Group 1
Group 2
Group 3
Group 4
Group 5
100
Cookies come in packs of 3, 6, 8, and 12. Marie got at least one pack of each size. If
Marie bought 12 packs and got a total of 121 cookies, how many packs of 8 cookies did
Marie buy?
To reach 121, we need odd number of 3 packs of cookies. The only solution
is 1 pack of 3, 2 packs of 8, 1 pack of 6, and 8 packs of 12.
The answer is 2
100
What is the difference between the product and the sum of the non zero digits of
20^10
when it is written in expanded form.
20^10
can be rewritten as
2^10*10^10
.
2^10=1024
and
10^10
will just add 10
zeroes at the end. So the product is
2 ∗ 4 ∗ 1 = 8
and the sum is
2 + 4 + 1 = 7
. The difference between the product and the sum of the non zero digits is
8− 7 = 1
100
At 12:22, a clock hour hand is what degrees away from the vertical position?
The hour hand moves 30 degrees in an hour. So in 22 minutes it will move
(22/60) * 30 = 11 degrees
100
If x is a whole number, what is the largest possible perimeter of a triangle with side lengths 3, 4, and x?
In a triangle, the third side length should be smaller than the sum of the first two side lengths. Hence the third side length can be at most 6. Then the perimeter is
3+4+6=13.
100
John wears his headphones only on cloudy days. The day after is cloudy day is a sunny day. At most, how many days do John wear his headphones in a week?
If Monday is cloudy, then Wednesday, Friday, and Sunday can also be cloudy.
Hence, at most 4 days in a week are cloudy.
200
32 ∗ 82 ∗ 52 = 62 ∗ ? ∗ 102
32 ∗ (2 ∗ 2 ∗ 2)2 ∗ 52 = (3 ∗ 2)2 ∗ 22 ∗ (5 ∗ 2)2
Hence the answer is
2^2=4
200
If the mean of three possible integers is 5. What is the highest possible product of those three integers.
If the mean of three integers is 5, then the sum is 15. To achieve the highest possible product, we choose the numbers to be 5, 5, and 5. Hence the product is 125.
The answer is 125
200
Mary has 7 coins worth of 49 cents. How many nickels do Mary has?
Mary has 4 pennies. 3 more coins worth of 45 cents is needed. The only possible combination is 1 quarter, 2 dimes. So Mary has 0 nickels.
200
If a small circle’s diameter is a larger circle’s radius, what is the ratio of smaller circle’s area to the larger circle’s area?
The ratio of the radii’s is 1/2. For area, we use
πr2
hence the ratio would be 1/4.
200
What is the greatest prime factor of
9^18-3^32
9^18 − 3^32 = 3^36 − 3^32 = 3^32(3^4-1) = 3^32(80)=3^32*2^4*5
The answer is 5
300
If John start writing all the numbers starting from 1 to 100 included, how many 1’s will he write?
There is one ”1” from 1 to 9, 11 ”1”s from 10 to 19, 8 ”1”s from 20 to 99, and one ”1” in 100. So that is a total of 21 ”1”s.
The answer is 21
300
The hundreds digit of the product
123456789 ∗ 234567890
is
We can just multiply the last three digits
789 ∗ 890 = 702210
. Hence, the hundreds digit is 2.
300
What is the ones digit of the product
1 ∗ 2 ∗ 3 ∗ · · · ∗ 98 ∗ 99
?
The product is divisible by 10 so the ones digit is 0
300
If a man drives to work at the rate of x km/hr and returns along the same route at a rate of y km/hr, what is the average rate for the entire round trip?
Let d be the distance to work. Then the average rate is
300
An 11 by 11 by 11 wooden cube is formed by gluing together 1331 unit cubes. What is the greatest number of unit cubes that can be seen from a single point?
