2005 CEMC Gauss (Grade 7) Problems

Problem 1

The value of $\frac{3 \times 4}{6}$ is

$\text{(A)}\ 1 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 3 \qquad \text{(D)}\ 4 \qquad \text{(E)}\ 6$

Solution

Problem 2

The value of $0.8 - 0.07$ is

$\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.71 \qquad \text{(C)}\ 0.793 \qquad \text{(D)}\ 0.01 \qquad \text{(E)}\ 0.73$

Solution

Problem 3

$[asy] //make the picture small and square size(80,80); //draw an arc from 0 to 75 degrees of radius 1 centered at the origin draw(arc((0,0),1,0,75)); //draw a line with an arrow on the end pointing to 25 degrees (scale it down by .95 so that it stays inside the arc) //dir(25) is a unit vector pointing 25 degrees draw((0,0)--scale(.95)*dir(25),Arrow); //put a label at the end of the 75 degree unit vector (and position it out 75 degrees) MarkPoint("9",dir(75),dir(75)); //put a label at the end of the 75 degree unit vector (rotate label 75 degrees to create a tick) MarkPoint(75,"-",scale(.85)*dir(75),dir(75)); MarkPoint("9.2",dir(60),dir(60)); MarkPoint(60,"-",scale(.85)*dir(60),dir(60)); MarkPoint("9.4",dir(45),dir(45)); //put a label at the end of the 45 degree unit vector - use NE to move it slightly NorthEast of this point (or use dir(45)) MarkPoint(45,"-",scale(.85)*dir(45),NE); MarkPoint("9.6",dir(30),dir(30)); MarkPoint(30,"-",scale(.85)*dir(30),dir(30)); MarkPoint("9.8",dir(15),dir(15)); MarkPoint(15,"-",scale(.85)*dir(15),dir(15)); //put a label at the end of the 0 degree unit vector - use E to move it slightly East of this point (or use dir(0)) MarkPoint("10",dir(0),E); MarkPoint(0,"-",scale(.85)*dir(0),dir(0)); [/asy]$

Contestants on "Gauss Reality TV" are rated by an applause metre. In the diagram, the arrow for one of the contestants is pointing to a rating closest to:

$\text{(A)}\ 9.4 \qquad \text{(B)}\ 9.3 \qquad \text{(C)}\ 9.7 \qquad \text{(D)}\ 9.9 \qquad \text{(E)}\ 9.5$

Solution

Problem 4

Twelve million added to twelve thousand equals

$\text{(A)}\ 12,012,000 \qquad \text{(B)}\ 12,120,000 \qquad \text{(C)}\ 120,120,000 \qquad \text{(D)}\ 12,000,012,000 \qquad \text{(E)}\ 12,012,000,000$

Solution

Problem 5

The largest number in the set { $0.109, 0.2, 0.111, 0.114, 0.19$ } is

$\text{(A)}\ 0.109 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 0.111 \qquad \text{(D)}\ 0.114 \qquad \text{(E)}\ 0.19$

Solution

Problem 6

At a class party, each student randomly selects a wrapped prize from a bag. The prizes include books and calculators. There are $27$ prizes in the bag. Meghan is the first to choose a prize. If the probability of Meghan choosing a book for her prize is $2/3$ , how many books are in the bag?

$\text{(A)}\ 15 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 21 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 18$

Solution

Problem 7

Karen has just been chosen the new “Math Idol”. A total of $1,480,000$ votes were cast and Karen received $83\%$ of them. How many people voted for her?

$\text{(A)}\ 830,000 \qquad \text{(B)}\ 1,228,400 \qquad \text{(C)}\ 1,100,000 \qquad \text{(D)}\ 251,600 \qquad \text{(E)}\ 1,783,132$

Solution

Problem 8

In the diagram, what is the measure of $\angle ACB$ in degrees? $[asy] size(300); draw((-60,0)--(0,0)); draw((0,0)--(64.3,76.6)--(166,0)--cycle); label("$A$",(64.3,76.6),N); label("$93^\circ$",(64.3,73),S); label("$130^\circ$",(0,0),NW); label("$B$",(0,0),S); label("$D$",(-60,0),S); label("$C$",(166,0),S); [/asy]$