1999 CEMC Gauss (Grade 7) Problems

Part A: Each correct answer is worth 5 points

Problem 1

$1999 - 999 + 99$ equals

$\text{(A)}\ 901  \qquad \text{(B)}\ 1099 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 199 \qquad \text{(E)}\ 99$

Solution

Problem 2

The integer $287$ is exactly divisible by

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 6$

Solution

Problem 3

Susan wants to place $35.5$ kg of sugar in small bags. If each bag holds $0.5$ kg, how many bags are needed?

$\text{(A)}\ 36 \qquad \text{(B)}\ 18 \qquad \text{(C)}\ 53 \qquad \text{(D)}\ 70 \qquad \text{(E)}\ 71$

Solution

Problem 4

$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}$ is equal to

$\text{(A)}\ \frac{15}{8} \qquad \text{(B)}\ 1\frac{3}{14} \qquad \text{(C)}\ \frac{11}{8} \qquad \text{(D)}\ 1\frac{3}{4} \qquad \text{(E)}\ \frac{7}{8}$

Solution

Problem 5

Which one of the following gives an odd integer?

$\text{(A)}\ 6^2 \qquad \text{(B)}\ 23-17 \qquad \text{(C)}\ 9\times 24 \qquad \text{(D)}\ 96\div 8 \qquad \text{(E)}\ 9\times 41$

Solution

Problem 6

In $\Delta ABC$, $\angle B = 72^{\circ}$. What is the sum, in degrees, of the other two angles?

$\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288$

Solution

Problem 7

If the numbers, $\frac{4}{5}$, $81\%$, and $0.801$ are arranged from smallest to largest, the correct order is

$\text{(A)}\ \frac{4}{5}, 81\%, 0.801 \qquad \text{(B)}\ 81\%, 0.801, \frac{4}{5}  \qquad \text{(C)}\ 0.801, \frac{4}{5}, 81\%  \qquad \text{(D)}\ 81\%, \frac{4}{5}, 0.801 \qquad \text{(E)}\ \frac{4}{5}, 0.801, 81\%$

Solution

Problem 8

The average of $10$, $4$, $8$, $7$, and $6$ is

$\text{(A)}\ 33  \qquad \text{(B)}\ 13  \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 10 \qquad \text{(E)}$ 7

Solution

Problem 9

André is hiking on the paths shown in the map. He is planning to visit sites A to M in alphabetical order. He can never retrace his steps and he must proceed directly from one site to the next. What is the largest number of labelled points he can visit before going out of alphabetical order?

$\text{(A)}\ 6 \qquad \text{(B)}\ 7 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 13$

Solution

Problem 10

In the diagram, line segments meet at $90^{\circ}$ as shown. If the short line segments are each $3$ cm long, what is the area of the shape?

$\text{(A)}\ 30 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 54$

Solution

Part B: Each correct answer is worth 6 points

Problem 11

The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles wide. The number of tiles that touch the walls of the room is

$\text{(A)}\ 26 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 46 \qquad \text{(E)}\ 50$

Solution

Problem 12

Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order. To decide who goes first in a game, they play "countdown". Henry starts by saying "34", with Iggy saying "33". If they continue to count down in their circular order, who will eventually say "1"?

$\text{(A)}\ Fred  \qquad \text{(B)}\ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)}\ Iggy \qquad \text{(E)}\ Joan$

Solution

Problem 13

In the diagram, the percent of small squares that are shaded is

$\text{(A)}\ 9 \qquad \text{(B)}\ 33 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 56.25 \qquad \text{(E)}\ 64$

Solution

Problem 14

Which of the following is an odd integer, contains the digit $5$, is divisible by $3$, and lies between $12^2$ and $13^2$?

$\text{(A)}\ 105 \qquad \text{(B)}\ 147 \qquad \text{(C)}\ 156 \qquad \text{(D)}\ 165 \qquad \text{(E)}\ 175$

Solution

Problem 15

A box contains $36$ pink, $18$ blue, $9$ green, $6$ red, and $3$ purple cubes that are identical in size. If a cube is selected at random, what is the probability that it is green?

$\text{(A)}\ \frac{1}{9} \qquad \text{(B)}\ \frac{1}{8} \qquad \text{(C)}\ \frac{1}{5} \qquad \text{(D)}\ \frac{1}{4} \qquad \text{(E)}\ \frac{9}{70}$

Solution

Problem 16

The graph shown at the right indicates the time taken by five people to travel various distances. On average, which person travelled the fastest?

$\text{(A)}\ Alison \qquad \text{(B)}\ Bina \qquad \text{(C)}\ Curtis \qquad \text{(D)}\ Daniel \qquad \text{(E)}\ Emily$

Solution

Problem 17

In a "Fibonacci" sequence of numbers, each term beginning with the third, is the sum of the previous two terms. The first number in such a sequence is $2$, and the third term is $9$. What is the eighth term in the sequence?

$\text{(A)}\ 34 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 107 \qquad \text{(D)}\ 152 \qquad \text{(E)}\ 245$

Solution

Problem 18

The results of the hair colour of $600$ people are shown in this circle graph. How many people have blonde hair?

$\text{(A)}\ 30 \qquad \text{(B)}\ 160 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 420$

Solution

Problem 19

What is the area, in $m^2$, of the shaded part of the rectangle? $\text{(A)}\ 14 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 33.6 \qquad \text{(D)}\ 56 \qquad \text{(E)}\ 42$

Solution

Problem 20

The first 9 positive odd integers are placed in the magic square so that the sum of the numbers in each row, column and diagonal are equal. Find the value of A + E.

$\text{(A)}\ 32 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 26 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 16$

Solution

Part C: Each correct answer is worth 8 points

Problem 21

A game is played on the board. In this game, the player can move three places in any direction (up, down, right or left) and then can move two places in a direction perpendicular to the first move. If a player starts on S, which position on the board (P, Q, R, T, or W) cannot be reached through any sequence of moves?

$\text{(A)}\ P \qquad \text{(B)}\ Q \qquad \text{(C)}\ R \qquad \text{(D)}\ T \qquad \text{(E)}\ W$

Solution

Problem 22

Forty-two cubes with $1$ cm edges are glued together to form a solid rectangular block. If the perimeter of the base of the block is $18$ cm, then the height, in cm, is

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ \frac{7}{3} \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4$

Solution

Problem 23

$JKLM$ is a square. Points P and Q are outside the square such that triangles JMP and MLQ are equilateral. The size, in degrees, of angle $PQM$ is

$\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 25 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 150$

Solution

Problem 24

Five holes of increasing size are cut along the edge of one face of a box as shown. The number of points scored when a marble is rolled through that hole is the number above the hole. There are three sizes of marbles: small, medium and large. The small marbles fit through any of the holes, the medium fit only through holes 3, 4, and 5, and the large fit only through hole 5. You may choose up to 10 marbles of each size to roll and each rolled marble goes through a hole. For a score of 23, what is the maximum number of marbles that could have been rolled?

$\text{(A)}\ 12 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 14 \qquad \text{(D)}\ 15 \qquad \text{(E)}\ 16$

Solution

Problem 25

In a softball league, after each team has played every other team 4 times, the total accumulated points are: Lions 22, Tigers 19, Mounties 14, and Royals 12. If each team received 3 points for a win, 1 point for a tie and no points for a loss, how many games ended in a tie?

$\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 10$

Solution

See also

1999 CEMC Gauss (Grade 7) (ProblemsAnswer KeyResources)
Preceded by
1998 CEMC Gauss (Grade 7)
Followed by
2000 CEMC Gauss (Grade 7)
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CEMC Gauss (Grade 7)