AMO 2021 – Primary 6 (Grade 6)

Question 1

Sarah has a collection of stickers. Three-eighths are flowers, and two-fifths of the flower stickers are red roses. What fraction of all her stickers are not red roses?

1. $\frac3{20}$
2. $\frac18$
3. $\frac35$
4. $\frac58$
5. $\frac{17}{20}$

Question 2

A bottle of $2\%$ reduced-fat milk states that it has $37\%$ less fat than regular milk. Approximately what percentage of regular milk is milkfat?

1. $3.2\%$
2. $6.8\%$
3. $39\%$
4. $18.5\%$
5. $1.8\%$

Question 3

What is $5\frac34+0.0000001+10\frac{12}{14}+\frac{234}{100000}$ rounded to the nearest ten-thousandth? Original choices: A 16.3693; B 16.5672; C 16.6094; D 16.7431; E 16.609. Adapted response format: none of these is the correctly rounded value. Enter the correct rounded number instead of a letter.

Question 4

If the dot pattern shown continues, how many dots are there at step $98$? Figure labels: Step means the step number.

1. $9999$
2. $9801$
3. $10000$
4. $9898$
5. $9595$

Question 5

Helen has an $8$ cm by $15$ cm rectangle of red cloth. She cuts out a triangular flag of the largest possible area, then uses all the remaining cloth to make two flags of equal area. What is the area of each smaller flag in square centimeters?

1. $30$
2. $60$
3. $90$
4. $120$
5. $150$

Question 6

Triangle $ABC$ is isosceles with $AB=AC$ and $\angle CAB=40^\circ$. Extend $AB$ beyond $B$ to $D$ so that $\angle ACD=90^\circ$. Find $\angle BDC$.

1. $30^\circ$
2. $40^\circ$
3. $50^\circ$
4. $60^\circ$
5. $70^\circ$

Question 7

Four classroom lights work independently. Each has a $90\%$ probability of still working after $1000$ hours. What is the probability that at least one is still working then?

1. $90.50\%$
2. $99.99\%$
3. $98.88\%$
4. $95.00\%$
5. $89.10\%$

Question 8

If $R$ is divisible by $9$ and $S$ is divisible by $8$, what is the minimum number of factors greater than $1$ of $RS$? Use positive integers $R,S$ and positive factors.

1. $8$
2. $11$
3. $13$
4. $17$
5. $18$

Question 9

A class of $25$ students averaged $89$ points on a test. Tony says that if he had scored $96$, the class average would have been $90$. What was his actual score?

1. $81$
2. $65$
3. $71$
4. $75$
5. $55$

Question 10

Among $140$ households, $90$ have Internet, $70$ a landline and $60$ cable TV. Of these, $50$ have Internet and a landline, $20$ have a landline and cable TV, and $15$ have all three. Five have none. How many have both Internet and cable TV (including those with all three)? Diagram labels: I = Internet, L = landline, TV = cable TV.

1. $15$
2. $20$
3. $25$
4. $30$
5. $45$

Question 11

Which option describes all solutions of $3m-6\ge8+5m$?

1. $m\ge7$
2. $m\ge-7$
3. $m\le7$
4. $m\le-7$
5. $m\ge14$

Question 12

Points $C,D,E,F$ lie on a circle with center $A$ on $CE$. Given $CE=2$ cm, $CD=DE$ and $\angle ECF=30^\circ$, find the perimeter of $CDEF$ in centimeters.

1. $\sqrt5-\sqrt2+2$
2. $\sqrt3+2\sqrt2+1$
3. $2\sqrt3+\sqrt2-1$
4. $\sqrt6-2\sqrt2+5$
5. $\sqrt3+4\sqrt2-1$

Question 13

Positive integers $a,b,c$ satisfy: $a$ is even, $b$ is prime, $c$ is odd, and $abc=5168$. What is $a+b+c$? Clarification: select the only listed value that can occur; the original conditions do not determine a unique sum.

1. $24$
2. $35$
3. $52$
4. $68$
5. $97$

Question 14

The front and back views show a solid built from unit cubes, with no missing cubes at the bottom or inside. Find its total surface area, including the underside, in square units. Figure labels: Front View and Back View show the front and back.

1. $48$
2. $74$
3. $68$
4. $60$
5. $64$

Question 15

In Mrs. Smith’s class, the ratio of boys to girls is $4:6$. If six boys join, the ratio becomes $1:1$. How many students are in the class now, before they join? Diagram labels: B = boys, G = girls.

1. $24$
2. $25$
3. $28$
4. $30$
5. $32$

Question 16

Sam cuts a $24$ inch by $60$ inch rectangular sheet into the least possible number of squares, wasting no paper. How many squares are there? The squares need not be equal.

Question 17

The distinct nonzero digits $U,N,P$ satisfy $\overline{UN}+\overline{NU}=\overline{PUP}$. Find $P\times U\times N$.

Question 18

$DPQW$ is a square. Adjacent marked points on its boundary are $1$ cm apart; horizontal and vertical segments are parallel to its sides. Let $s$ be the shaded area and $w$ the unshaded area. Find $w\div s$.

Question 19

The data set $\{13,5,9,18,43,x,10,7,22,15,11,19\}$ has range $40$. Find the product of the smallest and largest possible values of $x$.

Question 20

Twelve identical blenders at a constant rate make $36$ smoothies in $6$ minutes. How many minutes do three such blenders need to make $90$ smoothies? Diagram: left numbers count blenders; right numbers count smoothies; min = minutes.