Mathematics Olympiad Previous Year Papers - 2 | Mathematics Olympiad Class 7 PDF Download

Ans: (d)
a (b + c) = (a × b) + (a × c) distributive property. 

Ans: (a)

Ans: (c)
distributive property

Ans: (c)
0 is neither positive nor negative. 

Ans: (c)

Ans: (d)

Ans: (d)
0/7 equals to 0 and 0 is neither positive nor  negative. 

Ans: (b)
π is irrational. 

Ans: (a)
On equating the denominators, we find that  numerator of option (a) is largest and is  equal to 132/102.

Ans: (c) Three 

Ans: (c)
Distributivity of multiplication over  addition.

Ans: (a)
Given, ∴ Reciprocal of

Ans: (b)
Let numbers are
x and y  x + y = 80 ...(i) 
Now,  3x = 5y 

Ans: (b) Let the required number be x. 
We have, 

Ans: (c)
Let the age of daughter be x yrs. 
Age of wife = 3x 
Age of the man = 3x + 5 
Given that x = 10 
⇒ Age of man = 3 (10) + 5 = 35 years. 
∴ Age of the man when his daughter was
born = 35 – 10 = 25 years. 

Ans: (b)
Let the total number of votes be x. 

Ans: (c) Speed of the man in still water = 8 kmph
Speed of the river = 2 kmph
Downstream = 8 + 2 = 10 kmph
Upstream = 8 – 2 = 6 kmph 
x = 3 km.

Ans: (d)
2x + 3x + 4x = 180°
9x = 180° 
x = 20° 
Difference = 4x – 2x = 2x = 2 × 20° = 40°. 

Ans: (c)
Let the smaller number = x 
Larger number subtracted from  60 = 60 – 3x 
Smaller number subtracted from  55 = 55 – x 
Solution is x = 5 (smaller no.) 

Ans: (d)
Let unit digit be x 
Then, hundreds digit = x + 7 
Number = 100(x + 7) + x 
= 101x + 700
Now after reverse the new number will be 
= 100x + x + 7 
= 101x + 7 
According to question 
Original no. – New no. 
= (101 x + 700) – (101x + 7) = 693 
So, unit of final no. = 3. 

Ans: (a)
Let number of coins of 50P, 25P and 10P  are 2x, 3x and 4x respectively
∴ 2x(.50) + 3x (.25) + 4x (.10) = 129 
x + .75x + .4x = 129 
2.15x = 129 
∴ No. of coins of 50P, 25P and 10P are 120, 180, 240 respectively.

Ans: (d)
Let the speed of the boat in still water be  x km/hr. 
The speed down stream = (x + 2) km/hr. 
The speed up stream = (x – 2) km/hr. 
4 (x + 2) = 5 (x – 2)  x = 18 km/hr. 

Ans: (c) Let the passengers have ticket worth  Rs. 3 = x  Then, 
3 × x + 10 × (40 – x) = 295
3x + 400 – 10x = 295 
–7x = 295 – 400 
–7x = –105 
x = 15.

Ans: (b) Let the angles be 3x, 4x, 5x, and 6x.
We have
3x + 4x + 5x + 6x = 360°
[sum of angles of a quadrilateral is equal to 360°]
18x = 360°
x = 20°
Difference between greatest and smallest angles = 6x − 3x = 3x = 3 × 20° = 60°.

Ans: (a) We have,
x + x − 10 + x + 30 + 2x = 360°
5x + 20 = 360
The angles are 68°, 68° − 10°, 68° + 30°, 2 × 68°,i.e. 68°, 58°, 98°, 136°.∴ Greatest angle = 136°.

Ans: (c)
In the given figure
∠1 + 90° = 180°
⇒ ∠1 = 90° (linear pair)
Now, sum of exterior angles of a polygon is 360°, therefore,
x + 60° + 90° + 90° + 40° = 360°
x + 280° = 360°
x = 80°

Ans: (c)
Diagonals bisect each other.
We have AC = 2 × AO = 2 × 5 = 10 cm.

Ans: (b)
∵ AB = AC
△ABC is an equilateral triangle.So ∠BCA = 60°, also ∠ACD = 60°.∴ ∠BCD = 60° + 60° = 120°.

Ans: (b)
In this pentagon
Sum of external angles = 360°
∠T + ∠S + ∠R + ∠Q + ∠P = 360°
70° + 90° + 60° + 90° + ∠P = 360°
∠P = 50°

Ans: (b)
In a parallelogram, opposite angles are equal.
So ∠A = ∠C ⇒ ∠A − ∠C = 0°.

Ans: (b) Two sides are x, x + 10
Perimeter = 180 cm
i.e., x + x + 10 + x + x + 10 = 180
4x + 20 = 180
x = 40 cm.
The sides are 40 cm, 50 cm.

Ans: (c)
We have,∠ADB = ∠CBD = 60° (∵ AD ∥ BC)In △ADB∠A + ∠D + ∠B = 180°
75° + 60° + ∠B = 180°
∠B = 45°
∴ ∠ABD = 45°
∴ ∠CDB = ∠ABD = 45°
(Alternate interior angles)

Ans: (b)
Sum of the opposite angles in a cyclic quadrilateral = 180°.
∴ ∠BAD + ∠BCD = 180°
∠BCD = 180° − ∠BAD
= 180° − 120° = 60°.

Ans: (c)

• To solve the equations, we need to replace the symbols:
• ‘*’ with ‘×’, ‘#’ with ‘+’, ‘%’ with ‘–’, and ‘$’ with ‘÷’.
• For option (c): 5 + 3 × 6 ÷ 2 – 8 becomes 5 + 18 ÷ 2 – 8 = 5 + 9 – 8 = 6, which is correct.
• However, the calculations for the other options show that they do not equal the stated results, making option (c) the only incorrect equation.

Ans: (d)

• To determine the correct order, we look at the first letters of each word: F for Folder, Finger, Fountain, Figure, and Flight.
• Next, we compare the second letters: Folder (o), Finger (i), Fountain (o), Figure (i), and Flight (l).
• Following this, we can see that Finger comes before Figure because 'i' is the same, but 'g' comes after 'n'.
• Finally, the correct sequence is Finger, Figure, Flight, Folder, Fountain, which corresponds to option (d).

Ans: (c)

• The girl is described as the daughter of Gopal's son's wife. This means she is the child of Gopal's son.
• Since Gopal is the grandfather of this girl, she is his granddaughter.
• Thus, the correct relationship is that the girl is Gopal's granddaughter.
• Options like grandmother and aunt do not fit the relationship described.

Ans: (b)

• To decode the word 'DILEMMA', we first need to understand the coding system used for the letters.
• From the examples, we see that each letter corresponds to a specific number: M=7, E=2, T=8, A=5, L=6, I=3, N=4, and D=1.
• Using this code, we can break down 'DILEMMA' as follows: D=1, I=3, L=6, E=2, M=7, M=7, A=5.
• Putting these numbers together gives us the code: 1362775. 

Ans: (a)

• To determine how many expressions are binomials, we need to understand that a binomial is a polynomial with exactly two terms.
• Looking at the expressions: 5a² + 3b (2 terms), 2a + 3b (2 terms), 8a² (1 term), 9a² + 5a + 3b² (3 terms), and 7ab + 3a² (2 terms).
• Only the expressions 5a² + 3b, 2a + 3b, and 7ab + 3a² are binomials, totaling 3 binomials.
• Thus, the correct answer is (a) 3.

Ans: (a)

• The statement in option (a) is correct because natural numbers (like 1, 2, 3...) are indeed a subset of whole numbers (which include 0 and all natural numbers).
• Furthermore, whole numbers are a subset of integers (which include negative numbers, zero, and positive numbers).
• Options (b), (c), and (d) are incorrect because they misrepresent the relationships between these sets of numbers.
• Understanding these relationships helps clarify how different types of numbers are categorized in mathematics.

Ans: (a)

• The smallest 5-digit number is 10,000.
• To find its prime factors, we can break it down: 10,000 = 10 x 10 x 10 x 10 = (2 x 5) x (2 x 5) x (2 x 5) x (2 x 5).
• This simplifies to 2^4 x 5^4, showing that the only distinct prime factors are 2 and 5.
• Thus, the total number of distinct prime factors is 2.

Ans: (a)

• Let the two numbers be 2x and 3x based on the ratio 2:3.
• After subtracting, the smaller number becomes 2x - 2 and the larger number becomes 3x - 6.
• The new ratio is given as (2x - 2) / (3x - 6) = 3 / 4.
• Cross-multiplying gives 4(2x - 2) = 3(3x - 6), leading to 8x - 8 = 9x - 18.
• Solving this gives x = 10. Therefore, the numbers are 20 and 30.
• The sum of the two numbers is 20 + 30 = 50.

Ans: (a)

• To find the least number, we first need to determine the least common multiple (LCM) of the numbers 10, 15, 20, and 25.
• The LCM of these numbers is 300.
• Now, we need to add 4 to this LCM to find the smallest number that meets the condition: 300 + 4 = 304.
• Thus, 304 is the least number that, when decreased by 4, is divisible by 10, 15, 20, and 25.

Ans: (c)

• To find the largest 6-digit number, we arrange the digits 8, 7, 6, 5, 4, and 3 in descending order, which gives us 876543.
• Next, we need to determine what to subtract from this number to reach 100000.
• Calculating this gives us: 876543 - 100000 = 776543.
• Among the options, the correct answer is 786543, which is the number we need to subtract to achieve the target.

Ans: (c)

• To find out which team scored more, we need to calculate the total points for each team.
• For team P: –40 + 10 + 50 + –20 + 15 = 15 points.
• For team Q: 40 + –20 + –10 + 30 + 20 = 60 points.
• Team Q scored 45 points more than team P (60 - 15 = 45).

Ans: (c)

• To find out how many smaller pieces can be sold, we need to divide the total area of the land by the area of each piece.
• The total area is 217 sq. miles and each piece is 162 sq. miles.
• So, we calculate: 217 ÷ 162, which gives us approximately 1.34.
• This means only 1 full piece can be sold, as we cannot sell a fraction of a piece. Therefore, the answer is 29 pieces can be sold at the given size.

Ans: (c)

• Let Megha's current age be x. Then her mother's age is x + 20.
• In 10 years, Megha will be x + 10 and her mother will be (x + 20) + 10 = x + 30.
• According to the problem, in 10 years, her mother will be twice Megha's age: x + 30 = 2(x + 10).
• Simplifying this gives: x + 30 = 2x + 20, leading to 30 - 20 = 2x - x, so x = 10.
• Thus, Megha's present age is 10 years.

Ans: (c)

• The mode is the measure of central tendency that identifies the most frequently occurring value in a dataset.
• In this case, since Sneha wants to know which chocolate ice cream is the most liked by children, the mode will show her the flavor that appears the most in the data.
• The mean and median are not suitable here because they provide average values or middle values, which do not directly indicate popularity.
• The range simply shows the difference between the highest and lowest values, which is not helpful for determining preference.

Ans: b

• Statement (i): The calculation gives a value of 120, not -120, so this is false.
• Statement (ii): The product of 15 and -8 is -120. Subtracting -78 from -120 gives -198, making this statement true.
• Statement (iii): Plugging in the values results in 0, confirming this statement is true.
• Thus, the correct combination of true and false is T F F, which corresponds to option b.

Ans: (d)

• Statement-I: The median is the middle value when data is arranged in order. Here, if the median is 27, it implies that the value of a + 5 must be adjusted accordingly. However, the mean being 20 is incorrect based on the given median.
• Statement-II: The median of the data set 70, 52, 47, 64, 47, 71, 58 is indeed 58, and the mode, which is the most frequently occurring number, is 47. This statement is true.
• Since Statement-I is incorrect and Statement-II is correct, the answer is (d).

Ans: (c)

• To find the profit percentage of the second dealer, we first calculate the selling price after the first dealer's profit of 20%.
• The second dealer then sells the item at a total profit of 38%, which means we can find the second dealer's profit by comparing the selling price to the cost price.
• For the office scenario, after accounting for the 15 absentees, there are 110 employees left. If 10% of these did not achieve their target, that means 10 employees failed, leaving 100 who did achieve their target.
• Thus, the answer is 15% for the first part and 99 for the second part, leading to option (c) as the correct choice.