The document provides examples of non-verbal reasoning questions and their solutions. It includes number series, letter series, logical reasoning, and mathdoku puzzles. For the number series questions, the correct answer is choosing the option that continues the same pattern to fill in the missing term. The letter and logic series involve analyzing the relationship between letters or numbers to determine the missing element. The mathdoku puzzles require logically placing the numbers 1 to 5 in the grid so that each row and column uses each number, and the sums or products of the bold outlined groups equal the given hints.

1. NON- VERBAL REASONING
BY : --- INDU THAKUR
1.

2. 2.

3. 3.

4. 4.

5. 5.

6. 6.

7. 7.

8. 8.

9. 9.

10. 10.

11. 11.

12. 12.

13. 13

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 company's 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 and
August?
20, 30, 40, 50, 60

18. SEE GRAPH ABOVE:
(1). What was the largest number of students in any year that went on to
further study?
561, 576, 585, 592, can’t say
(2). What was the decrease in the number of graduates in employment
between 2002 and 2004?
125, 135, 140, 180, can’t say
(3). In 2004 how many social science students were in employment after
graduating?
260, 272, 284, 290, can’t say

19. SEE GRAPH ABOVE:
(1). Which month showed the largest total decrease in PC sales over the
previous month?
March, April, May, June, July
(2). What percentage of Manufacturer 2's sales were made in April (to the
nearest percent)?
16, 22, 27, 33, 38
(3). If the average profit made on each PC sold by Manufacturer 3 over all 5
months was 78 pounds what was the total profit in pounds on all sales in this
period by that manufacturer?
650,400, 820,700, 980,300, 1,095,600, 1,177,800

20. LOGIC REASONING
BY:--INDU THAKUR
This test involves letter sequences and tests your ability to think
logically 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 9
A. 11 B. 10 C. 2 D. 5 E. 3
(8). What is the missing number in this series?
1 4 10 19
A. 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 sequence
38, 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. Mathdoku
Place numbers into the puzzle cells in such a way that each row and column
contains each of the digits from 1 up to the size of the puzzle(5).Like a Sudoku
puzzle, no number is repeated in any row or column. Each bold- outlined group
of cells contains a hint consisting of a number and one of the mathematical
symbols +, x, -, /. The number is the result of applying the mathematical
operation represented by the symbol to the digits contained within the
domain. 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 3
5 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) 16
2 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 5
2 1 3 5 4 Answers of slide no. 29 & 30
4 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) 21
3 5 4 1 2 [(27+54)/9=9] (8) 49 [18+19-2=35] (9) 184 [square of
5 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. 31
2 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 [cube
4 5 1 2 3 of 1-1]
5 1 2 3 4
1 2 3 4 5

24. Mathdoku BY:--INDU THAKUR
Place numbers into the puzzle cells in such a way that each row and column contains
each of the digits from 1 up to the size of the puzzle(5).Like a Sudoku puzzle, no number
is repeated in any row or column. Each bold- outlined group of cells contains a hint
consisting of a number and one of the mathematical symbols +, x, -, /. The number is the
result of applying the mathematical operation represented by the symbol to the digits
contained within the domain. The solution to each puzzle is arrived at logically and is
unique.
6x 1- 2x
7+ 10x
9+ 1- 12+
6+ 2/ 10+

25. Mathdoku
Place numbers into the puzzle cells in such a way that each row and column contains each
of the digits from 1 up to the size of the puzzle(5).Like a Sudoku puzzle, no number is
repeated in any row or column. Each bold- outlined group of cells contains a hint
consisting of a number and one of the mathematical symbols +, x, -, /. The number is the
result of applying the mathematical operation represented by the symbol to the digits
contained within the domain. The solution to each puzzle is arrived at logically and is
unique.
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 will
continue 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 15
2.
8 12 20
[ 5, 10, 15, 21 ]
4 6 ?
6 11 25
3.
8 6 16 [ 18, 16, 12, 10 ]
12 5 ?

28. 13 54 ? ? 13 49
4.
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 61
6. 7.
84 35 12 64 30 32
45 ? 9 35 ? 43
[ 15, 18, 20, 25 ] [ 25, 27, 32, 37 ]

29. 8 7 7
1.
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 10
3. [ 25, 37, 41, 47 ]
5 19 3 7 ? 5 6 29 4
4 6 5
4.
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 32
6.
[ 10 , 15, 20, 25 ]
4 10 ?
27 54 ? 42
42 84
7.
[ 12, 21, 24, 35 ]
9 14 7
18 19 22 24 26 27
8.
[ 49, 76, 89, 94 ]
35 43 ?
12 16 7 25 21
8
9.
[ 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 +1
A E F H R T 2 0 3 1 0 0
5! X 2 + 4! X 0 + 3! X 3 + 2! X 1 + 1! X 0 + 0! X 0 = 260 +1 =261
2. 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 = 6193
6. 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, -1
are 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 , let
n=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 ¼
which 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]