Playing with Numbers | Maths Olympiad Class 6 PDF Download

Q1: What is the minimum number of students in a class that can be grouped into sizes of 2, 3, 5, and 6?
(a) 40
(b) 30
(c) 35
(d) 45
Ans: (B)

• The minimum number of students is found by calculating the L.C.M. (Least Common Multiple) of the group sizes: 2, 3, 5, and 6.
• To find the L.C.M., we take the highest powers of all prime factors involved: 2, 3, and 5.
• The calculation is: 2 × 3 × 5 = 30.
• Thus, the least number of students that can be divided into these groups is 30.

Q2: The minimum number of square tiles required to cover a plot measuring 225 m by 30 m is _____.
(a) 30 tiles
(b) 15 tiles
(c) 25 tiles
(d) 45 tiles
Ans: (A)

• The largest side length of the square tile is determined by the H.C.F. (Highest Common Factor) of 225 and 30.
• Calculating the H.C.F., we find that H.C.F. (225, 30) = 15.
• To find the number of tiles needed, we use the formula: Number of tiles = Area of plot / Area of one tile.
• Thus, the calculation is: 225 m x 30 m / (15 m x 15 m) = 30 tiles.

Q3: Three boys step off together from the same location. Their step lengths are 63 cm, 70 cm, and 77 cm, respectively. What is the least distance each should travel so that all can complete their steps evenly?
(a) 6930 cm
(b) 6000 cm
(c) 7000 cm
(d) 6520 cm
Ans: (A)

• The minimum distance all boys need to cover is the L.C.M. (Least Common Multiple) of their step lengths: 63 cm, 70 cm, and 77 cm.
• To find the L.C.M., we break down each number into its prime factors: 63 = 3 × 3 × 7, 70 = 2 × 5 × 7, and 77 = 7 × 11.
• Next, we take the highest power of each prime factor: 2, 3, 3, 5, 7, and 11.
• Multiplying these together gives us: 2 × 3 × 3 × 5 × 7 × 11 = 6930 cm.
• Thus, 6930 cm is the minimum distance each boy must cover to ensure they all complete their steps evenly.

Q4: If two tankers hold 850 litres and 680 litres of kerosene oil respectively, what is the largest size of a container that can measure the kerosene oil from both tankers using an exact number of times?
(a) 170 litres
(b) 85 litres
(c) 34 litres
(d) 20 litres
Ans: (A)

• To find the maximum capacity of the container, we need to determine the HCF (Highest Common Factor) of the two amounts: 850 litres and 680 litres.
• The HCF of 850 and 680 is 170 litres. This means that a container of this size can measure both amounts exactly.
• Thus, the largest container that can be used to measure the kerosene oil from both tankers is 170 litres.
• In summary, the answer is 170 litres, as it is the largest size that can be used to measure both quantities without any remainder.

Q5: What is the length of the longest tape that can exactly measure the dimensions of a room with lengths of 403 cm, 434 cm, and 465 cm?
(a) 31 cm
(b) 30 cm
(c) 25 cm
(d) 35 cm
Ans: (A)

• The dimensions of the room are 403 cm, 434 cm, and 465 cm.
• To find the length of the longest tape that can measure all these dimensions exactly, we need to calculate the H.C.F. (Highest Common Factor) of these three numbers.
• Calculating the H.C.F. of 403, 434, and 465 gives us 31.
• Therefore, the length of the longest tape that can measure the room is 31 cm.