Maths Olympiad Model Test Papers -2 | Maths Olympiad Class 6 PDF Download

Ans: (a)

• To find the code for SEARCH, we need to look at the coding pattern from the previous examples.
• Each letter corresponds to a specific number: S=3, E=6, A=9, R=5, C=7, H=8.
• So, for SEARCH, we combine the numbers: S(3), E(6), A(9), R(5), C(7), H(8) which gives us 369578.
• Thus, the correct code for SEARCH is 369578.

Ans: (c)

• To find the number of 3's that are preceded by 9 and followed by 6, we need to look closely at the sequence.
• In the series, the relevant 3's are: 9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 3 3 6 9 3 6.
• Only the 3's at positions 1 and 10 meet the criteria of being preceded by 9 and followed by 6.
• Thus, there are two such occurrences of 3 in the series.

Ans: (d)

• In the pair AG : IO, the letters are transformed by moving forward in the alphabet: A to I (8 steps) and G to O (8 steps).
• To find the missing term for MS, we need to apply the same transformation.
• Starting from M, moving 8 steps forward gives us U, and from S, moving 8 steps forward gives us A.
• However, we need to find a pair that fits the pattern, and the correct transformation leads us to EK.

Ans: (b)

• The letters C, E, I, V can be rearranged to form words.
• Among these letters, the only meaningful word is "CIV."
• Thus, there is only one valid English word that can be formed.
• Therefore, the answer is (b) One.

Ans: (c)

• Kanika's information indicates that Pratik's birthday is after Thursday and before Sunday, which means it could only be Friday or Saturday.
• Vipul's information states that Pratik's birthday is after Friday and before Monday, which means it could only be Saturday.
• Since both statements point to Saturday as the only day that fits both conditions, we conclude that Pratik's birthday is on Saturday.

Ans: (b)

• P refers to "my mother's father," which means he is talking about his grandfather.
• The phrase "the only daughter of the father of my mother" indicates that the person in the photograph is P's mother.
• Since P is the child of his mother, he is her son.
• Thus, P is related to the person in the photograph as her son.

Ans: (b)

• To find Raman's rank from the bottom, we need to subtract his rank from the total number of students.
• There are 50 students in total, and Raman is 22nd from the top.
• So, his rank from the bottom is calculated as: 50 - 22 + 1 = 29.
• This means Raman is in the 29th position from the bottom.

Ans: (d)

• First, calculate the sum of the integers –9853 and –3187.
• The sum is –9853 + (–3187) = –13040.
• The additive inverse of a number is what you add to it to get zero. So, the additive inverse of –13040 is 13040.
• Thus, the correct answer is (d) 13040.

Ans: (c)

• First, calculate the sum of 3.25 and 5.79, which is 9.04.
• Next, add 6 tenths (or 0.6) to this sum: 9.04 + 0.6 = 9.64.
• Thus, the final answer is 9.64.

Ans: (c)

Ans: (c)

Ans: (c)
One dot is common to the circle and the square. Another dot is common to the circle and the rectangle. And the last dot is common to the square and the rectangle. 

Ans: (d)

Ans: (b)
In the first figure, 15 × 6 = 90 and 15 × 5 = 75 
In the second figure, 18 × 6 = 108 and 18 × 5 = 90 
So, in the third figure, 21 × 6 = 126 and 21 × 5 = 105

Ans: (c)

Ans: (a)

• Statement P is correct because a variable indeed can take on different values in mathematics.
• Statement Q is also correct as the value that satisfies an equation is known as the solution of that equation.
• Since both statements are true, the correct option is (a).
• This understanding is fundamental in algebra, where variables and their solutions play a crucial role.

Ans: (c)

• To determine if a number is divisible by 4, you only need to check the last two digits of that number.
• If the number formed by these last two digits is divisible by 4, then the entire number is also divisible by 4.
• This rule simplifies the process, as you don't have to consider the whole number.
• For example, in the number 132, you would check 32, and since 32 is divisible by 4, so is 132.

Ans: (a)

• A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself.
• The number 6 has divisors 1, 2, and 3, and their sum is 1 + 2 + 3 = 6.
• Other options like 12, 24, and 10 do not meet this criterion, as their divisors do not sum up to the numbers themselves.
• Thus, the only perfect number among the options is 6.

Ans: (d)

• To determine if a set of angles can form a triangle, the sum of the angles must equal 180°.
• For option (d), 90° + 45° + 45° = 180°, which satisfies the triangle condition.
• In contrast, the other options do not sum to 180°: (a) 185°, (b) 175°, and (c) 183°.
• Thus, only option (d) is valid for forming a triangle.

Ans: (b)

• The product of a natural number (let's say n) and its successor (n + 1) is n(n + 1).
• Since one of these numbers is always even (either n or n + 1), their product will also be even.
• For example, if n = 2, then 2 * 3 = 6, which is even.
• Thus, the correct answer is that the product is always an even number.

Ans: (c)

• First, convert all mixed numbers and fractions to decimals for easier calculation.
• 12 1/2 becomes 12.5, and 3 4/5 becomes 3.8.
• Now, perform the operations step by step: 12.5 - 5.375 + 8.125 - 2.9 + 10 - 3.8 + 11.08.
• After calculating, you will find that the final result is 29.63.

Ans: (d)

• The total number of students is x.
• The number of girls is y, so the number of boys is (x - y).
• The ratio of boys to total students is (x - y) : x.
• This means for every (x - y) boys, there are x students in total.

Ans: (d)

• Additive identity for whole numbers is 0 because adding 0 to any number does not change its value.
• Multiplicative identity for whole numbers is 1 since multiplying any number by 1 keeps it the same.
• Thus, the correct identities are 0 for addition and 1 for multiplication.
• Therefore, the answer is (d) 0, 1.

Ans: (d)

• To find the largest 7-digit number, arrange the digits in descending order: 9, 7, 4, 3, 0, 0, 0, which gives 9743000.
• For the smallest 7-digit number, arrange the digits in ascending order: 0 cannot be the leading digit, so we start with 3, followed by 0, 0, 4, 7, 9, which gives 3004790.
• Now, calculate the difference: 9743000 - 3004790 = 6738210.
• However, we need to ensure we use all digits at least once, so the correct largest number is 9997403 and the smallest is 3000004, leading to a difference of 6996951.

Ans: (b)

• To find the fraction, we first convert the decimal 0.65 into a fraction. This can be done by recognizing that 0.65 is equivalent to 65/100.
• Next, we simplify 65/100 to its lowest terms, which gives us 13/20.
• Now, we need to express this fraction with a denominator of 120. We can do this by multiplying both the numerator and denominator of 13/20 by 6, resulting in 78/120.
• Thus, the fraction with a denominator of 120 that equals 0.65 is 78/120.

Ans: (c)

• To determine if ratios are in proportion, we check if the cross products are equal.
• For option (c), 3 L : 12 L simplifies to 1 : 4, while 400 mL : 1050 mL simplifies to 8 : 21.
• Since 1 : 4 is not equal to 8 : 21, these ratios are not in proportion.
• Thus, option (c) is the correct answer as it does not maintain the same ratio.

Ans: (a)

• To find the expression, we first multiply p by 5, which gives us 5p.
• Next, we need to subtract this result from 8. This means we take 8 and subtract 5p from it.
• The resulting expression is 8 - 5p, which matches option (a).
• Thus, the correct answer is (a) 8 – 5p.

Ans: (b)

Ans: (b) 
Face value of 3 in the number 8453 = 3.
Place value of 3 in the number 8453 =3 × 1 = 3
Difference between face value and place
value of 3 in the number is = 3 - 3 = 0

Ans: (c) 
We have, 66 × 93 + 66 × 7 = 66 × (93 + 7) 
This property is distributive property.

Ans: (c) 
41 and 43 are consecutive odd numbers.

Ans: (b) 
The lowest composite number is 4 and successor of 4 = 4 + 1 = 5

Ans: (a) 
Factors of 46 are = 1, 2, 23, 46

Ans: (c)

Ans: (c)

Ans: (c)

• To find the longest tape that can measure the room's dimensions exactly, we need to determine the greatest common divisor (GCD) of the three dimensions.
• The dimensions in centimeters are: 825 cm (8 m 25 cm), 675 cm (6 m 75 cm), and 450 cm (4 m 50 cm).
• The GCD of 825, 675, and 450 is 75 cm, which means a tape of this length can measure all dimensions without leaving a remainder.
• Thus, the longest tape that can measure the room's dimensions exactly is 75 cm.

Ans: (b)

• To find the total distance covered, we first need to calculate the perimeter of the rectangular park.
• The formula for the perimeter of a rectangle is 2 × (length + width).
• Here, the length is 140 m and the width is 60 m. So, the perimeter is 2 × (140 + 60) = 2 × 200 = 400 m.
• Since the athlete takes 4 rounds, the total distance covered is 4 × 400 m = 1600 m.

Ans: (d)

• First, calculate the speed of the car: 180 km / 6 hours = 30 km/h.
• Next, calculate the speed of the bus: 315 km / 9 hours = 35 km/h.
• Now, find the ratio of the car's speed to the bus's speed: 30 km/h : 35 km/h.
• This simplifies to 6 : 7, which means the car travels 6 parts for every 7 parts the bus travels in one hour.

Ans: (c)

• Kartik has read 200 pages out of 320 pages.
• To find out how many pages Kanika read, we calculate 3/5 of 320, which equals 192 pages.
• Comparing the two, Kartik read 200 pages while Kanika read 192 pages.
• Thus, Kanika read fewer pages than Kartik by 8 pages (200 - 192 = 8).

Ans: (b)

• To find the total amount spent, we calculate the cost of each item:
• Shirts: 2 shirts x ₹250 = ₹500
• Scarfs: 2 scarfs x ₹175.50 = ₹351
• Belts: 4 belts x ₹75.75 = ₹303
• Now, add all these amounts together: ₹500 + ₹351 + ₹303 = ₹1154
• Thus, the total amount spent by Tarun is ₹1154.

Ans: (d)

• The initial temperature at 7 p.m. was 6°C.
• At midnight, the temperature fell to –4°C.
• To find the temperature drop, calculate the difference: 6°C - (–4°C) = 6°C + 4°C = 10°C.
• Thus, the temperature fell by 10 degrees.

Ans: (c)

• First, determine the number of revolutions per hour: 115 revolutions in 0.5 hours means it makes 230 revolutions in 1 hour.
• Next, multiply the hourly revolutions by the total hours: 230 revolutions/hour * 8 hours = 1840 revolutions.
• Thus, the wheel will make a total of 1840 revolutions in 8 hours.
• The correct answer is option (c) 1840.

Ans: (d)

• To find the total number of fruits Nandini had initially, we first calculate the total fruits in the packets: 36 packets × 12 fruits = 432 fruits.
• Then, we add the 6 leftover fruits: 432 fruits + 6 fruits = 438 fruits.
• Thus, the total number of fruits Nandini had at first is 438.

Ans: (b)

• The number 2874 in Roman numerals is broken down as follows:
• 2000 is represented as MM.
• 800 is represented as DCCC (500 + 300).
• 70 is represented as LXX (50 + 20).
• 4 is represented as IV.
• Combining these gives us MMDCCCLXXIV, which is the correct representation for ₹2874.

Ans: (a)

• Initially, the shopkeeper has 423 kg of sugar.
• He sells 42 kg daily, so in 6 days, he sells 42 kg x 6 = 252 kg.
• After 6 days, the remaining sugar is 423 kg - 252 kg = 171 kg.
• Rounding 171 kg to the nearest hundred gives us 200 kg.

Ans: (b)

Ans: (d)

Ans: (c)

Ans: (c)

Ans: (c)