Analytical Reasoning — 8 Aptitude Questions and Answers with Explanations

Analytical Reasoning — Questions and Answers

Analytical Reasoning in the non-verbal section is figure counting: how many triangles, squares or rectangles a composite diagram contains. Guessing always undercounts, because the larger composite shapes are easy to miss. Count systematically by size — smallest units first, then combinations — and use the standard grid formulas where they apply.

8 solved questionsNon Verbal ReasoningFree · no signup

Analytical Reasoning— Concepts, Formulas & Shortcuts

Count by size: single units first, then pairs, then the whole figure.
Squares in an n × n grid = 1² + 2² + … + n².
Rectangles in an n × n grid = C(n+1, 2) × C(n+1, 2).
A square with both diagonals drawn contains 8 triangles.
In a strip of n cells, the number of rectangles is n(n + 1)/2.
Label the regions before counting; unlabelled counting is where errors occur.

Analytical Reasoning Practice Questions with Answers

Attempt each question first, then open the explanation. All 8 questions below are free to read and require no signup.

Q1.How many squares are there in a 2 × 2 grid?
Moderate
- A4
- B5
- C6
- D8
+Show Answer & Explanation
Answer: B. 5
Explanation: Four 1×1 squares plus the single 2×2 square gives 5.
Analytical Reasoning question 1 of 8
Q2.How many squares are there in a 3 × 3 grid?
Difficult
- A9
- B12
- C14
- D16
+Show Answer & Explanation
Answer: C. 14
Explanation: 1² + 2² + 3² = 9 + 4 + 1 = 14.
Analytical Reasoning question 2 of 8
Q3.How many rectangles can be formed in a strip of 3 cells in a row?
Moderate
- A3
- B5
- C6
- D9
+Show Answer & Explanation
Answer: C. 6
Explanation: n(n + 1)/2 = 3 × 4/2 = 6 rectangles.
Analytical Reasoning question 3 of 8
Q4.How many triangles are formed when both diagonals of a square are drawn?
Difficult
- A4
- B6
- C8
- D10
+Show Answer & Explanation
Answer: C. 8
Explanation: Four small triangles plus four larger half-square triangles gives 8.
Analytical Reasoning question 4 of 8
Q5.A triangle is divided by one line from a vertex to the opposite side. How many triangles are there in total?
Moderate
- A2
- B3
- C4
- D5
+Show Answer & Explanation
Answer: B. 3
Explanation: The two smaller triangles plus the original whole triangle gives 3.
Analytical Reasoning question 5 of 8
Q6.How many rectangles are there in a 2 × 2 grid?
Difficult
- A4
- B6
- C9
- D12
+Show Answer & Explanation
Answer: C. 9
Explanation: Choosing 2 of the 3 horizontal lines and 2 of the 3 vertical lines gives 3 × 3 = 9 rectangles.
Analytical Reasoning question 6 of 8
Q7.The minimum number of straight line segments needed to enclose a region is:
Easy
- A2
- B3
- C4
- D5
+Show Answer & Explanation
Answer: B. 3
Explanation: Three segments form a triangle, the simplest closed rectilinear figure.
Analytical Reasoning question 7 of 8
Q8.In an n × n grid, the total number of squares is given by:
Moderate
- An²
- BThe sum of squares from 1 to n
- C2n
- Dn³
+Show Answer & Explanation
Answer: B. The sum of squares from 1 to n
Explanation: Squares of every size from 1×1 up to n×n contribute, giving 1² + 2² + … + n².
Analytical Reasoning question 8 of 8

Analytical Reasoning — Frequently Asked Questions

How many squares are there in a 3 × 3 grid?+

14 — nine 1×1 squares, four 2×2 squares and one 3×3 square, since the total is 1² + 2² + 3².

Why do candidates usually undercount?+

Because they count only the smallest cells and forget the larger composite shapes formed by combining them. Counting size by size prevents this.

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