Maths Olympiad Previous Year Paper -3 | Maths Olympiad Class 6 PDF Download

Ans: (c)

• P is the father of Q, making Q his child.
• R and S are the sons of Q, which means P is their grandfather.
• T is the mother of S, which means she is married to Q.
• Thus, T is the daughter-in-law of P because she is the wife of P's son Q.

Ans: (b)

• First, replace the symbols with their meanings: 20 ÷ 4 × 7 + 3 – 7.
• Next, perform the operations in the correct order: start with division and multiplication from left to right.
• Calculate: 20 ÷ 4 = 5, then 5 × 7 = 35.
• Now, add and subtract: 35 + 3 = 38, and finally 38 – 7 = 31.

Ans: (c)
First Term = 6.
Second term = 6*2 -1 = 11.
Third term = 11* 3 - 2 = 31.
Fourth term = 31 *4 - 3 = 124 -3 = 121.
Fifth term = 121*5 - 4 = 601.
Sixth term = 601 *6 = 3606 - 5 = 3601.

Ans: (c)

Ans: (b)
The sequence is doubling each time. (2×2=4, 4×2=8, 8×2=16, so 16×2=32).

Ans: (a)
If the tree is 7th from either end, there are 6 trees on each side of it, making a total of 6 + 6 + 1 = 13 trees.

Ans: (c)

Ans: (a)
A Ruby is a red precious stone and sapphire is a blue precious stone.

Ans: (b)
23+11=34
11+34=45
34+45=79
45+79=124.

Ans: (a)
8² = 64 - 1= 63
9² = 81 - 1 =80

Ans: (b) 
 Letter ‘E’ is absent in the above word hence, word ‘TRADE can’t be formed.

Ans: (b)

Ans: (c)

Ans: (c)

Ans: (b)

Ans: (c)

• The successor of a number is the number that comes immediately after it, while the predecessor is the number that comes immediately before it.
• For the number 205575, the successor is 205576 and the predecessor is 205574.
• The difference between the successor and predecessor is calculated as 205576 - 205574, which equals 2.
• Thus, the correct answer is 2.

Ans: (a)

• The pattern involves a formula where each step follows the structure: n × (n + 2) + 1 = (n + 1)² .
• For example, in the first case, 1 × 3 + 1 = 4, which equals (2)² .
• Continuing this, the last known calculation is 9 × 11 + 1 = 64, which equals (8)² .
• Following the pattern, the next step would be 10 × 12 + 1 = 121, which equals (10)² .

Ans: (b)

• To find the additive inverse, we change the sign of the number.
• The additive inverse of –100 is 100.
• The additive inverse of 52 is –52.
• Now, we add these two results: 100 + (–52) = 100 - 52 = 48.
• Thus, the answer is 48.

Ans: (c)

• First, we need to find a common denominator for both sides of the equation. The common denominator for the fractions on the left side (2/7, 3/21, 5/14) is 42.
• Convert each fraction: 2/7 = 12/42, 3/21 = 6/42, and 5/14 = 15/42. Adding these gives us 12/42 + 6/42 + 15/42 = 33/42.
• Now, for the right side (3/7, 2/6, 1/42), the common denominator is also 42. Convert: 3/7 = 18/42, 2/6 = 14/42, and 1/42 = 1/42. Adding these gives us 18/42 + 14/42 + 1/42 = 33/42.
• Now we compare: 33/42 = 33/42, so the answer is equal.

Ans: (b)

• First, convert the mixed numbers into improper fractions: 4 3/5 = 23/5, 2 7/9 = 25/9, and 1 2/15 = 17/15.
• Now, rewrite the expression: 23/5 - 25/9 - 17/15 - 2/5.
• Find a common denominator, which is 45, and convert each fraction: 23/5 = 207/45, 25/9 = 125/45, 17/15 = 51/45, and 2/5 = 18/45.
• Now, perform the subtraction: 207/45 - 125/45 - 51/45 - 18/45 = 13/45.

Ans: (b)

• First, let's break down the Roman numerals:
• CDLXIV = 464
• CCXXIV = 224
• LXXV = 75
• Now, add them together: 464 + 224 + 75 = 763.
• Thus, the correct answer is 763, which corresponds to option (b).

Ans: (c)

• The statement indicates that Riya's age (Q) is five more than three times her son's age (P).
• This can be expressed mathematically as Q = 3P + 5, which matches option (c).
• Options (a), (b), and (d) do not correctly represent the relationship described in the statement.
• Thus, the correct equation that justifies the statement is Q = 3P + 5.

Ans: (c)

• The perpendicular bisector of a line segment is a line that divides the segment into two equal parts at a 90-degree angle.
• For any given line segment, there is exactly one unique perpendicular bisector.
• This means that no matter how long or short the segment is, there will always be just one line that meets these criteria.
• Thus, the correct answer is one.

Ans: (a)

• To solve for m, start by simplifying the left side: 1/2(m - 1/3) becomes m/2 - 1/6.
• Now, rewrite the equation: m/2 - 1/6 = 2/7m + 1/3.
• Next, eliminate fractions by multiplying the entire equation by 42 (the least common multiple of 2, 6, 7, and 3) to make calculations easier.
• This gives you 21m - 7 = 12m + 14. Rearranging leads to 9m = 21, so m = 21/9, which simplifies to 7/3.

Ans: (d)

• To find the number to add, we need to subtract 18.243 from 31.472.
• Calculating this gives us: 31.472 - 18.243 = 13.229.
• Thus, the number that needs to be added is 13.229.
• This means that if you add 13.229 to 18.243, you will get 31.472.

Ans: (d)

• First, round 423308 to the nearest thousand: it becomes 423000.
• Next, round 42568 to the nearest hundred: it becomes 42600.
• Now, find the difference: 423000 - 42600 = 380400.
• Thus, the final answer is 380400.

Ans: (c)

• In the word COMPARISON, there are 5 vowels: O, A, I, O.
• There are 3 consonants: C, M, P, R, S, N (total 6 consonants).
• The ratio of consonants to vowels is therefore 6:4, which simplifies to 3:2.
• Thus, the correct answer is 3:2.

Ans: (c) 
Clearly, the playground is of rectangular  shape.  
So the required length of the wire  = Perimeter of the rectangle  
= 2 (length + breadth)  
= 2 (250 + 20) 
= 540 m.

Ans: (a)
Diameter (d) = 2r = 14 
r = 7 cm 

Ans: (c)
Area of equilateral triangle = 4√3

(side)² = 4 × 4  
side = 4 cm

Ans: (b) 
Area left for gardening  = Area of garden + area of two paths at the  centre – Area of paths  
= 60 × 30 + 4 – 120 – 60  
= 1800 + 4 – 180 = 1624 m² 

Ans: (a) 
Perimeter = sum of lengths of all sides of  the closed figure  
= 5 + 8 + 11 + 7 + 2 + 6 + 6 + 4 + 3 + 1 = 53 cm 

Ans: (b)
Circumference of large = 2π(30)
Circumference of small = 2π(15)
Perimeter of shaded region = circumference of larger circle + circumference of smaller circle
=2π(30)+2π(15)=2π(30+15)
=2π(45)=2×22/7×45=282.85cm

Ans: (d)

Perimeter of figure  = 10 + 10 + 10 + 10 = 40 cm 

Ans: (c)

Ans: (c)

• To find the total length of wire needed for fencing, we calculate the perimeter of the garden.
• The formula for the perimeter of a rectangle is P = 2 × (length + width).
• Substituting the values: P = 2 × (526.75 m + 225.46 m) = 2 × 752.21 m = 1504.42 m.
• Thus, the total wire required for fencing the garden is 1504.42 m.

Ans: (b)

• The credit card limit is ₹50,000.
• Nitin spends ₹62,000 on a cellphone, which exceeds his limit.
• This results in a deficit of ₹12,000 (₹62,000 - ₹50,000 = –₹12,000).
• Thus, the amount shown in his bank statement will be negative, indicating he owes money.

Ans: (a)

• First, we need to find the total parts in the ratio: 2 + 5 + 7 = 14 parts.
• The total weight is 126 kg 350 g, which is equal to 126350 g.
• Now, to find the weight of one part, we divide the total weight by the total parts: 126350 g / 14 = 9025 g.
• The weight of the heaviest person, who has 7 parts, is 7 * 9025 g = 63175 g, which converts to 63 kg 175 g.

Ans: (b)

• The boy starts with 222 red balls.
• Each time he removes 6 red balls and adds 12 white balls.
• To find out how many times he can do this, we divide 222 by 6, which gives 37 times (with a remainder).
• In total, he adds 12 white balls for each of those 37 times, resulting in 444 white balls added to the basket.

Ans: (b)

• Reena's current age is calculated as 1/4 of her father's age. Since her father is 52 years old, Reena is 52 / 4 = 13 years old.
• In 7 years, Reena will be 13 + 7 = 20 years old.
• Thus, the answer is 20 years, which corresponds to option (b).

Ans: (a)

• The total number of steps is described as 10 less than 4 times the step Aarav is on, which is m.
• To express this mathematically, we calculate 4 times m, which is 4m.
• Then, we subtract 10 from this value, leading to the expression 4m - 10.
• Thus, the correct expression for the total number of steps is 4m - 10.

Ans: (b)

• To find the total number of bolts produced, first calculate the number of days in the four months: September (30 days), October (31 days), November (30 days), and December (31 days).
• This gives a total of 30 + 31 + 30 + 31 = 122 days.
• Now, multiply the number of days by the daily production: 122 days * 1020 bolts/day = 124440 bolts.
• Thus, the total number of bolts manufactured in these four months is 124440.

Ans: (b)

• First, calculate the distance traveled by bus: 1420 km - 920 km = 500 km.
• Next, find the fraction of the total distance that this represents: 500 km / 1420 km.
• Simplifying this fraction gives us 25/71.
• Thus, the fraction of the distance covered by bus is 25/71.

Ans: (c)

• The statement in option (c) claims that the sum of –8 + 23 + (–31) is greater than the sum of –31 + 7 – (–3).
• Calculating the first sum: –8 + 23 + (–31) equals –16.
• Calculating the second sum: –31 + 7 + 3 equals –21.
• Since –16 is actually greater than –21, the statement is incorrect.

Ans: (c)

Ans: (a)

Ans: (d)
One way to draw the required square is shown in the diagram. The smaller square has a side length of 2 cm and the larger a side length of 4 cm. This gives the side length of the larger square to be 6 cm and an area of 36 cm².

Ans: (b)
The butcher gained $0.21 on each kg he sold and thus he dishonestly made (0.21)(1800) = $378.00. After paying the $500 fine, he would have a loss of $500 - $378 = $122.

Ans: (d)
5 : 7 = 5/7
Then, equivalent ratios are 

Ans: (a)
(a) 100 notebooks = 1500 sheets 
12 notebooks = 1500/100 x 12
= 180 sheets