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Difference between revisions of "1999 CEMC Gauss (Grade 7) Problems"
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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
 
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)}\ \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\%</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 7|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 7|Solution]]
Line 58: Line 58:
  
 
== Problem 9 ==
 
== 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?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 6 \qquad \text{(B)}\ 7 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 13</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 9|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 9|Solution]]
  
 
== Problem 10 ==
 
== Problem 10 ==
 +
In the diagram, line segments meet at <math>90^{\circ}</math> as shown. If the short line segments are each <math>3</math> cm long, what is the area of the shape?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 30 \qquad \text{(B)}\ 36 \qquad \text{(C)}\ 40 \qquad \text{(D)}\ 45 \qquad \text{(E)}\ 54</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 10|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 10|Solution]]
Line 88: Line 90:
 
In the diagram, the percent of small squares that are shaded is
 
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)}\ 9 \qquad \text{(B)}\ 33 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 56.25 \qquad \text{(E)}\ 64</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 13|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 13|Solution]]
Line 109: Line 111:
 
The graph shown at the right indicates the time taken by five people to travel various distances. On average, which person travelled the fastest?
 
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)}\ Alison \qquad \text{(B)}\ Bina \qquad \text{(C)}\ Curtis \qquad \text{(D)}\ Daniel \qquad \text{(E)}\ Emily</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 16|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 16|Solution]]
Line 123: Line 125:
 
The results of the hair colour of <math>600</math> people are shown in this circle graph. How many people have blonde hair?
 
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)}\ 30 \qquad \text{(B)}\ 160 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 420</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 18|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 18|Solution]]
Line 136: Line 138:
 
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.
 
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)}\ 32 \qquad \text{(B)}\ 28 \qquad \text{(C)}\ 26 \qquad \text{(D)}\ 24 \qquad \text{(E)}\ 16</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 20|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 20|Solution]]
Line 143: Line 145:
  
 
== Problem 21 ==
 
== 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?
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ P \qquad \text{(B)}\ Q \qquad \text{(C)}\ R \qquad \text{(D)}\ T \qquad \text{(E)}\ W</math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 21|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 21|Solution]]
  
 
== Problem 22 ==
 
== Problem 22 ==
 +
Forty-two cubes with <math>1</math> cm edges are glued together to form a solid rectangular block. If the perimeter of the base of the block is <math>18</math> cm, then the height, in cm, is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
<math>\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ \frac{7}{3} \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4</math>{(E)}\ <math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 22|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 22|Solution]]
  
 
== Problem 23 ==
 
== Problem 23 ==
 +
</math>JKLM<math> 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 </math>PQM<math> is
  
−
<math>\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ </math>
+
</math>\text{(A)}\ 10 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 25 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 150<math>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 23|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 23|Solution]]
  
 
== Problem 24 ==
 
== Problem 24 ==
−
 
+
Five holes of increasing size are cut along the edge
−
<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>
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 24|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 24|Solution]]
Line 168: Line 173:
 
== Problem 25 ==
 
== Problem 25 ==
  
−
<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)}\ $
  
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 25|Solution]]
 
[[1999 CEMC Gauss (Grade 7) Problems/Problem 25|Solution]]

Revision as of 08:58, 15 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

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

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

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ \frac{7}{3} \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4${(E)}\ $[[1999 CEMC Gauss (Grade 7) Problems/Problem 22|Solution]]

== Problem 23 ==$ (Error compiling LaTeX. Unknown error_msg)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$[[1999 CEMC Gauss (Grade 7) Problems/Problem 23|Solution]]

== Problem 24 == Five holes of increasing size are cut along the edge$ (Error compiling LaTeX. Unknown error_msg)\text{(A)}\ \qquad \text{(B)}\ \qquad \text{(C)}\ \qquad \text{(D)}\ \qquad \text{(E)}\ $[[1999 CEMC Gauss (Grade 7) Problems/Problem 24|Solution]]

== Problem 25 ==$ (Error compiling LaTeX. Unknown error_msg)\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)
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CEMC Gauss (Grade 7)
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