AIMO FINAL P3

Answer explanation

3, 4, 5, 6, 7

239, 249, 259, 269, 279

563, 564, 565, 566, 567

When two numbers are added, the unit digit of one of the numbers, which is 3, is mistakenly written as 9. The tens digit of another number, which is 0, is mistakenly written as 6. The result obtained is 1083. What is the correct sum?

(a)  

Answer explanation

1083 - 60 - 6

60 is the difference in tens

6 is the difference in ones

If Aiden solves 15 problems every day, he will finish all the problems for 24 days. If he solves 5 more problems every day, how many day(s) earlier will he finish all the problems?

(a)  

Answer explanation

15x24/20 = 18 days

24 - 18 = 6 days earlier

(443 - 185) + (257 + 829) - (315 +529) = ?

(a)  

Answer explanation

(443 + 257) + (829 - 529) - (315 + 185)

= 700 + 300 - 500 = 500

Aiden and Bella are now 32 and 35 years old. The ages of their four sons are now 12, 10, 7 and 4 years old respectively. How many years later will the sum of the ages of the four sons be equal to the sum of the ages of Aiden and Bella?

(a)  

Answer explanation

now:

Sum of sons' ages = 12+10+7+4 = 33 (each year goes up 4)

Sum of ages Aiden and Bella = 32+35 = 67 (each year goes up 2)

n years later:

67 + 2n = 33 + 4n

2n = 67 - 33

2n = 34

n = 17

25 squares with the perimeter of 24 cm, form a larger square. How many cm is the perimeter of the larger square?

(a)  

Answer explanation

The small square's side = 24/4 = 6

The larger square = 5 x 5 of the smaller squares ==> the side: 5 x 6 = 30 cm

Perimeter of the larger square = 30 x 4 = 120 cm

There is a 480-metre-long straight road in front of the school. Trees are planted on both sides of the road, and the trees on the same side are at least 15 metres apart. Since one of the road is connected to the school gate, trees cannot be planted. How many trees can be planted on this straight road?

(a)  

Answer explanation

480/15 x 2 = 64

there are 32 trees in each side of the road.

According to the following number pattern, what is the sum of the 9th and 10th number from the left?

20, 23, 21, 25, 22, 27, 23, 29, __ , __

(a)  

Answer explanation

the 9th number = 24

the 10th number = 31

Given that 1 yard equals to 3 feet (plural of foot). 1 foot equals 12 inches. Aiden cuts a rope of 20 yards 2 feet and 3 inches into several 9 inches pieces. How many cuts are needed?

(a)  

Answer explanation

Length of the rope = (20 x 3 x 12) + (2 x 12) + 3 = 720 + 24 + 3 = 747 inches

Cut into 9-inch pieces = 747 : 9 = 83 parts

Cuts needed = 83 - 1 = 82