1998 CEMC Gauss (Grade 7) Problems

Revision as of 15:35, 29 January 2021 by Coolmath34 (talk | contribs) (Problem 14)

Part A: Each correct answer is worth 5 points

Problem 1

The value of $\frac{1998 - 998}{1000}$ is

$\text{(A)}\ 1 \qquad \text{(B)}\ 1000 \qquad \text{(C)}\ 0.1 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 0.001$

Solution

Problem 2

The number $4567$ is tripled. The ones digit (units digit) in the resulting number is

$\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 1$

Solution

Problem 3

If $S = 6\times 10,000 + 5\times 1,000 + 4\times 10 + 3\times 1$, what is $S$?

$\text{(A)}\ 6,543 \qquad \text{(B)}\ 65,043 \qquad \text{(C)}\ 65,431 \qquad \text{(D)}\ 65,403 \qquad \text{(E)}\ 60,541$

Solution

Problem 4

Jean writes five tests and achieves the marks shown on the graph. What is her average mark on these five tests?

[insert bar graph with 5 bars: 80, 70, 60, 90, 80]

$\text{(A)}\ 74 \qquad \text{(B)}\ 76 \qquad \text{(C)}\ 70 \qquad \text{(D)}\ 64 \qquad \text{(E)}\ 79$

Solution

Problem 5

If a machine produces 150 items in one minute, how many would it produce in 10 seconds?

$\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 20 \qquad \text{(D)}\ 25 \qquad \text{(E)}\ 30$

Solution

Problem 6

In the multiplication question, the sum of the digits in the four boxes is:

[Multiply $879 \times 492$ using long multiplication. Find the sum of the four numbers in the thousands place column.]

$\text{(A)}\ 13 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 27 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 22$

Solution

Problem 7

A rectangular field is 80 m long and 60 m wide. If fence posts are placed at the corners and are 10 m apart along the 4 sides of the field, how many posts are needed to completely fence the field?

$\text{(A)}\ 24 \qquad \text{(B)}\ 26 \qquad \text{(C)}\ 28 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 32$

Solution

Problem 8

Tuesday’s high temperature was 4 C warmer than that of Monday’s. Wednesday’s high temperature was 6 C cooler than that of Monday’s. If Tuesday’s high temperature was 22 C, what was Wednesday’s high temperature?

$\text{(A)} 20 \quad\text{(B)} 24\quad \text{(C)} 12\quad \text{(D)} 32 \quad \text{(E)} 16 \quad$


(all in Celsius)

Solution

Problem 9

Two numbers have a sum of 32. If one of the numbers is – 36, what is the other number?

$\text{(A)}\ 68 \qquad \text{(B)}\ -4 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 72 \qquad \text{(E)}\ -68$

Solution

Problem 10

At the waterpark, Bonnie and Wendy decided to race each other down a waterslide. Wendy won by 0.25 seconds. If Bonnie’s time was exactly 7.80 seconds, how long did it take for Wendy to go down the slide?

$\text{(A)}\ 7.8 \qquad \text{(B)}\ 8.05 \qquad \text{(C)}\ 7.55 \qquad \text{(D)}\ 7.15 \qquad \text{(E)}\ 7.5$

Solution

Part B: Each correct answer is worth 6 points

Problem 11

Kalyn cut rectangle R from a sheet of paper. A smaller rectangle is then cut from the large rectangle R to produce figure S. In comparing R to S,

[R is a rectangle with sides 8 and 6 cm. S is the same as R with a 4x1 rectangle cut from one of its corners.]

$\text{(A) the area and perimeter both decrease}$

$\text{(B) the area decreases and the perimeter increases}$

$\text{(C) the area and perimeter both increase}$

$\text{(D) the area increases and the perimeter decreases}$

$\text{(E) the area decreases and the perimeter stays the same}$

Solution

Problem 12

Steve plants ten trees every three minutes. If he continues planting at the same rate, how long will it take him to plant 2500 trees?

$\text{(A)}\ 1 \dfrac{1}{4} \text{h} \qquad \text{(B)}\ 3 \text{h} \qquad \text{(C)}\ 5 \text{h} \qquad \text{(D)}\ 10 \text{h} \qquad \text{(E)}\ 12 \dfrac{1}{2} \text{h}$

Solution

Problem 13

The pattern of figures (triangle, dark circle, square, dark triangle, circle) is repeated over and over again. The 214th figure in the sequence is

$\text{(A) triangle}$

$\text{(B) dark circle}$

$\text{(C) square}$

$\text{(D) dark triangle}$

$\text{(E) circle}$

Solution

Problem 14

A cube has a volume of $125 \text{cm}^3.$ What is the area of one face of the cube?


$\text{(A)}\ 20 \text{cm}^2 \qquad \text{(B)}\ 25 \text{cm}^2 \qquad \text{(C)}\ 41 \dfrac{2}{3} \text{cm}^2 \qquad \text{(D)}\ 5 \text{cm}^2 \qquad \text{(E)}\ 75 \text{cm}^2$

Solution

Problem 15

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 16

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 17

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 18

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 19

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 20

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Part C: Each correct answer is worth 8 points

Problem 21

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 22

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 23

$\text{(A)}\  \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 24

$\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}$

Solution

Problem 25

Two natural numbers, $p$ and $q,$ do not end in zero. The product of any pair, $p$ and $q,$ is a power of 10 (that is, 10, 100, 1000, 10 000 , ...). If $p > q$ , the last digit of $p-q$ cannot be

$\text{(A)}\ 1 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 9$

Solution

See also

1998 CEMC Gauss (Grade 7) (ProblemsAnswer KeyResources)
Preceded by
First Competition
Followed by
1999 CEMC Gauss (Grade 7)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
CEMC Gauss (Grade 7)
Invalid username
Login to AoPS