Maths Olympiad Previous Year Paper -1 | Maths Olympiad Class 6 PDF Download

Ans: (c)

• The numbers 81, 36, and 16 are all perfect squares (9x9, 6x6, and 4x4 respectively).
• However, 47 is a prime number, meaning it cannot be divided evenly by any number other than 1 and itself.
• This makes 47 the odd one out in this group.
• Thus, the correct answer is (c) 47.

Ans: (b)

• To find Amit's position from the right, we can use the total number of students and his position from the left.
• There are 60 students in total, and Amit is 30th from the left.
• His position from the right can be calculated as: 60 - 30 + 1 = 31.
• Thus, Amit is in the 31st position from the right end.

Ans: (c)

• The code shifts each letter in the word GREAT to the next letter in the alphabet, with a specific pattern.
• For example, G becomes J, R becomes T, and so on.
• Applying the same pattern to SIGHT, S shifts to V, I to K, G to H, H to J, and T to W.
• Thus, SIGHT is encoded as VKHJW.

Ans: (d)

• First, replace the symbols with their respective operations: 85 ÷ 17 × 4 + 18 – 5.
• Next, perform the operations in the correct order (BODMAS): start with division and multiplication from left to right.
• Calculate 85 ÷ 17, which equals 5.
• Then, multiply 5 by 4 to get 20.
• Now, add 20 and 18 to get 38.
• Finally, subtract 5 from 38, resulting in 33.

Ans: (a)

• To find the pairs, we need to look at the letters in the word CREATOR and see if the distance between them matches their positions in the English alphabet.
• For example, the letters C and E are two letters apart in the alphabet, and they are also two letters apart in the word.
• After checking all possible pairs, we find that there are two pairs that meet this criterion.
• Thus, the correct answer is two pairs of letters.

Ans: (c)

• The girl is the granddaughter of Arun's father's elder brother, which means she is the daughter of Arun's uncle.
• This makes her Arun's cousin, but since the question states she is a granddaughter, it indicates she is the daughter of Arun's sibling.
• Thus, the girl is Arun's niece, as she is the daughter of Arun's brother or sister.
• Therefore, the correct relationship is that the girl is Arun's niece.

Ans: (c)
The triangles formed are A, B, C, D, E, F, G, H, I, J, K, L, CD, EJ, FG, IH, GH, FI, DE, CJ, JEFI, DEFG
∴ Total number of triangles formed = 22

Ans: (a)
Number of cubes in the Layer 1 = 9
Number of cubes in the Layer 2 = 15
Number of cubes in the Layer 3 = 16
Number of cubes in the Layer 4 = 16
∴ Total number of cubes in the given figure = 9 + 15 + 16 + 16 = 56

Ans: (b)
Number of dots on the opposite faces are (1, 4); (2, 3); (5, 6).

Ans: (a)

1, 5, 6 - Two similar shapes one contained in other. 
2, 3, 4 - One shape with two intersecting lines in interior. 
7, 8, 9 - Two different shapes one circum-scribing the other.

Ans: (a)
Distance between starting point and final point =(20+15)m = 35 m 
So, Rohit is 35 metres far away from starting point and in East direction.

Ans: (a)

Ans: (b)
So, Pia is facing South.

Ans: (b)
Number of students between Kunal and Sonali = 35−(7+9)=19
Clearly, there are 9 students between Kunal and Pulkit, as well as Pulkit and Sonali. 
So, Kunal is at 10th position from Pulkit.

Ans: (a)
The letters of the word are written in a reverse order to obtain the code. So, code for ALIGATOR is ROTAGILA.

Ans: (b)

• Understanding the number: The population figure 1,210,193,422 can be broken down into parts to understand its value in the International System of Numeration.
• International System: In this system, the number is expressed in terms of billions and millions. Here, 1,210 million is equivalent to 1 billion and 210 million.
• Correct representation: Therefore, the correct option that represents this number is "One billion two hundred ten million one hundred ninety three thousand four hundred twenty two."
• Other options: The other options either use the Indian numbering system or misrepresent the value, making them incorrect.

Ans: (d)

• To find the number to subtract, we can set up the equation: 67.74 - x = 24.48.
• Rearranging gives us x = 67.74 - 24.48.
• Calculating this, we find x = 43.26.
• Thus, 43.26 is the value that needs to be subtracted from 67.74 to get 24.48.

Ans: (b)

• To find the largest 5-digit number, arrange the digits in descending order: 7, 5, 2, 1, 0, which gives 75210.
• For the smallest 5-digit number, arrange the digits in ascending order: 0 cannot be the first digit, so we start with 1, followed by 0, 2, 5, and 7, resulting in 10257.
• Now, add the two numbers: 75210 + 10257 = 85467.
• Thus, the sum of the greatest and smallest 5-digit numbers is 85,467.

Ans: (b)

• The temperature change is calculated by subtracting the initial temperature from the final temperature.
• For option (b), the change is from –4°C to 8°C, which is a rise of 12 degrees.
• In comparison, the other options show smaller increases: (a) 10 degrees, (c) 7 degrees, and (d) 8 degrees.
• Thus, the option with the maximum rise in temperature is indeed (b) – 4°C to 8°C.

Ans: (b)

• Co-prime numbers are those that have no common factors other than 1.
• To check if 161 and 192 are co-prime, we find their greatest common divisor (GCD).
• The GCD of 161 and 192 is 1, meaning they share no common factors.
• Thus, 161 and 192 are co-prime, while the other pairs have common factors.

Ans: (d)

• To determine the value of *, we need to check the divisibility rule for 11, which states that the difference between the sum of the digits in odd positions and the sum of the digits in even positions should be either 0 or a multiple of 11.
• For the number 653*47, the digits in odd positions are 6, 3, 4 (1st, 3rd, and 5th), and the digits in even positions are 5, *, 7 (2nd, 4th, and 6th).
• Calculating the sums: Odd positions = 6 + 3 + 4 = 13; Even positions = 5 + * + 7 = 12 + *.
• The difference is |13 - (12 + *)| = |1 - *|. For this to be divisible by 11, * must be 1.

Ans: (c)

• First, we can find the value of a and b using the given ratios. From the ratio a : 3 = 72 : 27, we can set up the equation a/3 = 72/27.
• Cross-multiplying gives us a = (3 * 72) / 27, which simplifies to a = 8.
• Next, using the ratio 40 : b, we have 40/b = 72/27. Cross-multiplying gives us b = (40 * 27) / 72, which simplifies to b = 15.
• Now, substituting a = 8 and b = 15 into the expression 2a + 5b gives us 2(8) + 5(15) = 16 + 75 = 91.

Ans: (a)

• The fraction 161/299 needs to be simplified to its lowest terms.
• To do this, we find the greatest common divisor (GCD) of the numerator (161) and the denominator (299).
• The GCD of 161 and 299 is 23, so we divide both by 23.
• This gives us 7/13, which is the simplest form of the fraction.

Ans: (b)

• To solve the equation, we need to find numbers that fit into the format: first number × second number + third number = 49.
• Testing option (b) with 5 × 8 + 9 gives us 40 + 9 = 49, which is correct.
• Other options do not satisfy the equation when calculated.
• Thus, the correct combination is 5, 8, 9.

Ans: (d)

• Roman Numerals to Arabic Numbers: 
  DXXXIX = 539

  CCCLXVII = 367

  DCLXXXI = 681

  Perform Calculation:

  Addition: 539 + 367 = 906

  Subtraction: 906 − 681 = 225

  Convert 225 to Roman Numerals:

  200=CC, 20=XX, 5=V → CCXXV

  Correct Answer: (d) CCXXV.

Ans: (b)

• When you add two odd numbers (x and y), the result is always even. This is because odd + odd = even.
• However, if you add 1 to that sum (x + y + 1), it becomes odd.
• The product of two odd numbers (xy) is also odd.
• Adding 2 to the product (xy + 2) results in an odd number as well.

Ans: (c)

• The concept of proportion means that the ratios of the numbers should be equal.
• In option (c), the ratios do not maintain equality, making them not proportional.
• For example, comparing the ratios of the first two numbers (21 and 35) with the last two (32 and 48) shows a discrepancy.
• Thus, option (c) is the only set that fails to meet the proportionality condition.

Ans: (a)

Ans: (d)

Ans: (a) If we bisect AB, that means we divide it  into two equal parts.  
∴ Length of each part = 18/2 = cm = 9 cm

Ans: (b) 
RQ = PQ – PR = (7.5 – 5.9) cm = 1.6 cm

Ans: (d)

Ans: (c) 
Since A is the mid point of PQ.

Ans: (a) 
Product of means = 3 × 4 = 12  
Product of extremes = 2 × 9 = 18  
Since, product of means ≠ product of  extremes  
Hence, ratios 2 : 3 and 4 : 9 are not in  proportion. 

Ans: (c)

Ans: (a)

• First, calculate the correct answer by multiplying 160 by 79, which equals 12640.
• Next, calculate the incorrect answer by multiplying 160 by 89, which equals 14240.
• Now, find the difference between the incorrect answer and the correct answer: 14240 - 12640 = 1600.
• Thus, Ansh's answer was greater by 1600 than the correct answer.

Ans: (b)

• To find the total cost, we need to add the prices of all items: ₹ 14//1/3 + ₹ 57//1/2 + ₹ 71//2/3.
• First, convert each mixed fraction to an improper fraction for easier addition.
• After performing the addition, we find that the total amount Rehan should pay is ₹ 143//1/2.
• This means he needs to give the shopkeeper ₹ 143 and a half rupee.

Ans: (b)

• To find the amounts for X and Y, first, we need to determine the total parts in the ratio 5:7, which is 5 + 7 = 12 parts.
• Next, we calculate the value of one part by dividing the total amount ₹4200 by 12, resulting in ₹350 per part.
• Now, for X, who gets 5 parts: 5 * ₹350 = ₹1750.
• For Y, who receives 7 parts: 7 * ₹350 = ₹2450.
• Thus, X will receive ₹1750 and Y will receive ₹2450, confirming the ratio of 5:7.

Ans: (d)

• Amisha starts by running 7 km South, which is represented as -7.
• Then, she runs 9 km North, which is represented as +9.
• To find her final position, we calculate: -7 + 9 = 2.
• Thus, her position from the initial point is 2 km North.

Ans: (a)

• The area of the square floor is calculated as side × side, which is 26 m × 26 m = 676 m².
• The length of the mat is 18 m, and its breadth is two-thirds of the length, which is 18 m × (2/3) = 12 m.
• The area of the rectangular mat is length × breadth, which is 18 m × 12 m = 216 m².
• To find the area of the floor that is not covered by the mat, subtract the area of the mat from the area of the floor: 676 m² - 216 m² = 460 m².

Ans: (b)

• The hour hand of a clock completes a full circle (360 degrees) in 12 hours.
• In this time frame from 10 p.m. to 7 a.m., the hour hand moves from the 10 to the 7, which is 9 hours.
• Every hour, the hour hand makes 2 right angles (90 degrees) at the 3 and 9 positions.
• During these 9 hours, the hour hand makes a total of 3 right angles, specifically at 12 a.m., 3 a.m., and 6 a.m.

Ans: (c)

• First, calculate the total amount of water in containers X and Y: 24.25 L + 17.75 L = 42 L.
• This total (42 L) represents one-fifth of the capacity of tank Z.
• To find the total capacity of tank Z, multiply 42 L by 5 (since 42 L is one-fifth): 42 L * 5 = 210 L.
• Thus, the total capacity of tank Z is 210 L.

Ans: (a)

• To find the number of students in the Arts stream, we need to subtract the total number of students in Science and Commerce from the overall total.
• The total number of students is 1,54,676 and those in Science and Commerce together is 1,26,136.
• So, the calculation is: 1,54,676 - 1,26,136 = 28,540.
• This means there are 28,540 students enrolled in the Arts stream.

Ans: (a)

• To find the minimum distance that all boys can walk in complete steps, we need to calculate the Least Common Multiple (LCM) of their step lengths: 63, 70, and 77.
• The LCM is the smallest number that is a multiple of all three step lengths.
• Calculating the LCM gives us 6930 cm, which means all boys can walk this distance in whole steps.
• Thus, the answer is 6930 cm, as it allows each boy to complete their steps without any fractions.

Ans: (a)

• First, convert the length of the cloth from meters and centimeters to just meters: 4 m 25 cm = 4.25 m.
• Next, multiply this length by the number of dresses: 4.25 m × 3 = 12.75 m.
• This gives the total length of cloth required to make 3 dresses.
• Thus, the answer is 12.75 m.

Ans: (c)

• The LCM (Least Common Multiple) of numbers is the smallest number that is a multiple of each of the numbers. In this case, the LCM of 102, 170, and 136 is indeed 2040.
• To find the LCM, we can use the prime factorization method or the method of listing multiples, and in this case, it confirms that 2040 is the correct answer.
• Option (a) is incorrect because 42 and 49 share a common factor (7), so they are not co-prime.
• Option (b) is incorrect as 376277 is not divisible by 3 (the sum of its digits is not divisible by 3).
• Option (d) is also incorrect since option (c) is true.

Ans: (a)

Ans: (c) 
We have, 1935 × 782 × 15  
= 1935 × 46 × (17 × 15)  
= 1935 × 46 × 255

Ans: (a) 
LCM of 2, 3, 4, 5 and 6 = 60  
Since we are looking for a number that is  divisible by 2, 3, 4, 5 and 6 and that number  + 1 being divisible by 7. 
On finding the  multiple of 60 such that the sum of multiple  and 1 is divisible by 7.  
We get the no. = 300 + 1 = 301

Ans: (b) 
475 × 102 is written as  
475 × (100 + 2) = 475 × 100 + 475 × 2  [∴ a × (b + c) = a × b + a × c]  
47500 + 950 = 48450