Non Verbal Reasoning

Counting of Figures - Expert Level

Non-Verbal Reasoning Exercise Mode

Counting of Figures - Expert Level

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3 Questions
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Challenge yourself with expert-level counting of figures questions featuring complex, overlapping and mixed shapes. Improve observation, accuracy and problem-solving speed.

Question 11

How many triangles are there in the given figure ?


Counting of Figures Question 11

A
16
B
14
C
8
D
12
Correct Answer: Option A

🔍 Solution

After carefully observing the labelled figure, count the triangles from the smallest to the largest.

Counting of Figures Solution

🔺 Small Triangles (8)

AEI, EBI, AHI, BFI, CGI, GDI, CHI, DFI

🔺 Medium Triangles (4)

ABI, ACI, BDI, CDI

🔺 Large Triangles (4)

ABD, ACD, ABC, BCD

Total Triangles = 8 + 4 + 4 = 16

✅ Correct Answer: Option (A) — 16 Triangles

Question 12

How many rectangles are there in the given diagram?


Counting of Figures Question 12

A
4
B
7
C
9
D
18
Correct Answer: Option D

🔍 Solution

Only the left rectangular grid contributes to the rectangle count. The right arrow portion has two slanting sides, so it does not create any additional rectangles.

Counting of Figures Solution 12

Rectangle Count

  • 1 × 1 rectangles: 6
  • 2 × 1 rectangles: 4
  • 3 × 1 rectangles: 2
  • 1 × 2 rectangles: 3
  • 2 × 2 rectangles: 2
  • 3 × 2 rectangle: 1
Rectangle Size Count
1 × 1 6
2 × 1 4
3 × 1 2
1 × 2 3
2 × 2 2
3 × 2 1

Total Rectangles = 6 + 4 + 2 + 3 + 2 + 1 = 18

✅ Correct Answer: Option (D) — 18 Rectangles

⚡ Quick Method

For any m × n rectangular grid, the total number of rectangles is calculated using:

Total Rectangles = C(m+1, 2) × C(n+1, 2)

Here, the figure contains a 3 × 2 rectangular grid.

= C(4, 2) × C(3, 2)
= 6 × 3
= 18 Rectangles
Exam Shortcut: Select any 2 vertical lines and any 2 horizontal lines. Every such combination forms exactly one rectangle.
Question 13

How many triangles are there in the given figure ?


Counting of Figures Question 13

A
29
B
38
C
40
D
35
Correct Answer: Option C

🔍 Solution

After carefully observing the labelled figure, count the triangles from the smallest to the largest.

Counting of Figures Solution

🔺The simplest triangles are (18):

PNO; PNM; MPQ; MQR; AQP; AQR; BRA; BRC; SRC; SCD; SGR; SGD; DFG; DFE; TLM; TJK; TLK; TIH

🔺 The triangles composed of two components (14):

PON; PMA; APR; RAM; RAC; RGC; DGC; DGE; MPR; GRD; DCR; TMK; TKI; TIG

🔺 The triangles composed of four components (6):

AMQ; AMC; CAG; CGE; MKI; GIK

🔺 Largest triangles (2):

SPI; DQK

Total Triangles = 18 + 14 + 6 + 2 = 40

✅ Correct Answer: Option (C) — 40 Triangles

⚡ Quick Method

In complex triangle-counting figures, never count randomly. Count triangles according to their size.

Triangle Size Count
Smallest Triangles 18
Two-Component Triangles 14
Four-Component Triangles 6
Largest Triangles 2
Total 40
18 + 14 + 6 + 2 = 40
Exam Shortcut: Start with the smallest triangles, then count triangles formed by combining 2 small triangles, then 4 small triangles, and finally the largest triangles. This systematic approach prevents missing or counting the same triangle twice.
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