Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1999 CEMC Gauss (Grade 7) Problems"

(Page is under construction)
Line 4: Line 4:
 
<math>1999 - 999 + 99</math> equals
 
<math>1999 - 999 + 99</math> equals
  
−
<math>\text{(A)}\ 901  \qquad \text{(B)}\ 1099 \qquad \text{(C)}\ 199 \qquad \text{(D)}\ 99 \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 901  \qquad \text{(B)}\ 1099 \qquad \text{(C)}\ 1000 \qquad \text{(D)}\ 199 \qquad \text{(E)}\ 99 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 1|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 1|Solution]]
Line 25: Line 25:
 
<math>1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}</math> is equal to
 
<math>1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}</math> is equal to
  
−
<math>\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} </math>
+
<math>\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} </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 4|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 4|Solution]]
  
 
== Problem 5 ==
 
== Problem 5 ==
 +
Which one of the following gives an odd integer?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\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 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 5|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 5|Solution]]
  
 
== Problem 6 ==
 
== Problem 6 ==
 +
In <math>\Delta ABC</math>, <math>\angle B = 72^{\circ}</math>. What is the sum, in degrees, of the other two angles?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 144 \qquad \text{(B)}\ 72 \qquad \text{(C)}\ 108 \qquad \text{(D)}\ 110 \qquad \text{(E)}\ 288 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 6|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 6|Solution]]
  
 
== Problem 7 ==
 
== Problem 7 ==
 +
If the numbers, <math>\frac{4}{5}</math>, <math>81\%</math>, and <math>0.801</math> are arranged from smallest to largest, the correct order is
  
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
Line 48: Line 51:
  
 
== Problem 8 ==
 
== Problem 8 ==
 +
The average of <math>10</math>, <math>4</math>, <math>8</math>, <math>7</math>, and <math>6</math> is
  
−
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 33 \qquad \text{(B)}\ 13 \qquad \text{(C)}\ 35 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ </math> 7
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 8|Solution]]
Line 68: Line 72:
  
 
== Problem 11 ==
 
== 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
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 26 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 34 \qquad \text{(D)}\ 46 \qquad \text{(E)}\ 50 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 11|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 11|Solution]]
  
 
== Problem 12 ==
 
== 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"?
  
−
<math>\text{(A)}\  \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ Fred \qquad \text{(B)}\ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)}\ Iggy \qquad \text{(E)}\ Joan </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 12|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 12|Solution]]
  
 
== Problem 13 ==
 
== Problem 13 ==
 +
In the diagram, the percent of small squares that are shaded is
  
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
Line 86: Line 93:
  
 
== Problem 14 ==
 
== Problem 14 ==
 +
Which of the following is an odd integer, contains the digit <math>5</math>, is divisible by <math>3</math>, and lies between <math>12^2</math> and <math>13^2</math>?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 105 \qquad \text{(B)}\ 147 \qquad \text{(C)}\ 156 \qquad \text{(D)}\ 165 \qquad \text{(E)}\ 175 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 14|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 14|Solution]]
  
 
== Problem 15 ==
 
== Problem 15 ==
 +
A box contains <math>36</math> pink, <math>18</math> blue, <math>9</math> green, <math>6</math> red, and <math>3</math> purple cubes that are identical in size. If a cube is selected at random, what is the probability that it is green?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\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} </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 15|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 15|Solution]]
  
 
== Problem 16 ==
 
== 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?
  
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
Line 104: Line 114:
  
 
== Problem 17 ==
 
== 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 <math>2</math>, and the third term is <math>9</math>. What is the eighth term in the sequence?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 34 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 107 \qquad \text{(D)}\ 152 \qquad \text{(E)}\ 245 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 17|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 17|Solution]]
  
 
== Problem 18 ==
 
== Problem 18 ==
 +
The results of the hair colour of <math>600</math> people are shown in this circle graph. How many people have blonde hair?
  
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
Line 116: Line 128:
  
 
== Problem 19 ==
 
== Problem 19 ==
−
 
+
What is the area, in <math>m^2</math>, of the shaded part of the rectangle?
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 14 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 33.6 \qquad \text{(D)}\ 56 \qquad \text{(E)}\ 42 </math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 19|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 19|Solution]]
  
 
== Problem 20 ==
 
== 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.
  
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>
 
<math>\text{(A)}\  \qquad \text{(B)}\  \qquad \text{(C)}\  \qquad \text{(D)}\  \qquad \text{(E)}\ </math>

Revision as of 22:11, 14 April 2025

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

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

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

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

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

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

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

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?

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

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?

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

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.

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

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

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

Solution

See also

1999 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by
1998 CEMC Gauss (Grade 7) 		Followed by
2000 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)
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1999_CEMC_Gauss_(Grade_7)_Problems&oldid=246692"