Figure Matrix

1- Select a figure from the four alternatives that would complete the figure matrix.
 
A.1
B.2
C.3
D.4
E.None of these

Answer & Explanation

Answer  -  D (4)

Explanation  -  

The third figure comprises of the parts which are not common to the first two parts. 

2- Select a figure from the four alternatives that would complete the figure matrix.

A.1
B.2
C.3
D.4
E.None of these

Answer & Explanation

Answer  -  B (2)

Explanation  -  

Figure "2" will complete the Figure Matrix.

3- Select a figure from the four alternatives that would complete the figure matrix.

A.1
B.2
C.3
D.4
E.None of these

Answer & Explanation

Answer  -  A (1)

Explanation  -  

In each row, the third figure comprises of a black circle and only those line segments which are not common to the first and the second figures.

4- Select a figure from the four alternatives that would complete the figure matrix.

A.1
B.2
C.3
D.4
E.None of these

Answer & Explanation

Answer  -  C (3)

Explanation  -  

In each column, the second figure (middle figure) is obtained by removing the upper part of the first figure (uppermost figure) and the third figure (lowermost figure) is obtained by vertically inverting the upper part of the first figure.

5- Select a figure from the four alternatives that would complete the figure matrix.

A.1
B.2
C.3
D.4
E.None of these

Answer & Explanation

Answer  -  C (3)

Explanation  -  

The third figure in each row comprises of objects common to the first two figures.

Directions for questions

Directions for questions  1-5:In each of the following questions, group the given figures into three classes using each figure only once.1.

A. 2,4,7; 1,6,9; 3,5,8
B. 1,3,5; 2,6,7; 4,8,9
C. 1,5,7; 2,3,6; 4,8,9
D. 1,3,5; 2,4,7; 6,8,9 

1, 6, 9 are figures which are half shaded by slanting lines.
2, 4, 7 are all divided into equal parts (either three or four parts) by straight lines and also have a black circle at the centre.
3, 5, 8 have similar designs and have their four corners shaded black.

Answer: Option A.

2.

A.1,7,9; 2,3,6; 4,5,8
B. 1,2,9; 3,4,6; 5,7,8
C. 1,6,8; 2,4,7; 3,5,9
D. 1,7,8; 2,9,3; 6,4,5 

1, 7, 9 contain two similar elements one inside the other but not touching each other.
2, 3, 6 contain two similar elements one inside the other and both touching each other.
4, 5, 8 are divided into equal parts by straight lines emerging from the centre.

Answer: Option A.

3.

A. 1,4,7; 2,5,9; 3,8,6
B. 2,6,9; 1,4,7; 5,8,3
C. 1,4,7; 2,3,6; 5,8,9
D. 3,5,1; 4,7,8; 6,2,9 

5, 8, 9 are objects having both base as well as upper lid.
2, 3, 6 are objects having base but not upper lid.
1, 4, 7 are objects which have neither a base nor an upper lid attached to them.

Answer: Option C.

4.

A. 1,3,9; 2,5,8; 4,6,7
B. 1,5,8; 4,6,7; 2,3,9
C. 2,5,9; 1,3,8; 2,6,7
D. 1,8,9; 4,6,7; 2,3,5 

1, 5, 8 are all open figures bisected by a line segment.
4, 6, 7 are all closed figures touching a line segment.
2, 3, 9 are all closed figures intersected by a line.

Answer: Option B.

5.

A. 1,2,6; 3,4,7; 5
B. 1,3; 2,6; 4,5,7
C. 1,2,6,7; 3; 4,5
D. 1,3; 2,4,5; 6,7 

1, 3 contain a V-shaped element inside a geometrical figure.
2, 4, 5 contain two similar elements, one placed inside the other and touching it.
6, 7 contain geometrical figures which are divided into four equal parts by two mutually perpendicular straight lines.

Answer: Option D.

 

Analogy questions

How to solve Analogy questions quickly in Reasoning Section

Reasoning is one of the most scoring subjects of SSC and all other competitive exams and one of the easiest chapter in this section is from “Analogy”. Around 8 – 12 questions are covered from this topic and if the candidate is able to apply his thinking ability properly, he can easily score well in these questions.

An analogy literally means ‘Drawing a comparison in order to show a similarity in some respect’. An analogy basically uses a relationship between two(or more) elements to show similar relationship among another set of elements. So, these questions aim to test overall logical understanding of the candidates and how coherently they understand the different kinds of relationships among various elements.
There are various types of relationships which are used in analogy-based questions. Below is one such list which shows the various relationships with one example each:

Let’s explore the various types of questions based on Analogy that are asked in SSC-CGL exams and the right way to solve them:

Types of Analogy:

I). Completing analogous pair. Such questions give relationship between a pair; first element of second pair is given and we have to find the second element of second pair based on similar relationship given by first pair.

For example:
1) Oasis: Sand ∷ Island: ?
a) River

b) Sea

c) Water

d) Waves
Here, first pair is ⇒ “Oasis: Sand” and second pair is “Island:?”. And, “∷” sign means first pair and second pair share similar relationship.
‘Oasis’ is a mass of water amidst ‘Sand’ similarly ‘Island’ is a mass of land amidst ‘water’. Note: It’d be Island: Sea had the first pair been Oasis: Desert. We’re given the name of thing desert is made of i.e. Sand. So, we’ll use the name of thing Sea  is made of i.e. Water.
2) Annihilation: Fire ∷ Cataclysm 
a) Earthquake

b) Flood

c) Emergency

d) Steam
Here, ‘Annihilation’ i.e. total destruction is the result of ‘Fire’. So, ‘Cataclysm’ i.e. the rising of a body of water and its overflowing onto normally dry land is the result of ‘flood’.

II). Simple Analogy. In such questions a simple statement is given where a relationship is given and we’re asked the second element for the term given in question, like the example below:
1) Sweet is to Chocolate as Book is to….?
a) Dictionary

b) Library

c) Encyclopedia

d) Atlas
Here, Chocolate can be sweet or bitter but ‘Sweet’ is the enlarged form of chocolate. Similarly, ‘Encyclopedia’ is an enlarged form of a ‘book’.

III). Choosing the analogous pair: In such questions, a pair is given in the question and we’ve to find a suitable pair from the options given that resembles the similar relationship as in the question like the examples below:
1) Borrow : Steal
a) Enter: Trespass

b) Tell: Speak

c) Ask: Beg

d) Hit: Kill
Here, for both ‘borrowing’ and ‘stealing’ we take someone else’s thing. The only difference being that the first thing we take is with the permission of another while second thing is taken without the permission of another. Similarly, among all the options, we see this option is seen in ‘Enter: Trespass’ where we ‘enter’ after taking permit while ‘trespassing’ is done without any permit whatsoever.
2) Cool: Frigid
a) Livid: Lurid

b) Pool: Placid

c) Tepid: Torrid

d) Lack: Abundant
Here, ‘Frigid’ means extremely cold. So, in Cool: Frigid, second is the extreme version of another. Let’s check the meaning of all options given:
a) Livid ⇒ Discolored beneath the skin: Lurid⇒ Ghastly pale  ⇒ This doesn’t give extreme version of paleness.
b) Pool⇒ A small lake : Placid⇒ a body of water free from disturbance by heavy waves  ⇒ This doesn’t give extreme version of pool.
c) Tepid⇒ Moderately warm: Torrid⇒Extremely hot ⇒ Torrid is the extreme version of Tepid.
d) Lack: Abundant⇒ Present in great quantity ⇒ These two are opposite not extreme version.
We can see that only option c) fulfills the criteria.

IV). Multiple word analogy: These are the type of questions discussed above with the only difference being that here three elements are given in a pair instead of two and we have to select the suitable option. Like the example below:
1) Music: Guitar: Performer
a) Dance: Tune: Instrument

b) Food: Recipe: Cook

c) Patient: Medicine: Doctor

d) Trick: Rope: Acrobat.
In, Music: Guitar: Performer, ‘Performer’ plays ‘Music’ on ‘Guitar’. So, III element is playing/doing I element on II element.
From options, we can clearly see that this pattern is followed only in option d) i.e. Acrobat (An athlete who performs acts requiring skill) performs ‘Tricks’ on a ‘Rope’.

V). Number-based analogy: Till now, we saw the analogy based on words now we’ve questions based on numbers too like shown below:
1) Completing analogous pair.
25: 37 ∷ 49: ?
a) 41

b) 56

c) 60

d) 65
Here, in 25: 37 the pattern can be explained as  where  is the first element as 25 = 5^2 and  is the second element as 36 = (5+1)2 + 1.
For 49, we know that 49 = 72 so second element = = 65 which is option d).

2) Choosing the analogous pair. 
Q. 7: 24
a) 30: 100

b) 23: 72

c) 19: 58

d) 11: 43
In 7: 24, 24 = 7×3 + 3 i.e. the relationship can be shown as 
Similar relationship can only be seen in option b) 23: 72 where 23×3 + 3 = 69 + 3 = 72.
3) Multiple number analogy: It’s just like multiple-word analogy:
Q. (9, 15, 21)
a) (10, 14, 21)

b) (7, 21, 28)

c) (5,10,25)

d) (4, 8, 12)
In (9, 15, 21) the pattern given is  as 15 =  = 15 where 9 and 21 are 1^st and 3^rdnumbers respectively.
Similar relationship can only be seen in so option d) where 8 (second no.) =  = 8

VI). Alphabet based analogy. In these types of questions, two words that are group of random letters are related to each other in some way. We’re supposed to complete the analogous pair based on that relationship:
FJUL: BOQQ∷ LHRX: ?
a) BKPR

b) MNCC

c) HRYY

d) HMNC
The relationship between FJUL: BOQQ can be illustrated as:

If we do similar operation on LHRX we can see following:

Hence, option d) is the answer.

VII). Mixed analogy: These types of questions mixed alphabet and number like shown below:
Q. 
a) 2

b) 3

c)    

d) 4
Here, in , T is 20^th element in the alphabet series while J is 10^th soSimilarly, X is 24^th element in alphabetical series while H is 8^th so  So,

Dot Situation

Dot Situation  Non Verbal Reasoning Questions.

Dot situation is for the assessment and testing of students sharewd observation power. A problem figure is given in which has one or more dots are placed in the space enclosed by two or more geometrical figures such as square, rectangle, circle, triangle, pentagon, hexagon, octagon etc. One has to identify the region(s) where the dot is/are situated in the problem figure. Then search for an answer figure in which dots are placed in a similar enclosed area.

Directions for questions 1 to 5: Select the appropriate alternatives, from among the answer figures marked (1), (2), (3), (4) and (5), satisfying the similar conditions of placement of dot(s) as in the problem figure.

Question 1

Solution: In the problem figure, one dot appers in a region common to both circle and rectangle only. Such a region is present in the answer figure (5). Choice (5)

Question 2

Solution: In the problem figure, there are two dots. One dot appears in a region common to both circle and square only and another dot appears in a region common to both triangle and square only. Such a region is present only in the answer figure (1).
Choice (1)

Question 3

Solution: In the problem figure, there are 3 dots. One dot appears in a region common to all the three figures; another dot appears in a region common to both circle and square only and another dot appears in a region common to both triangle and square only. Such a region is present only in the answer figure (5).
Choice (5)

Question 4

Solution: In the problem figure, there are 3 dots. One dot appears in a region common to both pentagon and circle only, another dot appears in a region common to both pentagon and triangle only and another dot appears in a region common to pentagon, triangle and square. Such a region is present only in the answer figure (1).
Choice (1)

Question 5

Solution: There are 4 dots in the problem figure. One dot appears in a region common to all the four figures; another dot appears in a region common to hexagon, circle and rectangle only; another dot appears in a region common to hexagon and circle only; another dot appears in a region common to hexagon and rectangle only. Such regions are present only in the answer figure (4). Choice (4)

Cube and Dice Test

Cube and Dice Test  

Cube & Dice Problems, Aptitude Basics, Practice Questions, 

Answers and Explanations

Important Study Content for 11-plus or Eleven plus exam

Geometry of Cube
A cube is a three-dimensional solid object bounded by six sides, with three meeting at each vertex. It features all right angles and a height, width and depth that are all equal ( length = width = height). It has two types: 1. Standard Cube; and 2. Non-Standard Cube

Important Facts: 

1. A cube has 6 square facesor sides. (Ref. Img 1)

2. A cube has 8 points (vertices). (Ref. Img 1)

3. A cube has 12 edges. (Ref. Img 1)

4. Only 3 sides are visible at a time (called "Joint Sides") and these joint sides can never be on opposite side to each other.

 5. Things that are shaped like a cube are often referred to as ‘cubic’.

6. Most dice are cube shaped, featuring the numbers 1 to 6 on the different faces.

7. Addition of number of dots (pips) or numbers from opposite sides of a standard cube or dice is always 7.

8. Total of two adjacent faces of cube can never be a 7.

9. 11 different ‘nets’ can be made by folding out the 6 square faces of a cube. (Ref. Img 2)

(Image 1)

(Image 2)

:: Problem Solving ::

Things to remember before stepping ahead:

Image 3: Painted Sides of a Cube

* We can categorise a cube (or a colour cube) after cutting it, in these four categories: (See Image 3)

a.) Central cube (Yellow): In middle of faces & has only one coloured side.

We can find out the total number of cubes with singe colour on any side with this formula: 

6(X-2)^2

b.) Middle Cube (Green): In middle of edges and have two coloured sides.

We can find out the total number of cubes with singe colour on any side with this formula: 

12(X-2)

c.) Corner cube (Blue): Cubes on corners and have three coloured sides.

A cube can have only 8 cut-corner cubes with colours on three sides. Hence answer will be always the same - 8.

d.) Inner Cube (No Colour): Cubes inside faces & has no coloured side.

We can find out the total number of cubes without any colour on any side (inner cube) with this formula: (X-2)^3

***Note: To find out total number of cubes we use this formula- (X)^3

Types of Problems Based on Cube and Dice:

Question Type 1 : Determining the opposite sides

Question Type 2 : Cutting a Colorful Cube

Question Type 3 : Making big cube by addingsmall cubes

Question Type 4 : Determining number of cubes placed in stacks

"Elevenplus" / "Eleven Plus Practice Questions and Papers"

Examples: Question Type 1

Que. 1: This cube is a 'standard cube'. What will be the number on opposite faces of it? (नीचे दिया गया घन एक मानक घन है। बताइये कि इसकी विपरित फलकों पर क्या-क्या अंकित होगा?)

1. Opposite to 1 - ?
2. Opposite to 2 - ?
3. Opposite to 3 - ?

Solution: We know the rule of standard cube - "Addition of number of dots (pips) or numbers from opposite sides of a standard cube or dice is always 7." Hence, the rule = 7-N (N stands for number on facing side). 

1. Opposite to 1 = (7-1) = 6
2. Opposite to 2 = (7-2) = 5
3. Opposite to 3 = (7-3) = 4

Que. 2: Study these cubes and find out the numbers on opposite sides of front facing sides of these. (दी गई आकृतियों का अध्ययन कर बताइये कि कौनसी संख्या किसके पीछे अंकित होगी?)

Solution: To solve this question we'll follow this rule - "Only 3 sides are visible at a time (called "Joint Sides") and these joint sides can never be on opposite side to each other."

* From cube A) and B) - 1, 2, 3, 4 and 5 can never be on opposite side of 3 (common number in cube A & B). Hence the answer will be = 6

* From cube B) and C) - 1, 3, 4, 6, and 5 can never be on opposite side of 5 (common number in cube B & C). Hence the answer will be = 2

  
* From cube A) and C) - 1, 2, 3, 5 and 6 can never be on opposite side of 1 (common number in cube A & C). Hence the answer will be = 4

Conclusion : 

Opposite to 1 = 4

Opposite to 3 = 6

Opposite to 5 = 2

Examples: Question Type 2
 

Que : Directions: (Questions 1 to 10) A solid cube of each side 8 cm, has been painted red, blue and black on pairs of opposite faces. It is then cut into cubical blocks of each side 2 cm.

1. How many cubes have no face painted?
A) 0 
B) 4 
C) 8 
D) 1 2

Ans: Cubes have no face painted = Inner Cubes (No Colour): We can find out the total number of cubes without any colour on any side (inner cube) with this formula: (X-2)^3

Implementation of formula: X = 4

(4-2)^3 = 2^3 = 8

2. How many cubes have only one face painted?
A) 8 
B) 16 
C) 24 
D) 28

Ans: Cubes have only one face painted =Central cubes : In middle of faces & has only one coloured side.

We can find out the total number of cubes with singe colour on any side with this formula: 6(X-2)^2

Implementation of formula: X = 4

6(4-2)^2 = 6(2)^2 = 24

3. How many cubes have only two faces painted?
A) 8
B) 16 
C) 20 
D) 24

Ans: Cubes have only two faces painted =Middle Cubes: In middle of edges and have two coloured sides.

We can find out the total number of cubes with singe colour on any side with this formula:12(X-2)

Implementation of formula: X = 4

12(4-2) = 12(2) = 24
  
4. How many cubes have only three faces painted?
A) 0 
B) 4 
C) 6 
D) 8

Ans: Cubes have only three faces painted =Corner cubes : Cubes on corners and have three coloured sides.

A cube can have only 8 cut-corner cubes with colours on three sides. Hence answer will be always the same = 8.

5. How many cubes have three faces painted with different colours?
A) 0 
B) 4 
C) 8 
D) 12

Ans: Cubes have three faces painted = Corner cubes : Cubes on corners and have three coloured sides.

A cube can have only 8 cut-corner cubes with colours on three sides. Hence answer will be always the same = 8.

6. How many cubes have two faces painted red and black and all other faces unpainted?
A) 4 
B) 8 
C) 16 
D) 32

Ans: Cubes have two faces painted red and black and all other faces unpainted = 4+4 = 8

7. How many cubes have only one face painted red and all other faces unpainted?
A) 4 
B) 8 
C) 12
D) 16  

Ans: Cubes have only one face painted red and all other faces unpainted = Central Cubes of Red Face = 4+4 = 8 

8. How many cubes have two faces painted black?
A) 2 
B) 4 
C) 8 
D) None

Ans:  None

9. How many cubes have one face painted blue and one face painted red? (the other faces may be painted or unpainted?
A) 16 
B) 12 
C) 8 
D) 0

Ans: Cubes have one face painted blue and one face painted red? (the other faces may be painted or unpainted = 4+4 = 8

10. How many cubes are there in all?
A) 64 
B) 56 
C) 40 
D) 32

Ans: To find out total number of cubes we use this formula- (X)^3

Implementation of formula: X = 4

(4)^3 = 64

Mirror Image Problems

Mirror Image Problems

A mirror image is a reflected duplication of an object that appears identical but reversed (Lateral Inversion). In simple words - when we see a reversed object in mirror, right part of the object appears in the left and vice-versa, but the upper and lower part remains constant, it is called a "Mirror Image". There are few images which always have the same reflection (not reversed) as they are in mirror, i.e.

In Alphabet: A, H, I, M, O, T, U, V, W, X, Y - ( 11 )

In Numerical Digits: 0, 8 - ( 2 )

In Geometry: □, △, ○, ◇......... etc.

Lateral Inversion: 

:: Problem Solving ::

Directions to Solve: 

In each of the following questions you are given a combination of alphabets and/or numbers followed by four alternatives (A), (B), (C) and (D). Choose the alternative which is closely resembles the mirror image of the given combination.

"Elevenplus" / "Eleven Plus Practice Questions and Papers"

Example 1:  Choose the alternative which is closely resembles the mirror image of the given combination.

Explanation:
A) Non-reversed geometry having two extra dots.

B) Its up-down reflection. 

C) Non-reversed geometry with dots in wrong direction.

D) Perfect lateral inversion Hence, the right answer.

Example 2:  Choose the alternative which is closely resembles the mirror image of the given combination.

:: Practice Questions ::

Exercise:

Problem 1: Choose the alternative which is closely resembles the mirror image of the given combination.

Problem 2: Choose the alternative which is closely resembles the mirror image of the given combination.

Problem 3: Choose the alternative which is closely resembles the mirror image of the given combination.

Problem 4: Choose the alternative which is closely resembles the mirror image of the given combination.
 

Problem 5: Choose the alternative which is closely resembles the mirror image of the given combination.

Problem 6: Choose the alternative which is closely resembles the mirror image of the given combination.

Try to Solve These Problems.

:: Answers ::

Problem 1: C
Problem 2: B
Problem 3: D
Problem 4: B 
Problem 5: C 
Problem 6: D   

:::: CLOCKS AND MIRRORS ::::

Such problems are based on reflection of watch and its hands in mirror. For example - 

On seeing in the mirror the clock is showing the time as 8:35. what is the actual time?

A) 8:35
B) 3:25
C) 8:25
D) 4:25

Graphical Representation of above example:

Hence, the answer is B) 3:25