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    • By Learning Pundits
      9 TIPS on cracking Aptitude Questions on Visual-Spatial Problem Solving
      Tip 1: For pattern construction questions, remember that the resultant pattern must be formed using only the given figures
      Question: Find out which of the figures (1), (2), (3), (4) can be formed from the pieces given in figure (X).

      Solution:
      The figure must consist of a right triangle, a trapezium and an irregular pentagon, as shown above. Looking at the options one by one, we see that option (1) consists of the given figures rotated by 90⁰, the triangle and trapezium, clockwise, and the pentagon, anti-clockwise. (2) is not made of any of (X) except the trapezium. Similarly, (3) does not contain the pentagon and (4) consists of all shapes other than those in (X). Thus, the correct option is (1).
      Question: Find out which of the figures (1), (2), (3), (4) can be formed from the pieces given in figure (X).

      Solution:

      (X) Consists of 2 isosceles triangles and 2 right angled triangles. Now, (1), (2) and (4) cannot be formed using only these figures. Only (3) can be made using them, as follows:
      Thus, the answer is (3).
      Tip 2: Sometimes, it is quicker to just eliminate the invalid options
      Question: Find out how the key figure (X) look will like after rotation.

      Solution:
      We analyze the options one by one. (1) Can be eliminated since it contains more sections than the given figure. Similarly, (2) and (3) are also different from (X). Hence the answer is (4).
      Question: Select the alternative in which the specified components of the key figure (X) are found.

      Solution:
      Analyzing the options one by one, we see that (1) and (2) do not consist of ( ̶ ), while (3) consists of (ᴓ), which is not present in (X) at all. Thus, all these options are eliminated, and the correct answer is (4), which, we may cross-check as containing all components of (X) only.
      Tip 3: For problems on Paper Cutting, imagine the process of folding, cutting and opening, and draw indicative diagrams if required
      Question: Choose a figure which would most closely resemble the unfolded form of Figure (Z).
      A. (1)     B. (2)     C. (3)        D. (4)

      Solution:
      The paper has been folded at 2 corners and 1 hole has been made on each fold. Since the paper was folded from either corner, when they are unfolded, there will be 4 holes, all on the diagonal joining them. Thus, figure (3) is the correct figure, and the answer is (C).
      Question: Choose a figure which would most closely resemble the unfolded form of Figure (Z).
      A. (1)     B. (2)      C. (3)        D. (4)

      Solution:
      The paper has been folded equally thrice. Now, when it is unfolded, it will consist of 4 symmetrical parts, that look exactly like the cutout in form (Z). Thus, one of (2) and (3) is correct. Now, figure (3) is incorrect since there is a cut along the base of the (Z) which will result in a joint shape. So the answer is (B).
      Tip 4: In Dot Situation problems, simply find the figure that contains all the sections as the dots in the original figure
      Question: Select the figure which satisfies the same conditions of placement of the dots as in Figure-X.

      Solution:
      In (X), one of the dots lies in the region common to circle and square only, another dot lies in the region common to square, triangle and rectangle only and the 3rd dot lies in the region common to triangle and rectangle only. In each of the figures (1), (2) and (3) there is no region common to square, triangle and rectangle only. Only fig. (4) Consists of all the 3 types of regions.
      Tip 5: For problems on Embedded Images, find the figure from the given options in which the original figure can be completely traced
      Question: Find out the alternative figure which contains figure (X) as its part.
      (A) 1         (B) 2           (C) 3            (D) 4

      Solution:
      Looking at the answer figures one by one: (X) Cannot be traced anywhere in (1). Again, in (2), the figure is the lateral inversion of (X). Similarly, in (4), the figure is broken. Thus, all of these can be eliminated. Only in fig. (3) can fig. (X) be traced. Therefore, the answer is (C).
      Question: Find out the alternative figure which contains figure (X) as its part.
      (A) 1         (B) 2           (C) 3            (D) 4

      Solution:
      From the figures, it is clear that fig. (X) cannot be traced in fig. (1), (2) and (3), but can be traced only in fig. (4). Thus, the answer is (D).
      Tip 6: Mirror Image of a figure has all parts of the figure laterally inverted but not vertically
      Some points to note are:
      1.    Mirror images of alphabets A, H, I, M, O, T, U, V, W, X, Y, and digits 0, 8, are the same as the original ones.
      2.    The mirror image of a sequence of words and/or numbers is the mirror image of each, written in the reverse order.
      3.    The figure should remain the same vertically.
      Question: Choose the alternative which is closely resembles the mirror image of the given combination.

      Solution:
      Only the 2nd option can be correct since in all the other options the 1st and last characters are incorrect, i.e. not beginning with the mirror image of 2 and ending with A. Thus, the answer is (2).

      Question: Choose the correct mirror image of the figure (X) from amongst the alternatives

      Solution:
      Options (1) and (2) may be eliminated since they are vertically inverted as well. Now, since the small square appears on the left side of the line in (X), it should appear on the right side of the line in the mirror image. So the answer is (3). 
      Tip 7: Water Image of a figure has all parts of the figure vertically inverted
      Thus, here:
      1.    The water images of alphabets B, C, D, E, H, I, K, O, X, and of digits 0, 8, remain the same as the original.
      2.    The water image of a sequence of words and/or numbers is the water image of each, written in the same order.
      3.    The figure should remain the same vertically.
      Question: Choose the alternative which closely resembles the water-image of the given combination.

      Solution:
      Option (1) can be eliminated since it is laterally inverted as well. Again, in (2), L and in (3), E is laterally inverted as well. Only (4) is the correct water image of (X).
      Tip 8: While counting the number of figures, count smaller ones first followed by larger ones etc.
      Note: Remember to count all the figures. For example, if you are asked to count the no. of triangles in a figure, count the simplest triangles, triangles made by 2 simpler components, those made by 3 simpler components, etc. until no triangle can be formed any longer. 
      Question: Count the number of triangles and squares in the given figure.
      (A) 36 triangles, 7 squares    (B) 38 triangles, 9 squares
      (C) 40 triangles, 7 squares     (D) 42 triangles, 9 squares


      Solution:
      The figure may be labeled as follows:
      Triangles:
      Simplest triangles: BGM, GHM, HAM,
      ABM, GIN, UN, JHN, HGN, IKO, KLO,
      LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e. 18 in number.
      Triangles composed of 2 components each: ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ, LJI, LKD, KDE, DEL and ELK i.e. 16 in number.
      Triangles composed of 4 components each: BHI, GJK, ILD, AGJ, HIL and JKE i.e. 6 in number.
      Total number of triangles in the figure = 18 +16 + 6 = 40.
      Squares:
      Squares composed of 2 components each: MGNH, NIOJ and OKPL i.e. 3 in number.
      Squares composed of 4 components each: BGHA, GIJH, IKLJ and KDEL i.e. 4 in number.
      Total number of squares in the figure = 3 + 4 = 7.
      Therefore, the answer is (A).
      Tip 9: For problems on Paper Folding, draw mirror/water images as required for the folded section and merge with the other section
      Question: Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line.
      Solution:  

      The mirror image of the right side of the image is given by (C). Hence, it is the correct answer.
      Question: Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line.
      Solution:     

      Option (A) is clearly not the correct answer. Again, options (2) and (3) may be eliminated since in fig. (X), the two straight lines on the left side are vertical, and those on the right are horizontal. Thus, the answer is (D).

      (contd..) Tips on Non-Verbal Reasoning Test on Visual Spatial Problems - https://learningpundits.com/module-view/84-visual-spatial-problems/1-tips-on-visual-spatial-problems/

      LEARNING PUNDITS (https://learningpundits.com/) 
      Learning Pundits help Job Seekers make great CVs, master English Grammar & Vocabulary, ace Aptitude Tests, speak fluently in a Group Discussion, apply for jobs, participate in online contests.
    • By Learning Pundits
      5 TIPS on Cracking Aptitude Questions on Pattern Matching
      Tip #1: Find the sequence of transformations applied on the figures
      Some common transformations that are followed in this type of questions are:
      Rotation: A part or whole of the figure may be rotated by a certain angle.
      Illustration 1: Select a suitable figure from the answer figures to replace (?)


      In the figures, the shaded leaf rotates by 225⁰ in the clockwise direction while the un-shaded leaf rotates by 225⁰ in the anti-clockwise direction. Scanning through the options, we see that the 3rd figure satisfies these conditions. Thus, the answer is 3.
      Enclosure: A specific part or whole of the figure may be enclosed in some shape.
      Sides/ Lines: The number of sides/ lines in the figure may follow a certain progression.
      Illustration 2: Select a suitable figure from the answer figures to replace (?)


      In these figures, the polygon rotates 90⁰ Clock-Wise, gets smaller in size and gets enclosed by a figure with one less side than itself. So the last figure will have a rhombus enclosed in a triangle. Thus, the correct answer is 1.
      Vertical/ Lateral Inversion: The figure may be inverted vertically, laterally, or both during successive transformations.
      Illustration 3: Select a suitable figure from the answer figures to replace (?)


      Figure B is the result of vertical inversion of A. We may, thus, conclude that a figure is vertically inverted in the subsequent figure. Thus, the missing figure will be an inverted form of C. Looking at the answer figures, we see that figure 1 follows this transformation. Thus, the answer is 1.
      Shifting: A specific or whole of the figure may be shifted in any direction.
      Combination: A figure may follow more than one of the above mentioned transformations.
      Illustration 4: Select a suitable figure from the answer figures to replace (?)


      Except for the dots, the remaining part of the figure gets inverted and shifts to the opposite side of the square boundary. Thus, in the final figure, the sign ‘<‘will be inverted and will shift to the left side of the square boundary. This will be figure 3 from the answer figures. Thus, the answer will be 3.
      Tip #2: Break the figure into smaller parts to identify the pattern for figure completion
      Following are some of the ways of splitting a figure into smaller parts:
      Geometry: The figure may be broken into circles, triangles, quadrilaterals, polygons, etc. that overlap, touch each other, enclose some shape(s), or are just parts of the figure.
      Illustration 5: Identify the figure that completes the pattern.

      Each quarter of the triangle consists of 2 right angled triangles. Thus, option D is correct.
      Illustration 6: Identify the figure that completes the pattern.

      The missing section should have 4 lines. One of these lines should touch the bottom left of the square and another should touch the top right. Only (D) matches these requirements.
      Tip #3: Classify the figures on the basis of sides, geometry or dimensions
      Some of the common classification bases are as follows:
      No. of Sides: Figures can be classified depending on the no. of sides they have.
      Type of geometry: The figures may be classified as triangles, quadrilaterals, circles, etc.
      Dimension: You may classify the figures as 2-D or 3-D figures.
      Conjoined, enclosed, or overlapping: Some figures may be complex, consisting of conjoined shapes, smaller shapes enclosed within larger ones and/or partially or completely overlapping shapes, while others might be simple.

      Illustration 7: Group the given figures into 3 classes using each figure only once.

      The given figures can be classified on the basis of number of sides. Figures 1, 6 and 9 have 3 sides each; 3, 4 and 7 have 4 sides each; 2, 5 and 8 have 5 sides each.
      Answer: 1, 6, 9| 3, 4, 7| 2, 5, 8.
      Illustration 8: Group the given figures into 3 classes using each figure only once.

      1, 2 and 7 are simple figures.
      3, 5 and 9 each have one shape enclosing another smaller shape.
      4, 6 and 8 each have two shapes each that are touching each other.
      Thus, the given figures can be classified as:
      1, 2, 7| 3, 5, 9| 4, 6, 8.
      Tip #4: Analyze the options one by one and eliminate choices that do not follow the rule
      Illustration 9: Choose the set of figures which follows the given rule.
      Rule: Closed figures gradually become open and open figures gradually become closed.

      The 1st choice can be eliminated since in the 2nd figure itself, the inner circle does not open, but is replaced by a triangle. In the next set, the inner square does not open in the 2nd figure. All the figures in the 3rd option follow the rule, with the rectangle opening up and the straight line inside it closing into a rhombus. Thus, the answer is (3).
      Illustration 10: Choose the set of figures which follows the given rule.
      Rule: As the circle decreases in size, its sectors increase in number.

      In the 1st option, though the size of the circle decreases, the no. of sectors remains the same. In the 2nd option, the no. of sectors in the 4th figure is less than that in the 3rd. Again in the 3rd choice, the no. of sectors in the 2nd figure is less than that in the 3rd. Thus, none of these options follow the rule. The correct answer is (D) and we may confirm that in the 4th option, the size of the circle decreases consistently while the no. of sectors increases.
      Tip #5: Complexity of a figure is determined by the no. of sides, shapes, sections, etc.
      When a figure is said to become simpler, it means that one or more of the following happens:
      Lines: If the no. of consistent lines of the figure continuously decreases, then it may be concluded that the figure is becoming simpler. In other words, if the no. of sectors of the figure keeps decreasing, then it is said to be becoming simpler.
      Shapes: If a figure becomes simpler, the no. of shapes consisting some part or whole of the figure keeps on decreasing consistently.
      Curves: The figures may also consist of certain curves. The extent or length of the figure keeps decreasing as the figure becomes simpler.
      Opening of figure: At times, a part or whole of the figure opens up, thus making it simpler.
      Illustration 11: Choose the set of figures which follows the given rule.
      Rule: The series becomes simpler as it proceeds.

      Analyzing the sets one by one, we see:
      In the 1st set, the no. of sectors initially decreases, making the figure simpler, but then in the 5th figure, it again increases. Similarly, in the 2nd set, the complexity increases and decreases alternately. So none of them follow the rule. The figure in the 3rd choice, however, keeps becoming simpler as the no. of leaves and lines inside the circle keeps decreasing. The correct answer is (3).
      Illustration 12: Choose the set of figures which follows the given rule.
      Rule: The series becomes more complex as it proceeds.
       


      Analyzing the sets one by one, we see:
      In the 1st set, the last figure is simpler than its preceding one in that the curve forming the vein of the leaf shortens. Considering the 2nd set, the 4th figure is simpler than the 3rd one since the lower left circle opens up. So, both these options are eliminated. Now, the 3rd set keeps becoming complex as the no. of sectors, and then triangles (at the edges), keeps increasing. Answer: (3).
      Illustration 13: Choose the set of figures which follows the given rule.
      Rule: The series becomes more complex as it proceeds.
       


      Again, we analyze the options one by one.
      The 1st set can be eliminated as it alternates between becoming simpler and complex owing to the no. of lines in the figure. The 2nd option keeps becoming more complex as the no. of lines and hence, sectors, keeps increasing. Thus, the correct answer is (2).

      (contd..) Tips on Non-Verbal Reasoning Test For Pattern Matching - https://learningpundits.com/module-view/85-pattern-recognition/1-tips-on-pattern-recognition/
      LEARNING PUNDITS (https://learningpundits.com/) 
      Learning Pundits help Job Seekers make great CVs, master English Grammar & Vocabulary, ace Aptitude Tests, speak fluently in a Group Discussion, apply for jobs, participate in online contests.
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