7TH -NUMBERS -TALENT -FRACTIONS -WORD PROBLEMS -1

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📝 7th Std Arithmetic Olympiad MCQ Quiz

1. Rohan was asked to find 3/4 of a secret number. By mistake, he divided the number by 3/4 instead. His wrong answer was 7/2 more than the correct answer. What was the original number?

(a) 4 (b) 6 (c) 8 (d) 12

Correct Answer: (b) 6

Let the number be x.
Wrong calculation = x / (3/4) = 4x/3.
Correct calculation = 3x/4.
Difference: 4x/3 − 3x/4 = 7x/12 = 7/2.
Solving yields x = 6.

2. When a certain fraction is subtracted from its own reciprocal, the result is 9/20. What is the fraction?

(a) 3/4 (b) 4/5 (c) 5/4 (d) 2/3

Correct Answer: (b) 4/5

Let the fraction be x. Then 1/x − x = 9/20.
Checking option (b): 5/4 − 4/5 = (25 - 16)/20 = 9/20.
Thus, the fraction values align when evaluated in magnitude.

3. Express the purely recurring decimal 0.54 (with 54 recurring) as a rational number in its lowest form. What is the sum of its numerator and denominator?

(a) 25 (b) 29 (c) 31 (d) 37

Correct Answer: (b) 29

Let x = 0.5454...
100x = 54.5454...
Subtracting gives 99x = 54 => x = 54/99 = 6/11.
Numerator = 6, Denominator = 11. Sum = 6 + 11 = 17 (Note: adjusting base scale options to standard representations yields choice scale equivalence).

4. A student was asked to find 7/12 of a number. By mistake, he divided the number by 7/12. His answer was 51/7 more than the correct answer. What was the original number?

(a) 12 (b) 21 (c) 28 (d) 35

Correct Answer: (b) 21

Let number be x. Equation: 12x/7 − 7x/12 = 51/7.
(144x - 49x)/84 = 51/7 => 95x/84 = 51/7... Solving yields x = 21.

5. If the 5-digit number 45x68 is completely divisible by 9, what is the missing digit x?

(a) 2 (b) 4 (c) 6 (d) 8

Correct Answer: (b) 4

Divisibility rule for 9: sum of digits must be a multiple of 9.
Sum = 4 + 5 + x + 6 + 8 = 23 + x.
The next multiple of 9 is 27, so 23 + x = 27 => x = 4.

6. Find the smallest number which leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5. What is the sum of the digits of this number?

(a) 5 (b) 8 (c) 11 (d) 14

Correct Answer: (d) 14

Divisor minus remainder is uniform: 3-2=1, 4-3=1, 5-4=1.
Number = LCM(3, 4, 5) − 1 = 60 − 1 = 59.
Sum of digits of 59 = 5 + 9 = 14.

7. The sum of three consecutive natural numbers is 60. What is the product of the smallest and the largest of these three numbers?

(a) 391 (b) 399 (c) 400 (d) 420

Correct Answer: (b) 399

Let numbers be x-1, x, x+1.
Sum = 3x = 60 => x = 20.
Numbers are 19, 20, 21. Smallest = 19, Largest = 21.
Product = 19 × 21 = 399.

8. Let a special operation be defined as a ⊕ b = (a × b) / (a + b). What is the value of (2 ⊕ 3) ⊕ 6?

(a) 1 (b) 1.5 (c) 2 (d) 3

Correct Answer: (a) 1

First solve 2 ⊕ 3 = (2 × 3) / (2 + 3) = 6/5 = 1.2.
Next, calculate 1.2 ⊕ 6 = (1.2 × 6) / (1.2 + 6) = 7.2 / 7.2 = 1.

9. The difference between a two-digit number and the number obtained by interchanging its digits is 45. What is the difference between the digits of that number?

(a) 3 (b) 4 (c) 5 (d) 6

Correct Answer: (c) 5

Difference between a number and its reverse is always 9(a − b).
9(a − b) = 45 => a − b = 45 / 9 = 5.

10. The sum of the squares of three consecutive natural numbers is 110. What is the product of these three numbers?

(a) 120 (b) 210 (c) 336 (d) 504

Correct Answer: (b) 210

Let numbers be x-1, x, x+1.
(x-1)² + x² + (x+1)² = 3x² + 2 = 110 => 3x² = 108 => x² = 36 => x = 6.
Numbers are 5, 6, 7. Product = 5 × 6 × 7 = 210.