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Pinnacle SSC Reasoning, 11 + √16 = 11 + 4 = 15, 17 + √36 = 17 + 6 = 23, Similarly , 8 + √4 = 8 + 2 = 10., Sol 11. (b), 92 - 62 = 81 - 36 = 45 ;, 112 - 82 = 121 - 64 = 57 ;, 82 - 32 = 64 - 9 = 55., So , the missing number is 55., Sol 12. (b), 9 - 7 = 2 , 23 = 8, 5 - 2 = 3 , 33 = 27, 7 - 3 = 4 , 43 = 64, Sol 13. (a), 20 - 12 = 8 , 82 = 64, 24 - 17 = 7 , 72 = 49, 8 - 4 = 4 , 42 = 16., Sol 14. (c), 43 + 52 = 64 + 25 = 89, 33 + 42 = 27 + 16 = 43, 13 + 22 = 1 + 4 = 5, Sol 15. (a), 35 + 32 = 35 + 16 = 51 ;, 2, 18, 2, 28 +, = 28 + 9 = 37 ;, Similarly , 40 + 14 = 40 + 7 = 47., 2, So , the missing number is 40., Sol 16. (d), + 17 = 9 + 17 = 26, 18, 2, 28, 2, + 13 = 14 + 13 = 27, 2, Similarly , 50 + 11 = 25 + 11 = 36, Sol 17. (a), 72 + 82 = 49 + 64 = 113., 142 + 92 = 196 + 81 = 277., Sol 18. (c) 36 - 8 = 28 + 4 = 32., Difference between 1st and 2nd is double the difference between 2nd and 3rd., 52 - 12 = 40 + 6 = 46., 86 - 74 = 12 + 37 = 49., Sol 19. (b), 2 + 3 = 5 , 53 = 125 ;, 3 + 4 = 7 , 73 = 343 ;, 216 = 63 , 6 = 5 + 1., MTS 2019 Tier I, Sol 20.(b) 7+6+3=16 × 3=48, 4+9+8=21 × 3=63, 2+5+7=14 × 3=42, Sol 21.(c) 4+5+9=18, 11+6+13=30, 19+3=22, 2, Sol 22.(b) 5 × 6 + 6 × 6 = 30 + 18 =, 2, 48 ; 9 × 2 + 2 × 2 = 18 + 2 = 20 ;, 7 × 8 + 8 × 2 = 56 + 32 = 88., 8, Sol 23.(d) 7 × 7 - 1 = 48 ; 9 × 5 - 0 = 45, ;, 11 × 5 - 1 = 55 - 1 = 54., Sol 24(a). 3 + 4 + 9 = 16 + 1 = 17, 7 + 2 + 5 = 14 + 1 = 15, 6 + 8 + 3 = 17 + 1 = 18., Sol 25.(c) 3 × 3+6=15,, 4 × 2+4=12,, 7 × 5+2=37, Sol 26 (c) 7 + 8 + 4 = 19 - 1 = 18, 2 + 3 + 9 = 14 - 1 = 13, 5 + 6 + 8 = 19 - 1 = 18., Sol 27.(b)6 + 3 + 3+ 8 = 20 ; 11+ 4 + 4+ 7, = 26 ;, 9 + 5 + 5 + 1 = 20., Sol 28.(b) 5 + 6 + 9 + 9 = 29, 3 + 7 + 4 + 4 = 18, 1 + 3 + 9 + 9 = 22., Sol 29.(b) 9+6+4=19 × 2=38,, 3+2+5=10 × 2=20, 7+8+3=18 × 2=36, Sol 30.(d) 7+6+3=16 × 3=48, 4+9+8=21 × 3=63, 2+5+7=14 × 3=42, Sol 31.(a) 11 × 9 - 5 = 99 - 5 = 94, 6 × 5 - 14 = 30 - 14 = 16, 9 × 7 - 13 = 63 - 13 = 50, Sol 32.(d) 11 + 9 + 7 = 27 - 3 = 24, 17 + 6 + 4 = 27 - 3 = 24, 12 + 12 + 9 = 33 - 3 = 30., Sol 33.(a), 6+9+11=26, 26 ÷ 2=13, 12+4+6=22, 22 ÷ 2=11, Sol 34.(c), 5 x 9 = 45 - 6 = 39, 3 x 1 = 33 - 7 = 26, 8 x 5 = 40 - 4 = 36., Sol 35.(d) 7+12+3 = 22, 3+15+2 = 20, 5+6+9 = 20, Sol 36.(a) 6 x 5 + 4 = 30 + 4 = 34, 3 x 5 = 15 + 8 = 23, 7x + 9 = 30 ; 7x = 21 ; x = 3., Sol 37.(c), 13 - 1 = 12 , 6 x 12 = 72, 7 - 1 = 6 , 4 x 6 = 24, 11 - 1 = 10 , 9 x 10 = 90., Sol 38.(d), 6 + 13 = 19 ; 19 x 3 - 6 = 51, 4 + 7 = 11 ; 11 x 3 - 4 = 29, 19 + 11 = 30 ; 30 x 3 - 19 = 71, Sol 39.(a)In row 1st 39 + 28 = 67 ; 3rd row; 47 + 28 = 75 ;, 2nd row 51 - 14 = 37., Sol 40.(b) Logic is : In each row (a, b, c) is a + c = b + a/2, So, 32+61 = 93 - 16 = 77., Sol 41.(d)Here, in the 1st column, 1st term- 2 × 2nd term= 3rd term, 37 - 5 × 2 = 37 - 10 = 27 ;, 142 - 27 × 2 = 142 - 54 = 88 ;, 87 - 18 × 2 = 87 - 36 = 51., Sol 42.(c)For column 1st: 4 × 4 = 16 × 4, =64-1= 63 ;, 7 × 5=35 × 5=175-1=174, 8 × 6 =48 × 6 = 288-1=287, Sol 43.(d)7 + 5 = 12 , (12)2 = 144 ;, 9 + 4 = 13 , (13)2 = 169 ;, 8 + 6 = 14 , (14)2= 196., Sol 44. (c) Here, the pattern : (25-8) × 4 + 8 = 76, (16-5) × 4 + 5 = 49, (22-7) × 4 + 7 = 67, Sol 45.(d) Here, in all rows: (sum of 1st & 2nd term)2= 3rd term., 225

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Missing Number, 6 + 7 = 13 , 13 * 13 = 169 ;, 10 + 9 = 19 , 19 * 19 = 361., 8 + 3 = 11 , 11 * 11 = 121., Sol 46.(b)In all rows: square root of (First number × Third number) = Second number, 11 × 11= square root of 121= 11 = second number, 27 × ? = (9)2, ? = 81/27= 3, Sol 47. (a) The logic followed here is: 1st row: 7 × (13-1)= 7 × 12= 84, 2nd row: 4 × (19-1)=4 × 18=72, Similarly, 3rd row: 8 × (14-1)= 8 ×, 13=104, Sol 48. (c), 1st Column: 3 + 14 = 17 × 2 = 34, 2nd Column:18 + 13 = 31 × 2 = 62, 3rd Column: 27 + 22 = 49 × 2 = 98, Sol 49.(d) In the first column , 48-28=20, × 3=60, Similarly. 71-65= 6 × 18=108, 98/7=14 (35-21), 35-21=14 × 7=98, so the answer will be 21., , Sol.50.(d) Logic is : In each Row, First number = Fourth number, Second number Third number, 18 / 4 = 4.5 × 2 = 9., So, the missing number is 4., Sol 51. (b) In the first row, Square of 4 + 3 = 16 + 3 = 19 ;, In the second row , square of 18 + 6 = 324 + 6 = 330 ;, So, in the 3rd row, 232 + 1 = 529+ 1 =, 530., Sol 52.(d) Logic is : (First number × Third number ) - Third number, 255 = (18x) - x, 255 / 17 = 15., So, the missing number is 15., Sol 53. (a) Logic is : In each column (first number × third number) + fourth number = second number., Similarly, in the 3rd column, 64 - 48 = 16, 16/8 = 2., Sol 54. (d) In the first row, 32 + 22 + 52, = 9 + 4 + 25 = 38 ;, In the 3rd row, 72 + 12 + 22, = 49 + 1 + 4 = 54 ;, Similarly , in the 2nd row , 52 + 32 + 42, = 25 + 9 + 16 = 50., Sol 55. ( a) Logic is : In each row n : 3n, + 1, As, 7 × 3+1=22, 22 × 3+1=67 and so on.., So, answer is 52 × 3+1= 157, Sol:.56.(d), Here, the pattern which is being followed, column wise is:, (1st term × 3rd term) - 3rd term = 2nd term, 6 × 8 = 48, 48-8 = 40, Thus,, 14 × 7 = 98, 98-7 = 91, Sol:57.(c) Here, in the first row, Square of the 1st term + Square of the 2nd term = 3rd term., Square of 15 + Square of 6 = 225 + 36 =, 261, Sol:58.(c)Here, the row-wise required pattern is as follows:, 1st term + 3rd term = Middle term 7 + 6 = 13, 4 + 18 = 22, 15 + 7 = 22, Sol:59.(d)The required pattern is: 28 × 36= 1008/4= 252, 30 × 32= 960/4= 240, 36 × 18= 648/4= 162, Sol:60.(d)The required pattern is: In the 1st column. 72 + 4= 53,, 112 + 6= 127, Similarly, 142 + 3= 199., Sol:61.(b), NN3 are given together in the pattern. 113= 11,, 223= 28,, 333= 327, 443= 464., 553= 5125, Sol:62.(a), The required pattern is: 10= 3 + 7[14/2], 49= 15 + 34[68/2], Similarly, 33 = 19 + 14[28/2], Sol:63.(d)The pattern: +6, +10, 14,, +18…& so on starting from 4., Thus, the gap between them is 4. For eg.4=(10-6) & next (14-10)..so on, Sol:64.(b) In this question, logic has been applied row wise i.e. (1st term × 3rd term), / 2nd term = 4th term., So, as per 4th row= (18 × 8) / x = 16 x= (18 × 8 )/16= 9, Sol:65.(d)In this question, logic has been applied column wise, i.e,, (1st no. × 2nd no.)- 100= 3rd no. 21 × 19= 399-100= 299, Similarly, 32 × 14=448-100= 348, Sol:66.(d)The logic: 42 × 6(18/3)= 252,, 37 × 8(24/3)= 296,, Similarly,, 45 × 12(36/3)= 540., Sol:.67.(b), (23 , 5 , 110) ⇒ 2 + 5 + 5 = 10 x 11 =, 110, ( 56 , 9 , 121 ) ⇒ 5 + 6 = 11 ⇒ 1 + 1 + 9, = 11 x 11 = 121, (49 , 3 , 77 ) ⇒ 4 + 9 = 13 ⇒ 1 + 3 + 4 =, 7 x 11 = 77, Sol:.68.(c), Logic is : In each row a, b, 2(a-b) So, (49-5)*2 = 44*2 = 88, Sol:.69.(b), In column i - 10 x(15-14) = 10 In column ii - 4 x (7-3) = 16, In column iii - 7 x (8-6) = 14, In column iv - 5 x (25-12)=65, Sol:.70.(a), 8, 50 × 56 = 350, 8, 48 × 32 = 192, 226

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Pinnacle SSC Reasoning, Similarly,, 8, 30 × 40 = 150., Sol:.71.(c), Here, the required, followed column-wise. In 1st column, pattern is being, 8 × 4 = 32 , 32 - 3 = 29, In second column, 11 × 7 = 77 , 77 - 6 = 71, Similarly,, In third column, 14 × 5 = 70 , 70 - 3 = 67, Sol:.72.(d) The pattern followed is:, 1st column (14 × 4)-7= 49 , (49 ×, 4)-7=189, For 2nd column (17 × 4)-7= 61, (61 ×, 4)-7= 237, For 3rd column (22 × 4)-7= 81, (81 ×, 4)-7= 317, Sol:.73.(a) Here, 3 × 6 =18, 3 × 9 = 27, 6 × 9 = 54, Sol:.74.(a) 7 x 3= 21 -(7+3)= 21-10= 11, 9 x 4= 36- (9+4)= 36-13=23, Similarly : 11 x 7= 77-(18)= 59, Sol:75.(c)112 - 43 =57, Similarly , 122 -53= 19, 182- 63 =108, Sol:.76.(c)Here the pattern is:, 1st Column (1st Number )2 – (2nd Number )2 =3rd Number, For Column 1:, 152 – 82, 225 – 64 = 161, For Column 2:, 182 – 92, 324 – 81 = 243, For Column 3:, 242 – 122, 576 – 144 = 432, Hence, “24” is the correct answer., , Sol:.77.(d) The logic: Row 1 ⇒, 11+2=13, 13+4= 17, Row 2 ⇒ 33+2=35, 35+4= 39, Similarly , Row 3 ⇒ 189+2= 191,, 191+4= 195, Sol 78. (a), In first figure:- (25)2 - (5)2 = 625 - 25 =, 600, In second figure:- (27)2 - (3)2 = 729 - 9 =, 720, Similarly,, In the third figure:- (?)2 - (9)2 = 880 ⇒, (?)2 = 880 + 81 = 961, ? = √961 = 31, Sol 79(b) 10+5+6=21 × 2=42, 17+3+14=34 × 2=68, 8+15+23=46 × 2=92, So , 23 will be the correct answer., Sol 80. (b), 6 × 5 = 30 × 3+1=91, 8 × 7 = 56 × 3+1=169, 10 × 7 = 70 × 3+1=211, 22 × 5 = 110 × 3+1=331, Sol 81. (d), 13 + 19 = 32 ⇒, 8, 32 = 4, 8, 71 + 9 = 80 ⇒ 80 = 10, 128 + 32 = 160 ⇒, 8, 160 = 20, Sol 82. (a), 5 6 4 26 ⇒ 5 × 6 - 4= 26, 7 6 5 37 ⇒ 7 × 6 - 5 = 37, 4 8 10 ? ⇒ 4 × 8 - 10 = 22, Sol 83. (b), 11 = √13 + 108 = √121, 9 = √26 + 55 = √81, 14 = √? + 157 ⇒ 196 = ? + 157 ⇒ ? =, 196 - 157 = 39, Sol 84 (c), 9+1=10 x 13=130, 14+1=15 x 9=135, 7+1=8 x 21=168, Sol 85. (b), The pattern followed, Even No., 2, : odd no. ×, 2, 15 = 5 × 6 = 5 × 3, 2, 18 = 9 × 4 = 9 × 2, 2, ? = 7 × 6 = 7 × 3 = 21, Sol 86. (a), (4)2 + (6)2 = 16 + 36 = 52;, (7)2 + (1)2 = 49 + 1 = 50;, = 26, = 25, 52, 2, 50, 2, Similarly,, 2, (5)2 + (3)2 = 25 + 9 = 34 ; 34 = 17, Sol 87. (a), 25 × 5-5 = 120, 23 × 7-7 = 154, 13 × 13-13 = 156, =(11+5+3)2 =(17+3+7)2, =(19)2, =361, =(27)2, =729, =(8+15+12)2, =(35)2, =1225, Sol 89. (b), In the given patterns the middle number in the sets is the product of the other two. (1,2,2):- 2 = 1 × 2, (7,35,5):- 35 = 7 × 5, Similarly, (12,96,?):- 96 = 12 × ?, Thus, ? = 8, Sol 90. (a) In column (i), 2, 16 + 4 = 20 ⇒ 20 =10, 2, In column (ii) , 30 + 34 = 64 ⇒ 64 = 32, 2, In column (ii) , 18 + 62 = 80 ⇒ 80 = 40, Sol 91. (c), The number in the third column is the square of the sum of numbers in the first two columns., 6 + 4 = 10 ⇒ (10)2 = 100, 7 + 5 = 12 ⇒ (12)2 = 144, Similarly,, 9 + 4 = 13 ⇒ (13)2 = 169, Sol 92. (d), The middle column has the (, HCF of numbers in the other two columns, 2, +)., HCF (162, 108) = 54, 2, ? = 54 = 27, Sol 93. (c), In figure (i) :- (7+6)2 = (13)2 = 169;, In figure (ii) :- (9+2)2 = (11)2 = 121;, Similarly,, In figure (i) :- (9+7)2 = (16)2 = 256;, Sol 94. (c), 5 = 2 + (8 - 5), 16 = 9 + (10 - 3), ? = 7 + (8 - 1) = 14, 227

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Missing Number, Sol 95. (a), 131 = (5)3 + 6 = 125 + 6, 348 = (7)3 + 5 = 343 + 5, ? = (9)3 + 8 = 729 + 8 = 737, Sol 96. (c), The sum of the alphabet numbers of, letters which are vertically opposite to each other is 19., A + R = 19, G + L = 19, Similarly, I + J = 19, Sol 97.(c) Here, row wise:, 10 x 2 = 20 , 20 - 2 x (2 - 1) = 18, 30 x 3 = 90 , 90 - 3 x (3 - 1) = 84, 4 x 68 = 272 , 272 - 4 x (4-1) = 260, Sol 98. (b), 9+3 = 12 = 12 × 4 = 48, 17+3 = 20 = 20 × 4 = 80, 33+3 = 36 = 36 × 4 = 144, Sol 99. (b), Logic is : a2 - b2 = c, So, 252 - 202 = 625 - 400 = 225, Sol 100. (b), 14 + 18 = 32 - 8 = 24, 8 + 2 = 10 - 2 = 18, 12 + 10 = 22 - 4 = 18, Sol 101 (d), (7+3) =10 ⇒ 102 = 100 + 16 = 116, (8+4) = 12 ⇒ 122 = 144 + 16 = 160, (13 + 2) = 15 ⇒ 152 = 225 + 16 = 241, Sol 102. (d)The logic : Row wise: (1st number × 2nd number)-[1st number × (1st number-1)], In first row:- (3 × 30)-3 × (3-1)=90-6=84, In second row:- (2 × 10)-2(2-1)=20-2=18, Similarly,, In the third row:- ? - 4 = x …. (i), ? + x × (4 - 1) = ? + x × (3) ⇒ ? + 3x =, 260 …. (ii), From 3 × (i) and (ii):-, 3 × ? - 3 × x = 12 …. (a), ? + 3x = 260 …. (b), (a) + (b) ⇒ 4 × ? = 272, 4, ? = 272 = 68, Sol 103. (c), 4 + 5 = 9 ⇒ 9 × 10 = 18 x 5, 9 + 2 = 11 ⇒ 11 x 10 = 22 x 5, 3 + 5 = 8 x 10 = 16 x 5, Sol 104. (c) Logic is : in each column (a+1)(b+1) = c, So 48=(7+1) × (5+1), 5 is the correct answer., Sol 105. (d) Logic is : (a, b, 4(a - b)) (54-40) × 4 = 56, (68-57) × 4 = 44, Similarly (47-39) × 4= 32, Sol 106. (c) Logic is : In each row *2 + 2 we give the next term., 28 × 2 +2 = 58, 58 × 2 +2 =118, similarly in second row, In 3rd row 47 × 2 + 2 = 96, 96 × 2 + 2 =, 194, Sol 107. (b) Logic is : (a, b, b2-a2), In (14, 16, 60) = 162-142 = 256 - 196 = 60, Similarly In (11, 17, 168) = 172 - 112 =, 289 - 121 = 168, Sol 108. (b) Logic is :In each row (a, b, ab/4), (14 × 28)/4=98, (7 × 48)/4=84 (x × 60)/4=60, So x=4., Sol 109. (b) Logic is : In each column (a+1)c = b, So, (19 + 1= 20) × 14 = 280, Sol 110. (d), Logic is : In each row, sum of digit of first two is equal to the third (4+5+0+7)+(7+0+7+7)= 37, (2+5+0+3)+(3+0+6+7)= 26, (3+3+0+7)+(4+0+6+1)= 24, Sol 111. (c) Logic is : In each column a, b, a2-b2, So, 82 - 32 = 64 -9 = 55, Sol 112. (c) Logic is : In each row (a, b, ab/2), (14 × 26) ÷ 2=182, Similarly (x × 22) ÷ 2=187 So, x = 17, Sol 113. (d) Logic is : In each column a, b, 2a+b, 17 × 2+15=49, 41 × 2+24=106, x × 2+29=85, Hence x is equal to 28., Sol 114. (d) Logic is : In each column a3, b, ab., √3 125 × 27 = 135, √3 8 × 55 = 110, √3 64 × 72 = 288, Sol 115. (b) Logic is : In each column a, b, (a+1)(b+1), (17+1) × (21+1)=396, (18+1) × (22+1)=437, (19+1) × (x+1)=520, So, x is 25, Sol 116. (d) Logic is : In each row a, b, ab/2, 14×4 = 28,, 2, 21×6, 2, = 63, Similarly,, 2, 45×8 = 180, Sol 117. (c)here logic follows as: (19+9)= 28, 28 × 5= 140, (17+9)=26, 26 × 5=130, Similarly,(x+5) × 5=120 x+5=120/5, x=24-5=19, Sol 118. (c) Logic is : In each row a2, a+b, b, So, in the third row 49, x, 61 7 + 61 = x, x = 68., Sol 119. (c) Logic is : In each column a, b, average of a and b, So, 504+612=1116/2=558., Sol 120. (d) Logic is : Row I and III are related in the same way as the row II and IV, As 12 × 1.5=18 in the same way 16 × 1.5=24, In column II,, 22 × 0.5=11 In the same way 42 × 0.5=21, Sol 121. (b), The difference between the first row and second row is a multiple of 3 and the difference between the second row and the third row is the multiple of 4, For ex 33-12=21(a multiple of 3, As 3 ×, 7=21), 40-12=28(a multiple of 4, As 4 × 7=28), 228

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Pinnacle SSC Reasoning, , similarly 61-28=33(a multiple of 3, As 11, × 3=33), 61-17=44 (a multiple of 4, As 11 × 4=44) So, 61 is the correct answer, , Sol 122. (d), Logic is : In each column, first number ✕, third number = (second number)2 8✕18=(12)2, 32✕ ? = 162, ? = 8, , Sol 123. (b) Logic is : In each row, the sum of first and second is equal to the third and fourth number., So, 32+16=? + 30, ? = 18, , Sol 124. (c), Logic is : in each row square of first, number is equal to the product of the other, So, 14 × 14 = 28 × ?, So ? = 7, , Sol 125.(d) Logic is : In each column product of first and third is equal to second fourth., 9 × 10= 90, 5 × 18=90, , Sol 126. (c) In each column : a, b, c, ab-c 8 × 7 - 5 = 51, , Sol 127 (c), Logic is : first number ±, √second number = third number 42 ± √64 = 50, 34, 50 is not an option so 34 is the correct answer., 229