AM the next day?
B.
111
C.
112
D.
122
E.
130
A manager wants to hire a good problem solver to work at her computer store for just four
weeks. When Terry applies, the manager offers him, "I will pay you $0.01 on Day 1, $0.02 on
Day 2, $0.04 on Day 3, $0.08 on Day 4, and so on, doubling your pay each day." Terry
laughed and walked out. How much would Terry have earned on Day 20 alone?
B.
$10.24
C. $1,024
D. $5,242.88
E. $10,485.76
A math teacher buys three sport coats and six ties. He teaches Monday through Friday.
Starting on a Monday, he wears a different combination of new sport coat and new tie each day
that he teaches. On which day of the week does he wear his last new combination?
A.
45.
C.
$0.30
A. $0.40
44.
LSGEM
M+E+G+S+L equals
A. 100
43.
-------------
Suzanne buys bagels for $6.60 per dozen. She spends $16.50 for the bagels and then sells all of
them for $23.70 . What is her average profit per bagel?
A.
42.
MEGSL
x 4
In this multiplication problem, replace each letter
with a digit chosen from 0 through 9, inclusive. M  0 .
Replace identical letters with the same number.
Different letters represent different numbers.
Monday
B. Tuesday
C.
Wednesday
D. Thursday
E. Friday
Among the 500 spectators at a basketball game, 30% were not students. Among the students,
30% were sophomores. Among the sophomores, 60% were boys. How many female
sophomores were spectators at the game?
A. 18
B.
27
C.
42
9
D.
54
E.
63
Sixth Grade Contest – 2016 Pellissippi State Math Competition
46.
A 27-year old mother has a 5-year old daughter.
In how many years will the mother be three times as old as her daughter?
A.
47.
C.
9
D.
15
E.
None of these
6
B.
7
C.
8
D.
9
E.
More than 9
3
B.
5
C.
7
D.
8
E.
9
The prime factorization of 200 can be written as 200 = 2x 5y . The sum x + y equals
A.
50.
6
For what value of x does: 1 + x + x + 8 + 13 + x3 + x3 + 83 = 1998 ?
A.
49.
B.
To build a set of book shelves, a carpenter needs 30 identical boards, each 2 feet 7 inches long. For this
type of wood, the lumber yard sells only 12 foot long boards.
How many 12 foot long boards must the carpenter purchase?
A.
48.
4
5
B.
6
C.
7
D.
8
E.
More than 8
A train traveling a constant 75 miles per hour departs from St. Louis to New Orleans at 2:00 PM. At
5:30 PM, a plane that flies a constant 350 miles per hour departs from St. Louis to New Orleans. When
the plane arrives at New Orleans at 7:00 PM, how far is the train from New Orleans? (Assume that the
distance from St. Louis to New Orleans by plane equals the distance by train.)
A. 150 miles
B. 175 miles
C.
262.5 miles
10
D. 375 miles
E. 525 miles