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 Analytical Reasoning Questions

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Q:

Determine the number of rectangles and hexagons in the following figure.

A) 30, 5 B) 32, 3
C) 28, 5 D) 30, 3
 
Answer & Explanation Answer: A) 30, 5

Explanation:

The figure may be labelled as shown

 

 

Rectangles :

 

The simplest rectangles are CVSR, VETS, RSWM and STKW i.e 4 in number.

 

The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e 4 in number.

 

The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e 4 in number.

 

The rectangles composed of four components each are CEKM, AVSP, PSWO,VGHS and SHIW i.e 5 in number.

 

The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e 4 in number.

 

The rectangles composed of six components each are ACMO and EGIK i.e 2 in number.

 

The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e 4 in number.

 

The rectangles composed of ten components each are AEKO and CGIM i.e 2 in number.

 

AGIO is the only rectangle having sixteen components

 

Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.

 

Hexagons :

 

The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure.

 

 

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Filed Under: Analytical Reasoning - Non Verbal Reasoning
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48 9398
Q:

Find the minimum number of straight lines in the below figure ?

                441484547526.png image

A) 20 B) 19
C) 17 D) 15
 
Answer & Explanation Answer: B) 19

Explanation:

The given figure can be labelled as :

  44-1u1484547679.png image 

Straight lines :

The number of straight lines are 19

i.e. BC, CD, BD, AF, FE, AE, AB, GH, IJ, KL, DE, AG, BH, HI, GJ, IL, JK, KE and DL.

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16 8701
Q:

Minimum number of straight lines required to form the below figure ?

                      21484547018.png image

A) 18 B) 17
C) 14 D) 16
 
Answer & Explanation Answer: C) 14

Explanation:

The given figure can be labelled as shown :

       2-11484547091.png image

The horizontal lines are AK, BJ, CI, DH and EG i.e. 5 in number.
The vertical lines are AE, LF and KG i.e. 3 in number.
The slanting lines are LC, CF, FI, LI, EK and AG i.e. 6 in number.
Thus, there are 5 + 3 + 6 = 14 straight lines in the figure.

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Filed Under: Analytical Reasoning - Non Verbal Reasoning
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24 8517
Q:

A university library budget committee must reduce exactly five of eight areas of expenditure—I, J, K, L, M, N, O and P—in accordance with the following conditions:

If both I and O are reduced, P is also reduced.
If L is reduced, neither N nor O is reduced.
If M is reduced, J is not reduced.
Of the three areas J, K, and N exactly two are reduced.

 

Question :

If both K and N are reduced, which one of the following is a pair of areas neither of which could be reduced?

A) I, L B) J, L
C) J, M D) I, J
 
Answer & Explanation Answer: B) J, L

Explanation:

This question concerns a committee’s decision about which five of eight areas of expenditure to reduce. The question requires you to suppose that K and N are among the areas that are to be reduced, and then to determine which pair of areas could not also be among the five areas that are reduced.

The fourth condition given in the passage on which this question is based requires that exactly two of K, N, and J are reduced. Since the question asks us to suppose that both K and N are reduced, we know that J must not be reduced:

Reduced         ::      K, N
Not reduced   ::      J

The second condition requires that if L is reduced, neither N nor O is reduced. So L and N cannot both be reduced. Here, since N is reduced, we know that L cannot be. Thus, adding this to what we’ve determined so far, we know that J and L are a pair of areas that cannot both be reduced if both K and N are reduced:

Reduced        ::      K, N
Not reduced  ::      J, L

Answer choice (B) is therefore the correct answer.

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Q:

Find the minimum number of straight lines required to make the given figure.

A) 9 B) 11
C) 15 D) 16
 
Answer & Explanation Answer: B) 11

Explanation:

  

The horizontal lines are DE, FH, IL and BC i.e. 4 in number.

The slanting lines are AC, DO, FN, IM, AB, EM and HN i.e. 7 in number.

Thus, there are 4 + 7 = 11 straight lines in the figure.

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76 7098
Q:

Find the number of triangles in the given figure?

A) 18 B) 20
C) 24 D) 27
 
Answer & Explanation Answer: C) 24

Explanation:

The simplest triangles are IJO, BCJ, CDK, KQL, MLQ, GFM, GHN and NIO i.e. 8 in number.

The triangles composed of two components each are ABO, AHO, NIJ, IGP, ICP, DEQ, FEQ, KLM, LCP and LGP i.e.10 in number.

The triangles composed of four components each are HAB, DEF, LGI, GIC, ICL and GLC i.e. 6 in number.

Total number of triangles in the figure = 8 + 10 + 6 = 24.

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37 6572
Q:

What is the minimum number of colour pencils required to fill the spaces in the below figure with no two adjacent spaces have the same colour ?

            631484547933.png image

A) 5 B) 2
C) 3 D) 6
 
Answer & Explanation Answer: C) 3

Explanation:

The given figure can be labelled as shown :

63-11484548871.png image

The spaces P, Q and R have to be shaded by three different colours definitely (since each of these three spaces lies adjacent to the other two).
Now, in order that no two adjacent spaces be shaded by the same colour, the spaces T, U and S must be shaded with the colours of the spaces P, Q and R respectively.
Also the spaces X, V and W must be shaded with the colours of the spaces S, T and U respectively i.e. with the colours of the spaces R, P and Q respectively. Thus, minimum three colour pencils are required.

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Filed Under: Analytical Reasoning - Non Verbal Reasoning
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22 5775
Q:

A line is an undefined term because it

Answer

A line is an undefined term because of it :


 


1. Contains an infinite number of points


2. can be used to create other geometric shapes


3. is a term that does not have a formal definition


 


In Geometry, unless it's stated, a line will extend in one dimension and goes on forever in both ways.

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