HighFour Mathematics
Category A: Grades 4 – 5
Round 4
Thursday, December 10, 2015
The use of calculator is not allowed.
Answer #1:
Explanation:
8am on Friday
Friday 3pm (or 15:00) in Tokyo is Thursday 10pm (or 22:00) in San
Francisco. This is the time of departure. 10 hours later it will be Friday 8am
in San Francisco.
Answer #2:
Explanation:
4/15
Writing 1/3 and 1/5 with the same denominator (15) gives that 1/3 = 5/15
and 1/5 = 3/15. Therefore, the number in between them is 4/15.
Answer #3:
Explanation:
600
Let’ say we have X number of bills in each denominations. Therefore, the
7000 dollars is made up of X number of 5, 10, and 20 dollar bills. Thus,
7000 = 5𝑋𝑋 + 10𝑋𝑋 + 35𝑋𝑋
7000 = 35𝑋𝑋
𝑋𝑋 = 200
Therefore, we have 200 of each of the 3 different denomination bills, giving
us a total of 600 bills.
Answer #4:
Explanation:
60, 120 and 180
The three numbers can be found quickly by trial and error or by finding
their Least Common Multiple(s) (LCM).
Answer #5:
Explanation:
20
20, because the sum of the dots on all six sides is 21 and 1 is face down,
which means it can’t be seen.
Round 4
Thursday, December 10, 2015
HighFour Mathematics
Category A: Grades 4 – 5
The use of calculator is not allowed.
Answer #6:
Explanation:
4
They are 53, 59, 61, and 67.
Answer #7:
Explanation:
166
Since the sum of the two prime numbers is an odd number, one of them
must be even. The only even prime number is 2. The other prime number is
85 – 2 = 83, and the product of these two numbers is 166.
Answer #8:
Explanation:
GBP 1.59
The 75-gram letter will cost 0.53 to post and the 215-gram letter will cost
1.06. Therefore the total cost is 0.53 + 1.06 = 1.59
Answer #9:
Explanation:
9 minutes
Jill arrives in 1/10 of an hour, which is 6 minutes. Jack arrives in 1/4 of an
hour which is 15 minutes. Thus, the time difference is 9 minutes.
Answer #10:
Explanation:
10
We have H = 8 – 7 = 1 and T = 8 – 2 + 5 = 11. Clearly 11 – 1 = 10, so our
answer is 10.
Round 4
Thursday, December 10, 2015
HighFour Mathematics
Category A: Grades 4 – 5
The use of calculator is not allowed.
Answer #11:
Explanation:
8 biscuits
A decision on how many to buy is made my dividing my nephew’s
maximum requirement by the minimum number of biscuits in a pack. This
is the only way of ensuring there are enough.
Thus, the most biscuits my nephew will eat in two weeks is 2 (weeks) times
5 (maximum visits per week) times 8 (maximum number of biscuits per
visit) = 80. The minimum number of biscuits in a pack is 10, so 8 packs will
be required.
Answer #12:
Explanation:
250 pages
Isabella read 3 × 36 + 3 × 44 pages in the first 6 days. Although this can be
calculated directly, it is simpler to calculate it as 3 × (36 + 44) = 3 × 80,
which gives that she read 240 pages. However, she read 10 more pages on
the last day, for a total of 250 pages.
Answer #13:
Explanation:
20000
Each one-legged person wears one sandal, and the others wear one sandal
each, on average.
Answer #14:
Explanation:
5
The area outside the small triangle but inside the large triangle is
16 – 1 = 15. This is equally distributed between the three trapezoids. Each
trapezoid has an area of 15/3 = 5.
Answer #15:
Explanation:
538
3
=
5
𝐴𝐴
55
=
303
𝐵𝐵
, gives 𝐴𝐴 = 33 and 𝐵𝐵 = 505, which means 𝐴𝐴 + 𝐵𝐵 = 538.
HighFour Mathematics
Category A: Grades 4 – 5
Round 4
Thursday, December 10, 2015
The use of calculator is not allowed.
Answer #16:
Explanation:
60 pennies
As a single package it would cost 25 pennies for the first 60 grams and 8x5
pennies for the remaining 78 grams, or 65 pennies in total.
If sent as two packages, it is most economical to have both at 60 grams or
more, as the first 60 grams is pro-rata cheaper than the remaining weight.
Thus, 60g + 78 g is as effective as any other split: this costs a total of 60
pennies.
Answer #17:
Explanation:
5th bounce
Each bounce is 2/3 times the height of the previous bounce. The first
bounce reaches 2 meters, the second 4/3, the third 8/9, the fourth 16/27,
and the fifth 32/81. Half of 81 is 40.5, so the ball does not reach the
required height on the 5th bounce.
Answer #18:
Explanation:
99%
In a rectangle with dimensions 10 × 10, the new rectangle would have
dimensions 11 × 9. The ratio of the old area to the new area is 99/100 or
99%.
Answer #19:
Explanation:
5
By adding a number from Bag A and a number from Bag B together, the
values we can get are 3, 5, 7, 5, 7, 9, 7, 9, 11. Therefore the number of
different values is 5.
Answer #20:
Explanation:
9
For this problem, all we need to do is find the amount of valid 4-digit
numbers that can be made from the digits of 3013, since all of the valid 4digit number will always be greater than 1000.
There can be only two leading digits, namely 1 or 3.
When the leading digit is 1, you can make 3 such numbers.
When the leading digit is 3, you can make 6 such numbers.
Summing the amounts of numbers, we find that there are 9 such numbers.