Tips on Visual Spatial Problem Solving

1. 9 TIPS on cracking Aptitude Questions on Visual-Spatial Problem Solving

2. 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).

3. Tip #2: Sometimes, it is quicker to just eliminate the invalid options Question: Find out how will the key figure (X) look 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.

4. 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).

5. 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.

6. 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, (X) (1) (2) (3) (4) 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 (X) (1) (2) (3) (4) (D).

7. Tip #6: Mirror Image of a figure has all parts of the figure laterally inverted but not vertically. • Some points to note are: • 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. • The mirror image of a sequence of words and/or numbers is the mirror image of each, written in the reverse order. • 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. (X) (1) (2) (3) (4) • So the answer is (3).

8. Tip #7: Water Image of a figure has all parts of the figure vertically inverted • Thus, here: • 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. • The water image of a sequence of words and/or numbers is the water image of each, written in the same order. • 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).

9. 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).

10. Tip #9: For problems on Paper Folding, imagine the process taking place 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: (X) (A) (B) (C) (D) 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: (X) (A) (B) (C) (D) 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).

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