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deepshikhasingh15
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G7 Math Olympiad
Math quiz helps us to enhance brains neural network.
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1) An article’s price is first decreased by 10% and then by 20%. Find the overall percentage decrease.
Net factor = 0.9 × 0.8 = 0.72 Overall decrease = (1 – 0.72) × 100 = 28%
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2) If in a certain code, digits of a number are reversed and then added to the original number, what will be the result for 63?
63 reversed = 36 Sum = 63 + 36 = 99 ✔
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3) Which 3D shape is created when the top of a cone is sliced off parallel to its base?
Slicing a cone parallel to the base creates a **frustum**.
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4) Simplify the following expression:
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5) The mean of 5 numbers is 24. Four of the numbers are 18, 30, 22, and 26. Find the missing number.
Total sum = 24 × 5 = 120 Sum of 4 numbers = 18 + 30 + 22 + 26 = 96 Missing number = 120 – 96 = 24
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6) A number is 72% of another number.If the sum of the two numbers is 86% of 500, what is the bigger number?
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7) Find the value of: 3 2/5 + 4 7/10 – 2 9/20
Convert mixed numbers to improper fractions: 3 2/5 = 17/5, 4 7/10 = 47/10, 2 9/20 = 49/20 Common denominator = 20 17/5 = 68/20, 47/10 = 94/20, 49/20 = 49/20 Sum = 68/20 + 94/20 – 49/20 = (68 + 94 – 49)/20 = 113/20 = 5 13/20
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8) Find the least common multiple (LCM) of 36, 48, and 54.
Prime factors: 36 = 2² × 3² 48 = 2⁴ × 3 54 = 2 × 3³ LCM = 2⁴ × 3³ = 16 × 27 = 432 Wait, that’s 432 (Answer 1). Recalculate: LCM takes highest powers: 2⁴ (from 48), 3³ (from 54) 2⁴ × 3³ = 16 × 27 = 432
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9) If the surface area of a cube is 150 cm², what is the length of one edge?
TSA = 6a² → 6a² = 150 → a² = 25 → a = √25 = 5 cm
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10) In a quadrilateral PQRS, if ∠P = ∠R = 100° and ∠S = 75°, then ∠Q =
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11) How many integer values of x satisfy −4 < 2x + 1 ≤ 5?
Solve: −4 < 2x + 1 ⇒ 2x > −5 ⇒ x > −2.5 2x + 1 ≤ 5 ⇒ 2x ≤ 4 ⇒ x ≤ 2 So −2 < x ≤ 2 ⇒ x = −1, 0, 1, 2 ⇒ 4 values
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12) A trader buys an article for $500 and sells it for $550. He then buys another article for $600 and sells it at the same percentage profit as before. Find the selling price of the second article.
Profit % = (550 – 500)/500 × 100 = 10% Selling price of second article = 600 + 10% of 600 = 600 + 60 = $660.Profit % = (550 – 500)/500 × 100 = 10% Selling price of second article = 600 + 10% of 600 = 600 + 60 = $660.
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13) What is the 50th term in the sequence: 1, -2, 3, -4, 5, -6, …
Odd terms positive, even terms negative 50th term is even ⇒ answer is -50 Correct Answer: Answer 2
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14) Simplify: [left(frac{a^3b^{-2}}{a^{-1}b^4}right)^2]
[frac{a^3}{a^{-1}} = a^{3+1} = a^4, quad frac{b^{-2}}{b^4} = b^{-2-4} = b^{-6} Rightarrow (a^4b^{-6})^2 = a^8b^{-12}]
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15) A regular polygon has 10 lines of symmetry. How many sides does it have?
The number of lines of symmetry of a regular polygon equals the number of sides.
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16) A sphere has:
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17) If the cost of a pen is ₹’p’ and t(he cost of a notebook is ₹”n’, what is the total cost of 2 pens and 3 notebooks?
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18) In triangle ABC, coordinates are A(1, 2), B(5, 6), and C(7, 2). Find the length of the median from vertex A.
Midpoint of BC = ((5+7)/2, (6+2)/2) = (6, 4)Length of median from A to midpoint = √((6 – 1)² + (4 – 2)²) = √(25 + 4) = √29 ≈ 5.39 ≈ 5
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19) A bank vault uses a 3-digit secret code.
Guard 1 says:“The sum of the digits is 12.”
Guard 2 says:“If you reverse the code, the new number is 141 less than three times the original number.”
What is the original 3-digit code?
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20) Find the unknown length x in figure.
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