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- 1. NON- VERBAL REASONING BY : --- INDU THAKUR1.
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- 14. 14. BY:---INDU THAKUR
- 15. ANSWERS WITH HINTS OF NON-VERBAL REASONING :1. (D) , square numbers. 2. (C) , on the top. 3. ( D) , mind the gap. 4. (B) , colour cycling.5. ( B) , count everything. 6. (C) , count the lines. 7. (E) , rectangle orientation . 8. (D) , clockwise . 9. ( B) , follow the leader. 10. (C) , lines. 11. ( A) , count squares. 12. ( E) , clockwise and anti. 13. (D) , V is the card referee. 14. ( B) , direction .ANSWERS OF NUMERICAL REASONING :16. (1) 2 Km. (2) 3 Km. (3) 24 Kmph. (student gets on bus at 8.15 am at 1 Km from home & bus at 8.25 am at 5 Km from home, therefore bus travels 4 Km in 10 mints.Bus would travel six times as far in one hour=6x4 Km in one hour =24)17. (1). Frying tonight (2). July (3). June(3+6+6+7+8=30) (4). 20 ( diff. b/w Hot house sales & sales in august = 6-5=1 , therefore 1/5=0.2 x 100=20%)18. (1). 585 (in 2004 , 39% of 1500) (2). 125 ( No. of graduates in employment in 2002= 40% of 1700=680 & in 2004= 37% of 1500=555) (3). can’t say, there is insufficient data.19. (1) May ( in April total is 10100 & in May total is 8600 , so decrease is 1500) (2) 22%( total sales = 17400, sales in April = 3800 , % of sales in April = 3800/17400x100= 21.8)(3) 1177800 ( total sales =15100, profit per pc = 78, total profit 15100x78
- 16. NUMERICAL REASONING SEE GRAPH ABOVE: (1). How far does the student walk in total? 1 km, 2km, 3km, 4km, 5km (2). How far is he from the university students union at 8.20 am? 1 km, 2km, 3km, 4km, 5km (3). What is the average speed of the bus? 14 kmph , 24, 32, 40, 48 BY:--INDU THAKUR
- 17. SEE GRAPH ABOVE :(1). Which companys sales were most consistent throughout the year?Hole in Roof , Hot House, Stones Throw , Leaky Windows , Frying Tonight(2). In which month did the sales of Hole in Roof and Stones Throw differ the most?January, March, July, august, October(3). Which month gave the largest number of sales for all the companies combined?April, May, June July, August(4). What was the percentage increase in sales for Hot House between July andAugust?20, 30, 40, 50, 60
- 18. SEE GRAPH ABOVE:(1). What was the largest number of students in any year that went on tofurther study?561, 576, 585, 592, can’t say(2). What was the decrease in the number of graduates in employmentbetween 2002 and 2004?125, 135, 140, 180, can’t say(3). In 2004 how many social science students were in employment aftergraduating?260, 272, 284, 290, can’t say
- 19. SEE GRAPH ABOVE:(1). Which month showed the largest total decrease in PC sales over theprevious month?March, April, May, June, July(2). What percentage of Manufacturer 2s sales were made in April (to thenearest percent)?16, 22, 27, 33, 38(3). If the average profit made on each PC sold by Manufacturer 3 over all 5months was 78 pounds what was the total profit in pounds on all sales in thisperiod by that manufacturer?650,400, 820,700, 980,300, 1,095,600, 1,177,800
- 20. LOGIC REASONING BY:--INDU THAKURThis test involves letter sequences and tests your ability to thinklogically and analytically.(1). What is the missing letter in this series: f g e h d i c ? [a, b, j, k, l](2). What is the missing letter in this series: b e h k n ? t [o, p, q, r, s](3). What is the missing letter in this series: y e w g u i ? [s, t, r, k, l ](4). What is the missing letter in this series: g ? d i j d k l d [f, e, c, h, d ](5). What is the missing letter in this series: q r k s t i u v ? [u, y, h, x, g ](6). What is the missing letter in this series: b c e g k ? q s [l, m, n, o, p]
- 21. (7) What is the missing number in this series?6 7 5 8 4 9A. 11 B. 10 C. 2 D. 5 E. 3(8). What is the missing number in this series?1 4 10 19A. 33 B. 31 C. 30 D. 28 E. 29(9). How much in percent is 15 out of 50 ?35, 25, 45, 32, 30(10). What is the next number in the sequence38, 48, 96, 106, 212, ?236, 222, 432, 216, 426(11). 40 % out of 125 = X. What is then 10 % of 2X ?15, 10, 100, 200, 20
- 22. MathdokuPlace numbers into the puzzle cells in such a way that each row and columncontains each of the digits from 1 up to the size of the puzzle(5).Like a Sudokupuzzle, no number is repeated in any row or column. Each bold- outlined groupof cells contains a hint consisting of a number and one of the mathematicalsymbols +, x, -, /. The number is the result of applying the mathematicaloperation represented by the symbol to the digits contained within thedomain. The solution to each puzzle is arrived at logically and is unique. 3/ 32x 8+ 5/ 2x 20x 40x 4+ 6+ 1- 1-
- 23. SOLUTIONS OF MATHDOKU Answers of Number series (slide no.26) (1). 33 [+6,+9…..+ (2) 81 [+5,+10…+ (3) 88 [+8,+10,+12…+1 4 2 3 5 (4) 35 [-21,-19…+ (5) 36 [+2,+4,+8…+ (6) 96 [÷2,x4…+ (7)3 5 4 1 2 27 [x2,x3/2…+ (8) 435 [15x11,15x13…+ (9) 203 [x2+1,x2- 1…+ (10) 122 [x2+1, x2+2…+4 1 5 2 35 2 3 4 1 Answers of missing numbers (slide no. 27 & 28 ) (2) 10 [6x(3/2), 6x(5/2),8x(3/2),8x(5/2)] (3) 162 3 1 5 4 [11x2+(6÷2) =25](4) 4 [13+(7x2)=27] (5) 5 [2x9+3x17=69] (6) 25 [(84÷12)x5=35] (7) 27 [5x1=5, 6x1=6 &5+6=11]1 3 2 4 52 1 3 5 4 Answers of slide no. 29 & 304 2 5 3 1 (2) 32 [(5x6x4)/10] (3) 41 [5x3+4] (4) 35 [(3x8x4)/2] (5) 16 [(12x14)/2=84] (6) 20 [(13+19)/8=4] (7) 213 5 4 1 2 [(27+54)/9=9] (8) 49 [18+19-2=35] (9) 184 [square of5 4 1 2 3 12-square of 8=80] (10) 9 [12,18,30 are multiple of 6]3 4 5 1 2 Answers of slide no. 312 3 4 5 1 (1) 18 [5x2=10] (2) 13 [1+2=3] (3) 343 cube of 2,3…+ (4) 39 [3x2-1=5] (5) 38 [9+square of 2=13] (6) 63 [cube4 5 1 2 3 of 1-1]5 1 2 3 41 2 3 4 5
- 24. Mathdoku BY:--INDU THAKURPlace numbers into the puzzle cells in such a way that each row and column containseach of the digits from 1 up to the size of the puzzle(5).Like a Sudoku puzzle, no numberis repeated in any row or column. Each bold- outlined group of cells contains a hintconsisting of a number and one of the mathematical symbols +, x, -, /. The number is theresult of applying the mathematical operation represented by the symbol to the digitscontained within the domain. The solution to each puzzle is arrived at logically and isunique. 6x 1- 2x 7+ 10x 9+ 1- 12+ 6+ 2/ 10+
- 25. MathdokuPlace numbers into the puzzle cells in such a way that each row and column contains eachof the digits from 1 up to the size of the puzzle(5).Like a Sudoku puzzle, no number isrepeated in any row or column. Each bold- outlined group of cells contains a hintconsisting of a number and one of the mathematical symbols +, x, -, /. The number is theresult of applying the mathematical operation represented by the symbol to the digitscontained within the domain. The solution to each puzzle is arrived at logically and isunique. 2/ 3/ 6+ 100x 15x 6+ 2- 6x 8+ 9+ 8x
- 26. A number series is given with one term missing, choose the correct alternative that willcontinue the same pattern & replace question mark in the given series:Q.1 6 , 12, 21, ? , 48 [ (a) 33 (b) 38 (c) 40 (d) 45 ]Q.2 6, 11, 21, 36, 56, ? [ (a) 42 (b) 51 (c) 81 (d) 91 ]Q.3 10, 18 , 28, 40, 54, 70, ? [ (a) 85 (b) 86 (c) 87 (d) 88 ]Q.4 120, 99, 80, 63, 48 , ? [ (a) 35 (b) 38 (c) 39 (d) 40 ]Q.5 22, 24, 28, ?, 52, 84 [ (a) 36 (b) 38 (c) 42 (d) 46 ]Q.6 48, 24, 96, 48, 192, ? [ (a) 76 (b) 90 (c) 96 (d) 98 ] Q.7 1, 2, 3, 6, 9, 18, ?, 54 [ (a) 18 (b) 27 (c) 36 (d) 81 ] Q.8 165, 195, 255, 285, 345, ? [ (a) 375 (b) 390 (c) 420 (d) 435 ] Q.9 6, 13, 25, 51, 101, ? [ (a) 201 (b) 202 (c) 203 (d) 205 ] Q.10 6, 13, 28, 59, ? [ (a) 111 (b) 113 (c) 114 (d) 122 ] BY:--INDU THAKUR
- 27. INSERTING THE MISSING CHARACTER :1. 3 6 8 [ 6, 7, 8, 9 ] 5 8 4 4 7 ? { Sum is 17 in each row, so ans. Is 6 or (8+4)/2 } 6 9 152. 8 12 20 [ 5, 10, 15, 21 ] 4 6 ? 6 11 253. 8 6 16 [ 18, 16, 12, 10 ] 12 5 ?
- 28. 13 54 ? ? 13 494. 5. 7 45 32 9 17 69 27 144 68 13 11 59 [ 42, 26, 6, 4 ] [ 5, 9, 10, 21 ] 28 20 7 51 11 616. 7. 84 35 12 64 30 32 45 ? 9 35 ? 43 [ 15, 18, 20, 25 ] [ 25, 27, 32, 37 ]
- 29. 8 7 71. 2 36 6 2 46 5 4 ? 6 [ 42, 46, 48, 50 ] 6 8 10 {Hint: 8x6 – 6x2, 7x8 – 5x2 }2. 5 6 6 21 7 4 ? 8 [ 22, 30, 32, None of these ] 12 4 5 103. [ 25, 37, 41, 47 ] 5 19 3 7 ? 5 6 29 4 4 6 54. 3 8 5 7 [ 27, 35, 54, 64 ] 48 ? 4 2 88 [ 16, 21, 61, 81 ]5. 84 81 14 12 9 ? 11 18
- 30. 13 19 71 9 128 326. [ 10 , 15, 20, 25 ] 4 10 ? 27 54 ? 42 42 847. [ 12, 21, 24, 35 ] 9 14 7 18 19 22 24 26 278. [ 49, 76, 89, 94 ] 35 43 ? 12 16 7 25 21 89. [ 184, 210, 241, 425 ] 80 207 ? 16 32 40 36 18 27 12 18 30 [ 6, 9, 12, 18 ]10. 6 8 ?
- 31. 3.1. 2. ? 14 ? 1 ? 8 10 8 2 216 5 27 7 9 5 3 64 125 [ 2, 3, 4, 6, 18 ] [ 10, 12, 13, 15 ] [ 4, 305, 343, 729 ] 4 5. 6. . ? 3 0 7 ? 9 22 5 ? 26 13 22 13 8 [ 1, 26, 39, 45, 50 ] [ 38, 39, 40, 44 ] [ 45, 50, 60, 63 ]
- 32. 1. Rank of word whose all letters are distinct : 5! 4! 3! 2! 1! 0![Arrange all letters , cross each letter when it occurs ] F A T H E R +1A E F H R T 2 0 3 1 0 05! X 2 + 4! X 0 + 3! X 3 + 2! X 1 + 1! X 0 + 0! X 0 = 260 +1 =2612. How to find fourth vertex in //gm. [ If A (x1,y1) , B ( x2,y2) , C (x3,y3) are three vertices ] then D ( x1+x3 – x2, y1+y3 – y2) .3. How to multiply in easy manner/way: 107 x 106 ( just over 100) 107 + 6/106 + 7 = 113 & 7 x 6 = 42 so 107 x 106 = 11342, find 103 x 105 = ? & 108 x 107 =?Now see another multiplication : 112 x 115 = 12880 [112+15 =127 & 12 x15 = 180 ]4. When first figures are the same and last figures add up to 10 : 32 x 38 = 1216 [ 2 x8 = 16 & 3 x 4 = 12 ]98 x 92 = 9016 [ 9 x 10 = 90 & 8 x 2 = 16 ]5. Multiply a number by 11: 72 x 11 = 792 [ outer figures are 72 & add the middle figures ]98 x 11 = 1078 [ addition of middle figures is two digit number ]235 x 11 = 2585 [outer figures 25 & sum of 2,3 & 3,5 ] similarly 563 x 11 = 61936. How to find cube of a number: (23)3 = 12167 , let a = 2 & b = 3, use formula of cube(a+b)3 = a3+3a2b+3ab2 + b3 a3 a2b ab2 b3 8 12 18 27 2a2b 2ab2 24 36 12 1 6 7 Find cube of 34 = 39304 BY:--INDU THAKUR
- 33. Short-cut methods(master values for series): A.P.→ *1,2,3,4….+ , G.P.→*1,2,4,8…+,H.P.→*3,4,6,12…+Q. 1 If a, b, c, d, e, f are in A.P. then the value of (e-c) [ (i) 2(c-a) (ii) 2(f-d) (iii) 2(d-c) (iv)(d-c) ] [Hint: put a=1,b=2,c=3,d=4,e=5,f=6 on the both sides ( e-c = 2), ans. Is (iii) ]Q.2 1/(1 + √x), 1/(1 – x) , 1/(1 - √x) are in : [ A.P., G.P., H.P. , None ] { put x=4, 1/3, -1/3, -1are in A.P. }Q.3 If p, q, r are in A.P. & x, y, z are in G.P. then xp-r . yr-p . z p-q = [ 1, 2, -1, none ] { put p=1,q=2,r=3 & x=1, y=2, z=4 , ans. Is 1}Q.4 If Sn denotes the sum of n terms of an A.P. Then Sn+3 – 3Sn+2 + 3Sn+1 – Sn = [ 0, 1, ½, 2 ] , Hint: in A.P. 1,2,3,4….. let n=3 ∴ Sn = S3 =6 , Sn+3 =21, Sn+2 =15, Sn+1=10, ans. Is 0}Q.5 If a1, a2, a3,………..,an are in H.P. then a1a2 + a2a3 + a3a4 +…….+ an-1an =[ (i) na1an (ii) (n-1)a1an (iii) (n+1)a1an (iv) none ] { Hint: put a1=3, a2=4, a3=6, a4=12 , letn=4, ans. Is (ii)=108 after putting the values in options also. }Q.6 If G be the geometric mean of x & y , then 1/(G² – x²) + 1/(G² – y²) =[ (i) G² (ii) 1/G² (iii) 2/G² (iv) 3G² ] { ∵ x, G, y are in G.P. ∴ let x = 1 G=2, & y=4 , ans. Is ¼which is (ii) }Q.7 (i) Sum of 1/(1.2) + 1/(2.3) +1/(3.4) +…………. [S =1/(2-1) =1] (ii) Sum of 2/(3.4)+3/(4.5)+4/(5.6)+…………… [ S= (2/3)/(4-3)=2/3 ]Q.8 Cos2(Ѳ+ ) – 4Cos(Ѳ+ ) x SinѲ x Sin + 2Sin² = [ Cos2Ѳ, Cos3Ѳ , Sin2Ѳ , Sin3Ѳ ] { Independent of ∴ put = 0°, ans. Is Cos2Ѳ }Q.9 tanѲ.tan(Ѳ+60°)+tanѲ.tan(Ѳ - 60°)+ tan(Ѳ+60°).tan(Ѳ - 60°) = [ 0, 3, -3, none]

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