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CAT Sample Questions: ›› Analytical Reasoning

# Analytical Section : Analytical Reasoning

Read the questions carefully and choose the correct answer from the given options.

Question 51

Count the number of squares in the following figure.

1. 14
2. 25
3. 26
4. 35
5. 32

Explanation:

The figure may be labeled as follows:

The simplest squares are AENM, EFON, FDOP, MNRQ, NOSR, OPTS, QRGB, RSHG, STCH i.e. 9 in number.
The squares composed of four components each are AFSQ, EDTR, MOHB, NPCG i.e. 4 in number.
The square composed of nine components is ADCB i.e. 1 in number.
Therefore, there are 9 + 4 + 1 = 14 squares in the given figure.

Question 52

How many squares are there in the following figure?

1. 12
2. 10
3. 13
4. 11
5. 15

Explanation:

One big square named ABCD
One small square named GHIJ
Squares composed of one component each are GKOM, KHNO, MOLJ, ONIL, AEOP, EBQO, POFD, OQCF i.e. 8 in number.
Therefore, there are 10 squares in all.

Question 53

Look at the following figure carefully and find out the total number of triangles and total number of squares in it.

1. 38 triangles and 7 squares
2. 38 triangles and 9 squares
3. 40 triangles and 10 squares
4. 44 triangles and 8 squares
5. 34 triangles and 5 squares

Explanation:

The simple triangles are CKF, GKJ, GLJ, HLI, HMI, DME, CKG, FKJ, GLH, JLI, HMD, IME, CAD, FBE i.e. 14 triangles in all.
The triangles composed of two components each are FCG, FJG, CFJ, JGF, GHJ, LHJ, GJI, GHI, IHD, IED, HIE, HDE i.e. 12 triangles in all.
The triangles composed of four components each are FGI, JHE, CJH, GID i.e. 8 triangles in all.
Therefore, the total number of triangles is 14 + 12 + 8 = 34.
Now,
The simple squares composed of two components each are KGLJ, LHMI i.e. 2 squares in all.
The squares composed of four components each are CFJG, GHIJ, HDEI i.e. 3 squares in all.
Therefore, the total number of squares is 2 + 3 = 5.

Question 54

Observe the following figure and find out the total number of squares and triangles in it.

1. 3 squares and 18 triangles
2. 4 squares and 18 triangles
3. 2 squares and 15 triangles
4. 2 squares and 18 triangles
5. None of the above

Explanation:

Let us name the figure first as follows:
The simple triangles are KFC, FKJ, GKJ, GKC, GLH, GLJ, JLI, HLI i.e. 8 triangles in all.
The triangles composed of two components are GCF, GJF, CFJ, CGJ, GJI, GHI, JGH, JIH i.e. 8 triangles in all.
The triangle composed of four components is FJI AND CJH i.e. 2 triangles in all.
Therefore the total number of triangles is 8 + 8 + 2 = 18.
Now, the simple square composed of two components is GKJL i.e. 1 square.
The squares composed of four components are CGJF, GHIJ i.e. 2 squares in number.
Therefore, the total number of squares is 1 + 2 = 3.

Question 55

Count the total number of squares in the following figure.

1. 16
2. 18
3. 20
4. 30
5. 6

Explanation:

Let us name the figure first as:

The squares composed of two components each are SWXY, WTZX, YXOV, XZUO i.e. 4 in number.
There is only one square composed of four components namely SPTX.
There is only one square composed of eight components namely STUV.
Therefore, there are 4 + 1 + 1 = 6 squares in the given figure.

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CAT Analytical Reasoning Question Number : 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 |56-59 | 60-64 | 65-69 | 70-74 | 75-79 | 80-84
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