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TYPE-I Alpha-Numeric lest A sequence made up of three different systems namely Alphabet or Letters (A, B, C, D,….Z,) Numeric or Digits (0, 1, 2, 3,..,9) and symbols is called Alpha-Numeric Sequence   TYPE-II Number Test In this type of problems generally a number sequence is given. A candidate is required to apply some rule(s) on the sequence.   TYPE-III Ranking Test In this type of problems, usually a rank puzzle is given. It may be in the form of comparison or sizes/ heights, weights,, strengths/ ages etc. among the objects/persons.   TYPE-IV Time Sequence Test In this type of problems, a time puzzle is given. One is required to decipher it. 1 ordinary year = 365 days 1 leap year = 366 days 1 century = 100 years Number of days in February in a non-leap year = 28. Number of days in February in a leap year = 29.     EXAMPLE   1.  Direction (I-II): Study the following arrangement of letters, digits and symbols to answer the questions given below:             A B 7 C D 9 Z Y * P 2 M © K S 3 T 5 N T @   (I)   Which of the following letters is exactly in the middle of the alphabets falling between C and 5? (a) K                             (b) M              (c) Y                             (d) P   (I)  It How many such digits are there in the sequence each of which is immediately preceded as well as followed by a letter? (a) Nil                            (b) Two            (c) Three                        (d) Four   Explanation: (I).      (d) The letters lying between C and 5 are: D, Z, Y, P, M, K, S. Clearly, the letter in the middle is P. (II).    (c) Let us mark the desired digits.                2.         How many 2's are there in the following number series which are preceded by 5 but not followed by an odd number?                           1 3 5 2 3 5 4 5 2 4 5 2 2 6 2 4 5 2 6 7 8 2 3 5 2 7 5 2 4              (a) One                          (b) Two            (c) Three                        (d)  None of these   Explanation (d): Let us mark the desired 2's in the given number series. Thus, there are four 2's.   3.        In a row of girls, Dia is 15th from the left end and Madhu is 23rd from the right end.             If they interchange their positions then Dia becomes 18th from the left end. Then at what position will Madhu be from the right end?             (a) 25th                          (b) 24th              (c) 26th                           (d) 20th   Explanation (c):         more...

  This chapter contains only mathematical operations but in different manner. The main key of solving problem in this chapter is BODMAS rule to which you are already familiar This chapter consists of the following two types of problems.   1.            Direct Substitution To solve such type of problems, substitute the symbols \[+,-,\text{ }\times ,\div \] etc., for the given letters or symbol as per the question and simplify the statement using BODMAS rule,   2.            Interchange of Numbers and Signs To solve such type of problems, interchange the numbers with signs as per the given questions and then apply the BODMAS rule.     EXAMPLE     1.         If '+' stands for \['\times ','{{\times }^{,}}\]stands for \['\div '\]stands for- 'and \['\div '\]stands for ?+? then what is the value of \[8+2\times 4-2\div 6?\]               (a) 20                                        (b) 12                            (c) 14                                        (d) 18   Explanation (a): Given: \[8+2\times 4-2\div 6\] After replacements above given expression becomes \[8\times 2-4\div 2+6=8\times 2-2+6=16-2+6=20,\]     2.         Select the correct set of interchanges which would make the given equation true.  \[\mathbf{8\times 9-3\div 7=13}\] (a) \[\times \text{ }and\text{ }\div \], 3 and 7                    (b) \[\times \text{ }and\text{ }\div \], 3 and 8 (c) \[\div and-\], 7 and 8                                                 (d) \[\div and-\]. 3 and 8   Explanation (c): The given equation is \[8\times 9-3\div 7=13\] Using interchanges as given in option (c), we get \[7\times 9\div 3-8=13\] \[\Rightarrow 7\times 3-8=13\Rightarrow 21-8=13\Rightarrow 13=13,\]which is true.  

  INSERTING THE MISSING CHARACTER In such type of problems, a figure/design/table or a group of figures is given. This figure consists of some numbers or letters or both following a certain pattern. In fact, one space for a number letter is left blank which is to be filled up. In order to fill in the blank space a student is required to decipher the pattern.   Trick: To decipher a pattern, use various mathematical operations viz, addition, subtraction, multiplication, division and their combinations.     EXAMPLE     1.         Select the number which will replace the mark'?' in pattern given below.   (a) 64                            (b) 100              (c) 81                            (d) 144   Explanation: (d) Figure 1 : \[{{\left[ \left( 8\text{ }+\text{ }4 \right)\text{ }-\text{ }\left( 6\text{ }+\text{ }3 \right) \right]}^{2}}=9\] Figure 2 : \[{{\left[ \left( 7\text{ }+\text{ }9 \right)\text{ }-\text{ }\left( 5\text{ }+\text{ }4 \right) \right]}^{2}}=49\] Figure 3 : \[{{\left[ \left( 8\text{ }+\text{ }9 \right)\text{ }-\text{ }\left( 2\text{ }+\text{ }3 \right) \right]}^{2}}=\text{ }144\] Thus, the required number is 144.     2.         Select a letter from the options which will replace the'?'.   (a) I                                (b) J (c) K                              (d) L   Explanation: (b) Let us consider row-wise, Row 1: \[A+2=C;\text{ }C+2=E;\] Row 3: \[K+2=M\text{ };\text{ }M+2=0\] Row 2: \[F+2=H\] So, \[H+2=\{\,J\,\}\] Thus, the required letter is ?J?.     3.         Find the missing number in the given figure.   (a) 5                              (b) 9               (c) 11                            (d) 13   Explanation: (b) Observing the given design, we see that Place value of W=23 and place value of T=20 Here, 23 - 20 = 3 The same rule is followed by the other two sets. Thus, place value of P = 16 Place value of G = 7 So, required number =16-7=9.  

  The chapter Series deals us with the group of figures which forms a series by using a certain rule. Obeying this rule, the figures depicts a change step by step. This chapter consists of the following types of problems and to solve each type, a student first needs to identify the rule or pattern. A student may come across two types of series: 1. To choose a figure which would continue the given series of figures. 2. To choose a missing figure that is capable to establish a series.     EXAMPLE     1.         Find the figure from the options which will continue the series established by the Problem figures.                      (a)                   (b)           (c)                   (d)   Explanation (a): Area enclosed by black shaded region in top left circle, increases by \[45{}^\circ \] and rotates anticlockwise by \[45{}^\circ \] in each stage. The same procedure happens for other circles. So the correct option is (a).     2.         Choose the missing figure from the four options to substitute the question mark(?), so that a series is formed.              (a)                  (b) (c)                   (d)   Explanation (c): We observe that the black shade in a circle moves 2 steps anticlockwise in each step. So, the correct option is (c).  

ANALOGY In such type of problems, generally we are given two pairs of figures, out of them one figure is missing. This missing figure has to be identified from amongst the four options. The figures in the complete pairs have a relationship between themselves. The same relationship has to be established by choosing an appropriate figure to complete the incomplete pair.             The complete pair may have any of the following relationships:                           1.     One is the mirror/water image of the other one. 2.     One is the reduced/enlarged size of the other one. 3.     One is rotated through an angle to form the other one. 4.     Elements of one figure can be changed to form the elements of the other figure.   CLASSIFICATION In this type of problems, generally we are given a set of four figures out of which three are alike in some manner. We have to select the one that is different, which is called an odd figure. This odd figure has to be chosen out from amongst the four option figures. To choose the odd figure, a student needs to detect a rule/manner obeying that the figures in the set have been arranged.     EXAMPLE     1.         Pair of figures on left side of : : have a relationship-between them.              Establish the same relationship in the pair of figures on right side of::.              Choose an appropriate figure to replace the mark"?".                                (a)                  (b)               (c)                  (d)     Explanation (a): First figure of the pair converted into three similar figures but reduced in size. These three figures from left to right are shaded, contains slanting lines and unshaded respectively. All these features are followed by figure in option (a).     2.         Choose odd one out.            (a)                  (b) more...

This chapter is based upon the counting of various geometrical figures in a given complex figure.     EXAMPLE     1.         Count the number of triangles in the given figure.   (a) 14                            (b) 15              (c) 16                            (d) 17   Explanation (c): Let us label the given figure as shown in the adjoining figure.   Triangles made up of one segment: ANH, AOH, LBN, MCO, BDI, CEI, IDJ, IEJ. These are 8 triangles. Triangles made up of two segments: ABI, ACI, IFK, IGK, ANO, IDE. These are 6 triangles. No triangles made up of 3 segments. Triangles made up of 4 segments: ABC, IFG. These are 2 triangles. Total number of triangles Thus. the given figure consists of 16 trianales in all.  

  Every human being often comes across mirror or water image of himself/herself or other objects. So, mirror and water images are common incidents in human life and so everybody is familiar with them. This chapter leads us mirror and water images of letters, words, numerals, figures, designs etc. Note: (i)     In the problems on mirror images, if not mentioned the mirror is assumed to be placed at vertical right of the object. (ii)    In the problems on water images, if not mentioned the water level is assumed to be the situated horizontally just below the object. (iii)   If the mirror is placed horizontally just below the object, then its mirror image and water image becomes identical.     EXAMPLE   1.         Select the correct mirror image of the Fig. (X). (a)                  (b) (c)                   (d)        Explanation (a):                           2.         Choose the correct mirror image of the following combination.  T 3 S 4 P 5 H 6 (a) 6 H S 4 P 4 S 3 T      (b) H 6 P 5 S 4 T 3   (c)           (d)   Explanation (d): The mirror image is shown below.     3.         Select the correct mirror image of the Fig. (X). (a)                  (b) (c)                   (d)   Explanation (c):       4.         Choose the correct water image of the given combination.  V A Y U 8 4 3 6 (a)            (b)     (c) more...

SPOTTING OUT EMBEDDED FIGURE In such type of problems, a figure (X) is followed by four option figures. A student is required to observe that the given figure (X) is exactly embedded in which of the option figures. Remember that the given figure (X), may be embedded after rotating it.   COMPLETSON OF INCOMPLETE PATTERN In such type of problems, a regular design is provided of which usually a quarter is missing and so it is left blank or a question mark is placed in it. A student is required to study the pattern and then select an appropriate segment from the given options which completes the pattern.   EXAMPLE   1.         Choose one figure from among the four option figures in which the given Fig. (X), is exactly embedded.                           (a)                  (b)             (c)                  (d)   Explanation (d):   2.         Select a figure from the options which will complete the pattern in Fig. (X)?                           (a)                  (b)              (c)                  (d)   Explanation (d):

 In such type of problems, a or  matrix is given. All the cells except one of the matrix contain a figure each. Thus a figure is missing. Figures in each row or column follow a common rule. In order to fill in the blank cell by taking a figure amongst the given alternatives, a candidate is required to identify the rule.     EXAMPLE    Select a figure from the options to complete the given matrix. (a)                  (b) (c)                   (d)   Explanation (c): The rule is followed row-wise in each figure. The alphabets are rotated  C W and ACW respectively. So, correct option is (c).  

This chapter carries two types of problems one of folding a transparent sheet carrying a design and other one of folding a paper, then cutting it and then unfolding it.   PAPER FOLDING In such type of problems, there is a design drawn on any one side of a transparent sheet. This sheet is to be folded along a dotted line marked on it. A candidate is required to identify which pattern would be visualized after folding the sheet along the dotted line.   PAPER CUTTING In such type of problems, a sheet of paper is folded twice or thrice or more as per the shown directions. Then some cuts/punches are made on it. Then the sheet is unfolded. Now the sheet shows a pattern. A candidate is required to identify this pattern from amongst the given options. Let us illustrate you with the help of a solved example of each type.     EXAMPLE       1.         You are given a transparent sheet with a pattern on it.              If this sheet is folded along the dotted line, then which type of pattern would appear?             (a)                (b)             (c)                 (d)     Explanation (c): It is clear from the four options the left half of the transparent sheet has been placed over the right half. The left arrow is smaller than the right one, so it lies in the interior of the right arrow. For other two shapes, the right shape is smaller than the left one. So it lies in the interior of the left shape. Thus, option (c) is correct.     2.         The three figures (i), (ii) and (iii) show a sequence of folding a sheet of paper.                          Figure (iii) shows the manner in which the folded sheet has been cut out.                          If then the sheet is unfolded which of the option figures (a), (b), (c), (d) would show the unfolded form? (a)                  (b) more...