SOF IMO 2023 previous year paper practice · PYQ-pattern set

SOF IMO 2023 PYQ-pattern questions

Showing 10 of the 18 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Analogy and Classification

   If 'Book' is to 'Read', then 'Pen' is to _____?

   • A. Write
   • B. Paper
   • C. Ink
   • D. School
   Answer and solution

   Answer: A

   A book is used for reading, similarly a pen is used for writing. This is a functional analogy.

2. Q2 · Ranking and Arrangement

   In a class of 40 students, Amit ranks 7th from the top. What is his rank from the bottom?

   • A. 33
   • B. 34
   • C. 35
   • D. 32
   Answer and solution

   Answer: B

   Rank from bottom = Total students − Rank from top + 1 = 40 − 7 + 1 = 34.

3. Q3 · Coding-Decoding

   In a certain code, 'MANGO' is written as '13-1-14-7-15'. How is 'PEACH' written in that code?

   • A. 16-5-1-3-8
   • B. 15-4-1-3-7
   • C. 16-5-1-4-8
   • D. 17-6-2-4-9
   Answer and solution

   Answer: A

   Each letter is coded as its position in the alphabet. P=16, E=5, A=1, C=3, H=8. So, 'PEACH' = 16-5-1-3-8.

4. Q4 · Paper Folding and Cutting

   A square piece of paper is folded twice and then a circular hole is punched through all layers. When the paper is completely unfolded, how many holes will appear?

   • A. 2 holes
   • B. 4 holes
   • C. 6 holes
   • D. 8 holes
   Answer and solution

   Answer: B

   Each fold doubles the number of layers. Two folds create 4 layers, so one punch creates 4 holes when unfolded.

5. Q5 · Coordinate Geometry

   Find the distance between the points A(3, 4) and B(7, 1).

   • A. 3 units
   • B. 4 units
   • C. 5 units
   • D. 6 units
   Answer and solution

   Answer: C

   Using distance formula: √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.

6. Q6 · Number Systems

   What is the HCF (Highest Common Factor) of 48 and 72?

   • A. 12
   • B. 18
   • C. 24
   • D. 36
   Answer and solution

   Answer: C

   Using prime factorization: 48 = 2⁴ × 3 and 72 = 2³ × 3². HCF = 2³ × 3 = 8 × 3 = 24.

7. Q7 · Lines and Angles

   Two parallel lines are cut by a transversal. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

   • A. 72°
   • B. 108°
   • C. 90°
   • D. 144°
   Answer and solution

   Answer: A

   When two parallel lines are cut by a transversal, alternate interior angles are equal. Therefore, the measure is 72°.

8. Q8 · Introduction to Euclid's Geometry

   Which of the following statements is an axiom in Euclidean geometry?

   • A. Two distinct lines cannot have more than one point in common
   • B. A triangle has three sides
   • C. Through a point outside a line, exactly one parallel can be drawn
   • D. Things which are equal to the same thing are equal to one another
   Answer and solution

   Answer: D

   This is Euclid's first axiom. Option C is a postulate, while A and B are definitions or basic properties.

9. Q9 · Areas of Parallelograms and Triangles

   A parallelogram and a triangle are on the same base and between the same parallels. If the area of the triangle is 48 cm², what is the area of the parallelogram?

   • A. 48 cm²
   • B. 72 cm²
   • C. 96 cm²
   • D. 144 cm²
   Answer and solution

   Answer: C

   A triangle and a parallelogram on the same base and between the same parallels have the property that the area of the triangle is half that of the parallelogram. Therefore, area of parallelogram = 2 × 48 = 96 cm².

10. Q10 · Statistics

    The mean of 8, 12, 16, x, 20 and 24 is 16. What is the value of x?

    • A. 14
    • B. 16
    • C. 18
    • D. 15
    Answer and solution

    Answer: B

    Mean = (8+12+16+x+20+24)/6 = 16. Thus, 80+x = 96, so x = 16.