Maths Olympiad Model Test Papers -3 | Maths Olympiad Class 6 PDF Download

Ans: (c)

• Kritika refers to "my father's wife," which is her mother.
• Since she mentions "the only daughter," it indicates that Kritika is the daughter of her mother.
• This means Kritika is the wife of Aman, as she is the mother of his daughter.
• Thus, Kritika is related to Aman as his wife.

Ans: (d)

• To arrange the words in dictionary order, we look at the first letter of each word.
• The first word starting with 'F' is Feather (5), followed by Feature (2), then Feeding (3), and Fenestration (4).
• Finally, Feminine (1) comes last as it starts with 'F' but is alphabetically after the others.
• Thus, the correct order is 5, 2, 3, 1, 4, which corresponds to option (d).

Ans: (a)

• First, replace the symbols according to the given definitions: 18 + 12 ÷ 6 × 5.
• Next, perform the operations in the correct order: division first, then multiplication.
• Calculate 12 ÷ 6 = 2, then 2 × 5 = 10.
• Finally, add 18 + 10 = 28, but since we have to subtract 12, we do 28 - 12 = 17.

Ans: (a)

• The question asks to find the odd one out among the numbers listed.
• All the numbers except 13 are composite numbers, meaning they have more than two factors.
• 13 is a prime number, which only has two factors: 1 and 13 itself.
• Thus, 13 is the only number that does not fit with the others in this context.

Ans: (b)

• First, reverse the digits of each number provided.
• Next, arrange these reversed numbers in descending order.
• Identify the second number in this ordered list.
• Finally, calculate the sum of its digits to find the answer.

Ans: (b)

Ans: (d)

Ans: (b)

Ans: (d)

Ans: (c)
The train travels 60 km per hour, so in 3.5 hours it will travel 60 × 3.5 = 210 km.

Ans: (b)
Perimeter of a rectangle is 2 × (length + width) = 2 × (8 + 5) = 26 cm.

Ans: (b)
The other number is 30 – 12 = 18.

Ans: (c) 
It will take 240 ÷ 30 = 8 days to finish the book.

Ans: (c)
The average is (6 + 8 + 10 + 12) ÷ 4 = 36 ÷ 4 = 9.

Ans: (a)
The ratio of red balls to blue balls is 20:30, which simplifies to 2:3.

Ans: (c)

• To find m, we use the property of proportions, which states that the product of the means equals the product of the extremes.
• Here, we set up the equation: m * 96 = 24 * 72.
• Calculating the right side: 24 * 72 = 1728.
• Now, we have m * 96 = 1728, so m = 1728 / 96 = 18.
• Thus, the value of m is 18, confirming that the numbers are in proportion.

Ans: (b)

• First, calculate two-fifths of 125: (2/5) * 125 = 50.
• Next, calculate three-eighths of 256: (3/8) * 256 = 96.
• Now, find the difference: 96 - 50 = 46.
• Thus, two-fifths of 125 is 46 less than three-eighths of 256.

Ans: (a)

• To find the perimeter of the rectangle, we first need to determine its length.
• Using the formula for the area of a rectangle, Area = Length × Breadth, we can rearrange it to find Length: Length = Area / Breadth.
• Substituting the values: Length = 49 cm² / 2.8 cm = 17.5 cm.
• Now, we can calculate the perimeter using the formula: Perimeter = 2 × (Length + Breadth).
• So, Perimeter = 2 × (17.5 cm + 2.8 cm) = 2 × 20.3 cm = 40.6 cm.

Ans: (c)

• The cube is a three-dimensional shape where all six faces are squares and are identical in size and shape.
• In contrast, a square pyramid has a square base and triangular faces, while a triangular prism has two triangular bases and rectangular sides.
• A sphere is a round shape with no faces at all, making it different from the cube.
• Thus, the only shape with all identical faces is the cube.

Ans: (c)

• To find the odd factors of 42, we first determine its prime factorization: 42 = 2 × 3 × 7.
• We ignore the factor of 2 since we are only interested in odd factors.
• The odd factors come from the product of the remaining prime factors: 3 and 7.
• The odd factors of 42 are: 1, 3, 7, and 21. Adding these gives us 1 + 3 + 7 + 21 = 32.

Ans: (c)

• To solve the expression, first calculate 0.004/0.4, which equals 0.01.
• Next, calculate 0.4/0.004, which equals 100.
• Now, add the two results: 0.01 + 100 = 100.01.
• Thus, the final answer is 100.01, which corresponds to option (c).

Ans: (c)

• To solve for x ÷ (y ÷ z), first calculate y ÷ z.
• Here, y = 40 and z = 8, so 40 ÷ 8 = 5.
• Now, substitute this back into the equation: x ÷ 5 where x = 30.
• Thus, 30 ÷ 5 = 6, which is the final answer.

Ans: (c)

• The equation demonstrates the Distributive Property, which states that multiplying a number by a sum is the same as multiplying that number by each addend and then adding the results.
• In this case, 3 is distributed to both 7 and 5 inside the parentheses.
• This property is essential in simplifying expressions and solving equations.
• Closure, Commutative, and Identity properties do not apply to this specific equation.

Ans: (a)

• The definition of a perfect number is that it is equal to the sum of its proper divisors (excluding itself).
• For example, the number 6 is a perfect number because its factors are 1, 2, and 3, and 1 + 2 + 3 = 6.
• When you include the number itself, the sum of all factors becomes twice the perfect number.
• Thus, the correct answer is that the sum of all factors of a perfect number is twice the number itself.

Ans: (b)

• First, calculate the sum of 23.456 and 18.75, which equals 42.206.
• Next, subtract this sum from 98.735: 98.735 - 42.206 = 56.529.
• Finally, round 56.529 to the nearest hundredths, which gives you 56.53.
• Thus, the correct answer is (b) 56.53.

Ans: (d)

• The perpendicular bisector is a line that cuts another line segment into two equal parts at a 90-degree angle.
• This means that the two segments created by the bisector are of equal length.
• Thus, the correct answer is that it divides the line segment into two equal parts.
• Options (a), (b), and (c) are incorrect because they suggest unequal or more than two parts.

Ans: (b)

• Statement P is false because V can also be subtracted from other Roman numerals, not just X.
• Statement Q is also false since the smallest 4-digit number formed by the digits 1, 4, 0, and 9 is actually 1049, not 1409.
• Thus, both statements are incorrect, leading to the conclusion that the correct answer is option (b).

Ans: (c)

• The integer -50 indicates a negative value, which is often used to represent something below a reference point.
• In this case, a submarine being 50 km below sea level is the correct interpretation of -50, as it signifies depth.
• The other options either represent positive changes or heights above sea level, which do not align with the negative integer.
• Thus, the correct answer is that the submarine's position is best represented by -50.

Ans: (d)

• To solve the equation 2p – p/3 = 35, first, we need to eliminate the fraction. We can do this by multiplying the entire equation by 3.
• This gives us 6p - p = 105 (since 3 * 35 = 105).
• Now, combine like terms: 5p = 105.
• Next, divide both sides by 5 to find p = 21.

Ans: (c) 
The product of a number by 3 is equal to 171.
3x = 171
x = 171/3 = 57 ⇒ x = 57

Ans: (a) 
The number which when multiplied by 12 gives 36
12 × x=36x 
x = 36/12 = 3

Ans: (b) 
The point Z lies in the interior of ∠SOP.

Ans: (b)

Ans: (a)

Ans: (d)

Ans: (d)

• Mrs. Sharma's total income is ₹45000.
• Her total spending is ₹38750.
• To find her savings, subtract spending from income: ₹45000 - ₹38750 = ₹6250.
• The ratio of her savings to her income is 6250 : 45000, which simplifies to 5 : 36.

Ans: (b)

• To find the temperature difference, subtract the lower temperature from the higher temperature.
• The higher temperature is –39°C and the lower temperature is –62°C.
• Calculating this gives: –39°C - (–62°C) = –39°C + 62°C = 23°C.
• Thus, the temperature difference between the two samples is 23°C.

Ans: (d)

• The total number of days in October, November, and December is 31 + 30 + 31 = 92 days.
• Daily production is 950 crankcases.
• To find the total production, multiply the daily production by the total number of days: 950 * 92 = 87400.
• Thus, the total number of crankcases manufactured in these three months is 87400.

Ans: (d)

• First, calculate the area of the room: 15 m * 13 m = 195 m².
• Convert the area to square centimeters: 195 m² = 1,950,000 cm² (since 1 m² = 10,000 cm²).
• Next, find the area of one tile: (25 cm)² = 625 cm².
• Finally, divide the total area of the room by the area of one tile: 1,950,000 cm² / 625 cm² = 3120 tiles.

Ans: (b)

• To find out how much money Sneha has left, we start with her total amount, which is ₹40x.
• She spent ₹250 on food, ₹75y on clothes, and ₹375 on travel, totaling ₹(250 + 75y + 375) = ₹(625 + 75y).
• She also received ₹1500 as a birthday gift, so we add this to her total.
• The final calculation for the money left is: ₹40x + ₹1500 - (₹625 + 75y) = ₹(40x - 75y + 875).

Ans: (c)

• First, calculate the total milk supplied: 28 litres in the morning + 36 litres in the evening = 64 litres.
• Next, find the total earnings by multiplying the total litres by the cost per litre: 64 litres × ₹62 = ₹3968.
• Thus, the milkman earns ₹3968 in a day from selling milk.

Ans: (a)

• To determine who bought more ribbon, we need to compare m and m.
• First, convert both mixed numbers to improper fractions: = 99/8 and = 110/9.
• Next, find a common denominator (which is 72) to compare the two fractions: 99/8 = 891/72 and 110/9 = 880/72.
• Since 891/72 is greater than 880/72, Sarthak bought more ribbon by 11/72 m.

Ans: (b)

• To round off the number 3546253 to the nearest ten thousand, we look at the digit in the thousands place, which is 6.
• Since 6 is greater than or equal to 5, we round up the ten thousand place from 4 to 5.
• This means that 3546000 becomes 3550000 when rounded to the nearest ten thousand.
• Thus, the rounded population is 3550000.

Ans: (c)

• To find out how much water Deepak has left, we need to subtract the amount he gave away from the total he had.
• He started with 17.45 litres and gave away 8.30 litres.
• So, we calculate: 17.45 - 8.30 = 9.15 litres.
• This means Deepak has 9.15 litres of water remaining.

Ans: (a) 
70°+y=100° 
y=100°-70° =30°

Ans: (b)

• Statement-1 is true because a chord indeed connects any two points on the circle.
• Statement-2 is also true as a segment of a circle refers to the area enclosed by a chord and the arc connecting its endpoints.
• Both statements accurately describe properties of a circle, making option (b) the correct choice.
• Understanding these definitions is essential for grasping basic circle geometry.

Ans: (a)

Ans: (a)

Ans: (d)
Area of room = 540 m²
2(l+b) h=540

Ans: (b)