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Difference between revisions of "1998 CEMC Gauss (Grade 7) Problems"

(→‎Problem 8)
(→‎Problem 8)
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== Problem 8 ==
 
== Problem 8 ==
  
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Tuesday’s high temperature was 4°C warmer than that of Monday’s. Wednesday’s high temperature
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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
+
was 6 C cooler than that of Monday’s. If Tuesday’s high temperature was 22 C, what was
 
Wednesday’s high temperature?
 
Wednesday’s high temperature?
  
−
<math>\text{(A)}\ 20^{\circ}C \qquad \text{(B)}\ 24^{\circ}C \qquad \text{(C)}\ 12^{\circ}C \qquad \text{(D)}\ 32^{\circ}C \qquad \text{(E)}\16^{\circ}C </math>
+
<math>\text{(A)} 20 \quad\text{(B)} 24\quad \text{(C)} 12\quad \text{(D)} 32 \quad \text{(E)} 16 \quad </math>
 +
 
 +
 
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(all in Celsius)
  
 
[[1998 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]
 
[[1998 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]

Revision as of 13:52, 29 January 2021

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

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

Solution

Problem 10

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

Solution

Part B: Each correct answer is worth 6 points

Problem 11

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

Solution

Problem 12

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

Solution

Problem 13

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

Solution

Problem 14

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

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) (Problems • Answer Key • Resources)
Preceded by
First Competition 		Followed by
1999 CEMC Gauss (Grade 7)
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CEMC Gauss (Grade 7)
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