## Quanta Test

Q-1 011 =?
(a) 11 (b) 0
(c) 2 (d) None

Q-2 Ö60 ´ Ö13
(a) Ö785 (b) Ö780
(c) Ö777 (d) None
Q-3 1 is
(a) Prime number
(b) Neither prime nor composite
(c) a & b
(d) None
Q-4 If S=15, P = 21, find eq.
(a) x2 + 12x + 19 = 0
(b) x2 + 26x + 181 = 0
(c) x2 + 15x + 21 = 0
(d) None
Q-5 Find the sum of 320th term
(a) 631 (b) 630
(c) 665 (d) 6:9
Q-6 What will be sum of 4 + 6 + 8 + 10 + 12 + 14
(a) 521 (b) 54
(c) 63 (d) 31
Q-7 Find 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16
(a) 73 (b) 74
(c) 71 (d) 72
Q-8 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
(a) 106 (b) 107
(c) 108 (d) 109
Q-9 75 ´ 35
(a) 2635 (b) 2625
(c) 2665 (d) None
Q-10 Find 75 ´ 75
(a) 5663 (b) 5625
(c) 5663 (d) 1925
Q-11 Find 315.65 + 30.25 – 119.361
(a) 225 (b) 226.539
(c) 236.563 (d) None
Q-12 10% of 90 = x (15)
Find the value of x
(a) 3/91 (b) 3/5
(c) 3/11 (d) None
Q-13 x % of 120 + 315 = 300
(a) – 160/14 (b) – 150/12
(c) – 130/21 (d) None
Q-14 Find (522 – 502) / (52 – 50) (52 + 50)
(a) 2 (b) 1
(c) 3 (d) 4
Q-15 15.21 + 14.263 + x = 35.65
(a) 6.178 (b) 6.177
(c) 6.1 (d) None
Q-16 Find (153 + 123) /(15)2 – 15 ´ 12 + (12)2
(a) 26 (b) 27
(c) 28 (d) 29
Q-17 15.63 + 56 + 9.631 – x = 25.65
(a) 55.611 (b) 56.65
(c) 57.65
(d) 58.671
Q-18 (99) 11
(a) 1081
(b) 1089
(c) 1079
(d) 1069
Q-19 29/6 + 2 ⅓ + 31/6 = x
Find x
(a) 13.3
(b) 13.4
(c) 13.5
(d) None
Q-20 Ö125/5 + Ö81/3 + Ö25/5 = x
Find x
(a) 5
(b) 6
(c) 7
(d) 8
Q-21 Ö196 + Ö256 = x
(a) 30
(b) 32
(c) 31
(d) 63
Q-22 Ö169/Ö225 = Ö256/x
Find x
(a) 18.46
(b) 18.48
(c) 18.96
(d) 18.41
Q-23 (15 ´ 13) + 16 – 11 = x
Find x
(a) 200
(b) 205
(c) 209
(d) 210
Q-24 15 + 65 ¸ 13 – 11 ´ 13 = x
(a) – 122
(b) – 123
(c) – 124
(d) – 129
Q-25 105 + 65 – 56 of 2 = x
(a) 55
(b) 58
(c) 59
(d) 60

1. b 0
2. b Ö780
3. b Neither Prime nor composite
4. b x2 + 26x + 181 = 0
5. b 630
6. b 54
7. d 72
8. c 108
9. b 2625
10. b 5625
11. b 226.539
12. b 3/5
13. b –150/12
14. b 1
15. b 6.177
16. b 27
17. a 55.611
18. b 1089
19. c 13.5
20. b 6
21. a 30
22. a 18.46
23. a 200
24. b –123
25. b 58

Reasons:      5 Sum of 320th term = 3(20(20 + 1)/2 = 30(21) = 630
6 4 + 6 + 8 + 10 + 12 + 14 = 2(2 + 3 + 4 + 5 + 6 + 7 +)
= 2(1 + 2 + 3 + 4 + 5 + 6 + 7 – 1)
=2 (å7 – 1)
= 2 (7(7 +1)/2 – 1) = 2 (7 (8)/2) – 1)
= 2 (28 – 1 ) = 2 (27) =54
7 Sum will be = 8(8 + 1) =723
8 Sum will be = (15 + 1)2/2 = 256/2 =108
9 75 ´ 35 = 7 ´ 3 + 5, 5 ´ 5 = 2625
10 75 ´ 75 = 7 (7+1) (5´5) = 5625
12 (10/100) ´9 = x(15) = 15x = 9, x = 9/5 = 3/5
13 (x/100) (120) + 315 = 300
(12/10) x + 315 = 300
12x/10 = – 15
12x = –150
x = –150/12
14 (52 – 50) (52 + 50)/(52 – 50) (52 + 50) = 1
16 Here we use
x3 + y3/ x2 – xy + y2 = x + y
15 + 12 = 27
18 (100 – 1) 11 = 1100 – 11 = 1089
19 29/6 + 7/3 + 31/6 = x
(29 + 21 + 31)/6 = x
51/6 = x, x = 13.5
20 Ö16/2 + Ö81/3 + Ö25/5 = x
4/2 + 9/3 + 5/5 = x
2 + 3 + 1 = x, x= 6
21 Ö196 + Ö256 = 14 + 16 = 30
22 13/15 = 16/x = x = (16 ´ 15)/13 = 18.46
23 (15´ 13) + 16 – 11 = x
195 + 16 – 11 = x
211 – 11 = x, x =200
24 15 + 5 – 11 ´ 13 = x
15 ´ 5 – 143 = x
20 – 143 = x, x = – 123
25 105 + 65 – 112 = 58

## Quantitative Aptitude

Q-1 In 5/6: : 9/8, 5/6 is
(a) IInd ratio (b) Ist ratio (c) Third ratio (d) None

Q-2 In 5/6 : : 9/5, 9/5 is
(a) Ist ratio (b) Third ratio (c) IInd ratio (d) None

Q-3 In 4/5 : : 9/7, : : is the symbol for
(a) Ratio (b) Proportional (c) a & b (d) None

Q-4 60 ´70 ´ 130
(a) 42 (b) 91 (c) 1 (d) None

Q-5 315/(150)
(a) 315 (b) 316 (c) 0 (d) ¥

Q-6 73 + 37
(a) 1110 (b) 110 (c) 100 (d) None

Q-7 Find (112 – 102) / (11 + 10)
(a) 1 (b) 2 (c) 3 (d) 4

Q-8 Find 35 + 4(1/5) ¸ 4/5
(a) 161/5 (b) 161/4 (c) 161/8 (d) 161/9

Q-9 In (x + 6)14, How many terms are there
(a) 15 (b) 16 (c) 17 (d) 18

Q-10 In (x + y)21, how many middle terms are there
(a) 2 (b) 1 (c) 3 (d) 4

Q-11 underroot 0.0196
(a) 0.15 (b) 0.16 (c) 0.14 (d) 0.19

Q-12 underroot 0.0225
(a) 0.14 (b) 0.15 (c) 0.16 (d) 0.18

Q-13 Find 3 underroot 0.000081
(a) 0.009 (b) 0.09 (c) 0.0009 (d) 0.9

Q-14 (515 ´ 252) / (125)2
(a) 511 (b) 512 (c) 513 (d) 514

Q-15 3 underroot 1 Find n
(a) 1/3 (b) 1/ 2 (c) 1/ 4 (d) 1 / 5

Q-16 252 =?
(a) 625 (b) 636 (c) 666 (d)639

Q-17 (26)2 =?
(a) 625 (b) 635 (c) 665 (d) 676

Q-18 (192 – 182) + (18)2
(a) 365 (b) 361 (c) 396 (d) 371

Q-19 underroot 50 ´ underroot 3 ´ underroot 6
(a) 35 (b) 34 (c) 30 (d) 40

Q-20 LCM 5, 10, 15, 20
(a) 65 (b) 60 (c) 70 (d) 90

Q-21 HCF 22 ´ 42 ´ 52, 23 ´ 4 ´ 53, 2 ´ 31 ´ 45
(a) 8 (b) 10 (c) 6 (d) 4

Q-22 Which is smaller No. of four digit?
(a) 1000 (b) 9999 (c) 1550 (d) 2000

Q-23 Mean Proportion of 4 and 5
(a) 9 (b) underroot20 (c) underroot 21 (d) underroot 22

Q-24 What will be duplicate ratio of 7:8
(a) 49:64 (b) 7:64 (c) 49:8 (d) None

Q-25 Find triplicate ratio of 1:5
(a) 1:125 (b) 1:25 (c) 1:64 (d) 1:29

1. b Ist ratio
2. c IInd ratio
3. b Proportional
4. c 1
5. a 315
6. b 110
7. a 1
8. b 161/4
9. a 15
10. a 2
11. c 0.14
12. b 0.15
13. b 0.09
14. c 513
15. b 1/2
16. a 625
17. d 676
18. b 361
19. c 30
20. b 60
21. a 8
22. a 1000
23. b underroot 20
24. a 49:64
25. a 1:125

#### Reasons:

4 60 ´70 ´ 130 = 1 ´ 1 ´ 1 = 1
6 73 + 37 = (7 +3) ´ 11 = 110
7 (112 – 102) / (11 + 10) = (11 – 10) (11 + 10)/(11 + 10) = 1
8 35 + 21/5/4/5 = 35 + 21/4 = 140 + 21/4 = 161/4
10 Since 21 + 1 = 22 is even
\ it have two middle term
14 (515 ´ 252) / (125)2 = 515´ (52)2/(53)2= 515 ´ 54 / 56
515 + 4 / 56 = 519/56 = 519 – 6 = 513
15 3 underroot 3 = 3n + 1 = (33)1/2 = 3n + 1
33/2 = 3n + 1
n + 1 = 3/2
n = 3/2 – 1 = ½
16 Since 625 is the only No. which unit digit = 5
18 192 – 182 + 182 = 192 = 361
19 underroot 50 ´ underroot 3 ´ underroot 6 = underroot (5 ´ 3 ´ 6) = underroot 900 = 30
21 HCF in 21 ´ 41 = 8
23 Mean proportion of 4 & 5 is underroot (4 ´ 5) = underroot 20
25 Triplicate ratio of 1 :5 is 13 : 53 = 1:125

## Mock Test Quantitative Ability 1

Only one of the four alternatives given under each question is correct. Choose the correct alternatives

Q-1 The L.C.M. of 3/9, 4/12, 8/24 is----.
(a) 1/3
(b) 2/3
(c) 8
(d) 1
Q-2 Which is the smallest out of the following?
(a) (4)2 + (6)2
(b) (7)2 + (3)2
(c) (5)2 + (8)2
(d) (3)2 + (8)2
Q-3 How will you remove ‘?’ out of the following 25/3% of ? = 150
(a) 1000
(b) 900
(c) 500
(d) 1800
Q-4 Remove the question mark out of the following:
? % of 30 + 40% of 40 = 50% of 50
(a) 60
(b) 40
(c) 30
(d) 80
Q-5 Remove the question mark out of the following:
Ö225/Ö9 = 625/ ?
(a) 125
(b) 100
(c) 115
(d) 120
Q-6 [(3.5)2 - (1.5)2 ] / (3.5 - 1.5)
(a) 5
(b) 2
(c) 10
(d) 5.25
Q-7 1.6 ´ 0.25 ´ 0.4=
(a) 1.6
(b) 0.16
(c) 1600
(d) 16
Q-8 Three person A,B and C distribute among themselves RS. 2600 in the ratio 11:18:23. The
share of B will be
(a) Rs. 500
(b) Rs. 800
(c) Rs. 600
(d) Rs. 900
Q-9 How many numbers between 15 and 90 are perfect squares?
(a) 7
(b) 9
(c) 8
(d) 6
Q-10 A fruit- seller sells 5 apples at the cost price of 6 apples. Find his profit percent
(a) 25 Percent
(b) 15 Percent
(c) 20 Percent
(d) 16 Percent
Q-11 A truck needs 15 liters of fuel for covering 255 km. How much fuel will it need to cover 170 km ?
(a) 15 liters
(b) 9 liters
(c) 10 liters
(d) 8 liters
Q-12 How many numbers are there in 9000, 1000, 1111, 9999 which have more than 4 digits?
(a) 2
(b) 3
(c) 1
(d) None
Q-13 How many numbers between 200 and 600 (both the numbers inclusive) are divisible by 4,5 and 6?
(a) 5
(b) 7
(c) 6
(d) 4
Q-14 A school has only 3 classes which contain 40,50 and 60 students respectively. The pass percentage of these classes is 10,20 and 10 respectively. The pass percentage of the school is
(a) 40/3
(b) 13 ½
(c) 13 ½
(d) 27/2
Q-15 the average age of 11 persons is 60 years. If the average age of the first 5 is 58 years and that of the last 5 is 56 years and that of the last 5 is 56 years, then the age of 6th person is
(a) 85 years
(b) 90 years
(c) 80 years
(d) 95 years
Q-16 30% of 240 + 10% of 200 is equal to
(a) 82
(b) 62
(c) 92
(d) 72
Q-17 999 ¸ 3 ¸ 0.3 is equal to
(a) 333
(b) 222
(c) 1110
(d) 444
Q-18 Divide Rs. 7700 among A, B and C in the ratio of 5:4:2. The shares of A, B, C are
(a) 1400, 3500, 2800
(b) 3500, 2800, 1400
(c) 2800, 1400, 3500
(d) None of these
Q-19 The cube of the figure 11 is:
(a) 1031
(b) 1231
(c) 1131
(d) 1331
Q-20 The average of 3 numbers is 24. If two of the numbers are 16 and 26, the third number is
(a) 32
(b) 34
(c) 28
(d) 30
Q-21 The total number of Prime numbers less than 30 is
(a) 10
(b) 9
(c) 12
(d) 11
Q-22 The greatest fraction among 7/8, 8/9, 9/10, 11/15 is
(a) 11/15
(b) 9/10
(c) 8/9
(d) 7/8
Q-23 If we divide 83 by three, the remainder will be
(a) 3
(b) 2
(c) 1
(d) 0
Q-24 Which of these is the smallest?
(a) -5
(b) -4
(c) 2
(d) 0
Q-25 In how many days will 8 men complete a work which 12 men take 24 days to finish?
(a) 38 days
(b) 36 days
(c) 20 days
(d) 25 days

### Answer With Reasons:-

1. (a) 1/3
L.C.M. of 3/9, 4/12, 8/24 = L.C.M. of 1/3, 1/3, 1/3
= L.C.M. of numerators / H.C.F. of denomenators
= L.C.M. of 1, 1, 1/ H.C.F. of 3, 3, 3 = 1/3

2. (a) (4)2 + (6)2
A = 72 + 32 = 49 +9 = 58
B = 52 + 82 = 25 + 64 = 89
C = 42 + 62 = 16 + 36 = 52
D = 32 + 82 = 9 + 64 = 73
Clearly (c) is the smallest
3. (d) 1800
25/3% of? = 150 = 25/ (3 ´ 100) of? = 150
? = (150 ´ 3 ´ 100) / 25 = 1800
4. (c) 30
? % of 30 + 40% of 40 = 50% of 50
?/100 ´ 30 + 40/100 ´ 40 = 50/100 ´ 50
3/10 ´ ? + 16 = 25
3/10 ´ ? = 25 - 16 = 9
? = (9 ´ 10) /3= 30
5. (a) 125
Ö225/Ö9 = 625/?
15/3 = 625/? = 15 ´ ? = 625 ´ 3
? = (625 ´ 3) / 15 = 125
6. (a) 5
[(3.5)2 - (1.5)2] / (3.5 - 1.5) = [(3.5 + 1.5) (3.5 - 1.5)] / (3.5 -1.5) = (3.5 +
1.5) = 5
7. (b) 0.16
1.6 ´ 0.25 ´ 0.4 = 1.6 ´ .100 = 1.6 ´ .1 = 0.16
8. (d) Rs. 900
Ratio = 11: 18: 23
Proportional sum = 11 + 18 + 23 = 52
B’s share = 18/52 ´ 2600 = Rs. 900
9. (d) 6
Numbers between 15 and 90, which are perfect squares, are 16, 25, 36, 49, 64, 81
These are six numbers
10. (c) 20 Percent
Let cost price of 6 apples be Re. 1
S.P. of 5 apples = Re. 1
S.P. of 1 apples = Re. 1/5
S.P. of 6 apples = 1/5 ´ 6 = Rs. 6/5
Profit = 6/5 - 1 = 1/5
Profit% = (1/5) / 1 ´ 100 = 20%
11. (c) 10 liters
Full needed for 255 km = 15 liters
Fuel needed for 1 km = 15/255 liters
Fuel needed for 170 km = 15/255 ´ 170 liters =10 liters
12. (d) None
None of the given numbers has more than four digits
13. (b) 7
L.C.M. of 4, 5 and 6 = 60
The numbers, which are divisible by 4, 5 and 6 are also divisible by 60
Required numbers between 200 and 600 are 240, 300, 360, 420, 480, 554 and 600
These are 7 numbers
14. (a) 40/3
Numbers of Pass students in first class = 40 ´ 10 / 100 = 4
Numbers of Pass students in second class = 50 ´ 20 /100 = 10
Numbers of Pass students in third class = 60 ´ 10 / 100 = 6
Total Students = 40 + 50 + 60 = 150
Total pass students = 4 + 10 +4 = 20
Total pass % = 20/150 ´ 100 = 40 / 3 = 40/3

15. (b) 90 years
Average age of 11 persons = 60
Total age of 11 persons = 60 ´11 = 660
Average age of first 5 persons = 58
Total age of first 5 persons = 58 ´ 5 = 290
Average age of last 5 persons = 56
Total age of last 5 persons = 56 ´ 5 = 280
Age of 6th person = 660 -(290 + 280)
= 660 - 570 = 90 years

16. (c) 92
30% of 240 + 10% of 200 = 30/100 ´ 240 + 10/100 ´ 200 = 72 + 20 = 92

17. (c) 1110
999 ¸ 3 ¸ 0.3 = 999 ´ 1/3 ´ 10/3 = 1110
18. (b) 3500, 2800, 1400
Ratio = 5 : 4: 2
Proportional sum = 5 + 4 + 2 = 11
A’s share = 5/11 ´ 7700 = Rs. 3500
B’s share = 4/11 ´ 7700 = Rs. 2800
C’s share = 2/11 ´ 7700 = Rs. 1400
19. (d) 1331
Cube of 11 = (11) 3 = 11 ´ 11 ´ 11 = 1331
20. (d) 30
Average of 3 members = 24
Sum total of these numbers = 24 ´ 3 = 72
Sum of given two numbers = 16 + 26 = 42
Therefore the third number = 72 - 42 = 30
21. (a) 10
Prime numbers less than 30 are 2, 3, 5, 7, 11, 17, 19, 23, 29. These are 10 numbers
22. (b) 9/10
7/8, 8/9, 9/10, 11/15 = (315, 329, 324, 264) / 360
324 is the greatest of all numerators
\ 9/10 is the greatest of all given fractions
23. (b) 2
83 = 27 ´ 3 + 2 , So the Remainder = 2
24. (a) -5
The number which lies on the left of all given numbers on the numbers line is -5. This is the least number

25. (b) 36 days
Time taken by 12 men to complete the work = 24 days
Time taken by 1 man to complete the work = 24 ´ 12 days
Time taken by 8 men to complete that work = (24 ´ 12) / 8 = 36 days

## Quanta

Q-1 5x + 6 = 252, then the value of x in
(a) 3
(b) 4
(c) –2
(d) 14
Q-2 a = 4, b = 9, what will be the value of
1/square root of a – square root of b
(a) 3
(b) – 1
(c) – 3
(d) 5
Q-3 x = 64, y = 125, then find the value of (x1/3 + y1/3)1/5
(a) 101/5
(b) 91/5
(c) 81/5
(d) None
Q-4 252 – 92 / (16) 4 =?
(a) 17/4
(b) 17/2
(c) 19/2
(d) None
Q-5 15.32 + 16.1 – 15.38
(a) 16/04
(b) 16.15
(c) 16.11
(d) 16.19
Q-6 square root of 40 × square root of 90 =?
(a) 5 square root of 10
(b) 6 square root of 10
(c) 11 square root of 10
(d) None
Q-7 515 × 54 =?
(a) 560
(b) 519
(c) 521
(d) 523
Q-8 5/9 + 11/7 – 1/3 + 1/9 =?
(a) 121/60
(b) 120/63
(c) 131/65
(d) 19/65
Q-9 3 ÷ 4 + 2 – 6 × 4
(a) – 31
(b) – 22
(c) – 33
(d) 64
Q-10 Which is at unit place of 255 × 135 × 111?
(a) 6
(b) 5
(c) 7
(d) 1
Q-11 15 ÷ 3 × 36 – 54 + 6
(a) 133
(b) 132
(c) 158
(d) None
Q-12 53 – 33/(52 + 32 + 15) =?
(a) 4
(b) 3
(c) 2
(d) 4
Q-13 (.31 × .31 – 0.11 × 0.11) / (0.31 + 0.11) = x, find the value of x
(a) 0.50
(b) 0.20
(c) 0.31
(d) None
Q-14 151 × 99
(a) 14449
(b) 14551
(c) 14751
(d) None
Q-15 99 × 99
(a) 9901
(b) 8801
(c) 1905
(d) None
Q-16 11 × 31 × 55, what will be at unit place?
(a) 5
(b) 6
(c) 7
(d) 8
Q-17 (a – b) (a2+ b2 +ab) =?
(a) a3 – b3
(b) a2 + b2
(c) a + c
(d) a + b
Q-18 a2 – b2 = (a – b)?
(a) (a + b)
(b) a – b
(c) a2 + b2
(d) None
Q-19 (15 + 25)2 – (15 – 25) 2 / 15 × 25 =?
(a) 5
(b) 4
(c) 8
(d) 9
Q-20 4 (– 3) ) – 1) ( – 2) =?
(a) – 24
(b) 24
(c) 15
(d) 18
Q-21 (–1)54 =?
(a) 1
(b) 2
(c) – 1
(d) 0
Q-22 (–1) + (–3) + (–6) =?
(a) – 10
(b) 10
(c) 11
(d) 9
Q-23 (–1)9 =?
(a) 2
(b) 1
(c) – 1
(d) 34
Q-24 1 + 1/(1/2) + 1/3 =?
(a) 10/5
(b) 10/3
(c) 9/5
(d) 11/3
Q-25 1 + 1/(1 + ½) = ?
(a) 5/4
(b) 5/2
(c) 5/9
(d) 15/4

1. c –2
2. b –1
3. b 91/5
4. b 17/2
5. a 16.04
6. a 5Ö10
7. b 519
8. b 120/63
9. b –22
10. b 5
11. b 132
12. c 2
13. b 0.20
14. a 14449
15. b 8801
16. a 5
17. a a3 – b3
18. a (a +b)
19. b 4
20. a –24
21. a 1
22. a –10
23. c –1
24. b 10/3
25. b 5/2

#### Reasons:

1. 5x + 6 = (52)2 = 5x + 6 = 54
x + 6 = 4 , x = 4 – 6 = –2
2. 1/ square root of a – square root of b = 1/ square root of 4 – square root of 9 = 1/
2 – 3 = 1/ –1 = –1
3. (x1/3 + y1/3)1/5 = (641/3 + 1251/3)1/5 = (4 + 5)1/5 = 91/5
4. 252 – 92/(16)4 = (25 – 9) (25 + 9)/(16)4 = (16) (34)/16(4) = 34/4 = 17/2
5. 15.32 + 16.1 – 15.38
31.42 – 15.38 = 16.04
6. square root of 40 × square root of 90 = 2 square root of 10 + 3 square root of10
= 5 square root of10
7. 515 × 54 = 1515 + 4 = 1519
8. (35 +99 – 21 + 7)/63 = [(35 + 99 + 7) –21]/63
= 141 – 21/63 = 120/63
9 3 ÷ 4 + 2 – 6 × 4
¾ + 2 – 6 × 4 = ¾ + 2 – 24 Bodmas
(11/4) – 24 = 11 – 96/4 = –88/4 = –22
11 15 ÷ 3 × 36 – 54 + 6
= 5 × 36 – 54 + 6
180 – 51 + 6 = 180 – 54 = 132
12 53 – 33/(52 + 32 + 15)= (5 – 3) (52 + 32 + 15) /52 + 32 + 15) = 2
13 (.31)2 –(0.11)2 / (0.31 + 0.11) = (0.31 – 0.11) (0.31 + 0.11)/(0.31 + 0.11)
= 0.20
14 151 × ( 100 –1) = 15100 – 151 = 1449
15 (99)2 = (100 – 1)2 = 1000 + 1 – 200
= 10001 – 200 = 8801
19 (15 + 25)2 – (15 – 25)2 / 15 × 25 = 4
Because (a + b)2 – (a – b)2/ab

## Quanta

Q-1 3x + 1 = 27x + 4
(a) 11/5
(b) 11/4
(c) 11/2
(d) 11/9
Q-2 Which value should be subtracted from the terms of the ratio 5:6 in order to get 2:3
(a) 4
(b) 3
(c) 9
(d) 11
Q-3 What is mean proportional of 3 & 27 ?
(a) 11
(b) 9
(c) 3
(d) 4
Q-4 Distribute 472 between M & N in the ratio of 1:3
(a) 118, 316
(b) 118, 354
(c) 118, 319
(d) 118, 331
Q-5 What is the third proportional of 3 & 5 ?
(a) 15/3
(b) 26/3
(c) 16/9
(d) 11/4
Q-6 Find the L.C.M. ½, 3/8, 4/6
(a) 9
(b) 6
(c) 7
(d) 8
Q-7 What will be the HCF of 9/2, 3/8, 6/12 ?
(a) 1/6
(b) 1/7
(c) 1/8
(d) 1/9
Q-8 321 × 34 = ?
(a) 10914
(b) 10915
(c) 11915
(d) 12914
Q-9 – 0.85/1.7 = ?
(a) – 0.5
(b) – 0.501
(c) 5.0
(d) 5.6
Q-10 1 + 2 + 3 + --------- + 12 = ?
(a) 68
(b) 62
(c) 78
(d) 71
Q-11 2m is
(a) Even number
(b) Odd No.
(c) Prime No.
(d) None
Q-12 What should be add in 2m so that it becomes odd ?
(a) 1
(b) 3
(c) 4
(d) 5
Q-13 5173× (999) =?
(a) 516782
(b) 5167827
(c) a & b
(d) None
Q-14 11:x = x:12, Find x
(a) 12
(b) 11
(c) 19
(d) 20
Q-15 If A:B = 5:2, B:C = 1:4
Then find A:B:C
(a) 5:3:8
(b) 5:2:8
(c) 5:4:8
(d) None
Q-16 When 270 liter of water fill half tank then 360 liter will be what part of tank ?
(a) 3/6
(b) 3/2
(c) 3/11
(d) None
Q-17 When 2x432 is divided by 3 then, what will come in place of x ?
(a) 4
(b) 3
(c) 14
(d) None
Q-18 451.64 + 354.6 + 421 + 6.5 =?
(a) 1235.74
(b) 1233.74
(c) 1237.74
(d) None
Q-19 45.98 – 36.003 =?
(a) 10.977
(b) 9.977
(c) 11.8
(d) None
Q-20 0.011 × 0.0121 = x
Find x
(a) 0.0001343
(b) 0.0001454
(c) 0.001451
(d) None
Q-21 0.09 × 111.4 × 0.008 =?
(a) 0.8209
(b) 0.080208
(c) 0.080209
(d) None
Q-22 4000 + 1531.4 + x = 60031
Find x
(a) 54499.6
(b) 554.66
(c) 54495.9
(d) None
Q-23 Difference between the square of two even integer is always divided by which number
(a) 4
(b) 5
(c) 9
(d) 8
Q-24 ( squarroot of 2 + squarroot of 3)/( squarroot of 2 – squarroot of 3) = x
Find x
(a) 5 – 2 squarroot of 6
(b) 5 +2 squarroot of 6
(c) 5 – 3 squarroot of 2
(d) None
Q-25 Which is the smallest No. to be subtracted from 141 so that it is divisible by 7?
(a) 2
(b) 1
(c) 3
(d) 4

1. c 11/2
2. b 3
3. b 9
4. b 118,354
5. b 25/3
6. b 6
7. c 1/7
8. a 10914
9. a –0.5
10. c 78
11. a Even number
12. a 1
13. b 5167827
14. b 11
15. b 5:2:8
16. b 3/2
17. a 4
18. b 1233.74
19. b 9.977
20. a 0.0001343
21. b 0.080208
22. a 54499.6
23. a 4
24. b 5 + 2 squarroot of 6
25. b 1

#### Reasons:

1. 3x + 1 = (33)x+4
3x+1 = 33x+12
x+1 = 3x+12
3x – x = 12 – 1
2x = 11x, x = 11/2
2. Suppose we subtract A from the terms
Then ratio
(5 – A) : (6 – A)
(5 – A) : (6 – A) = 2:3
5 – A/6 – A = 2/3
3(5 – A) = 2(6 – A)
15 – 3A = 12 – 2A
15 – 12 = 3A – 2A
3 = A
3. Mean Proportional = squarroot of (3 × 27) = squarroot of 81 = 9
4. T O M = (472 × ¼) = 118
T O N = (472 × ¾) = 354
5. 3:5 = 5:A
3/5 = 5/A, A = 25/3
6. L.C.M. = L.C.M. of 1,3,4/H.C.F. of 2,8,6 = 12/2= 6
7. H.C.F. = HCF of 9,3,6/LCM of 2,8,12 = 3/24 = 1/8
10 1 + 2 + 3 + ------ + 12 =Σ(n + 1)/2
12(12 + 1)/2 = 78
14. 11/x = x/12
121 = x2, x= 11
15. A:B = 5:2, B:C = 2:8
A:B:C = 5:2:8
17 2x432 = 2 + x + 4 + 3 + 2 = 11 + x
we can take 4 11 + 4 = 15
divisible by 3
22 x = 60031 – 4000 – 1531-4 = 54495.9
23 Let two even no. = 2,4
42 – 22 = 16 – 4 = 12
24 (squarroot of 2 + squarroot of 3)/( squarroot of 2 – squarroot of 3)× (squarroot of squarroot of 2 + squarroot of 3 / squarroot of 2 + squarroot of 3)
(squarroot of 2 + squarroot of 3)2 / 4 – 3 = 2 + 3+ 2 squarroot of 6 / 1
= 5 + 2 squarroot of 6

## Numerical Ability

Q-1 25! ¤ (25-25)! =2
(a) 25! (b) 30! (c) 25 (d) None
Q-2 Find x if 32 ´ 64 is divisible by 3?
(a) 4 (b) 3 (c) 5 (d) 9
Q-3 Here two no. have HCF 15 which cannot be its LCM ?
(a) 45 (b) 64 (c) 30 (d) 90
Q-4 0.08 ¤ 0.06
(a) 4 ¤ 5 (b) 4 ¤ 3 (c) 4 ¤ 9 (d) None
Q-5 147 ¤ 0.03
(a) 4500 (b) 4900 (c) 4600 (d) None
Q-6 1/0.008
(a) 126 (b) 125 (c) 191 (d) None
Q-7 7! / (3´2)! +4=?
(a) 12 (b) 11 (c) 19 (d) 20
Q-8 If x =7a +8 & y =9 + 8a
Find a if x =y
(a) 1 (b) -1 (c) 2 (d) 3
Q-9 x/8 -x/5 =11
Find x
(a) -440/3 (b) -440/9 (c) 9 (d) 8
Q-10 .13´.13´ 10
(a) .1691 (b) .1690 (c) .1661 (d) None
Q-11 If 3x + 5y =7
& 3x -6y = -15
find 5x + 9y
(a) 12 (b) 13 (c) 19 (d) 20
Q-12 Find the smallest fraction?
(a) 0.1 (b) 0.2 (c) 0.3 (d) 0.5
Q-13 0.00011 ´ 0.11
(a) 121 (b) 0.00121 (c) .0000121 (d) None
Q-14 315 ´ 10-3 =?
(a) .0315 (b) .315 (c) 311 (d) None
Q-15 13.15 ´ 104 =?
(a) 1315 ´ 102 (b) 1315 (c) 1318 (d) None
Q-16 315/ 010 = ?
(a) 10 (b) 315 (c) ¥ (d) None
Q-17 HCF of 91,104,117 in
(a) 12 (b) 91 (c) 13 (d) 18
Q-18 HCF of 105,135,150
(a) 105 (b) 15 (c) 13 (d) 18
Q-19 How many even prime no are possible?
(a) 1 (b) 2 (c) 3 (d) 10
Q-20 35/ 21 in a
(a) Natural no. (b) Rational no
(c) Complex no (d) None
Q-21 333 + 100 -20
(a) 415 (b) 433 (c) 413 (d) None
Q-22 (400 ¸5) -5
(a) 850 (b) 85 (c) 1850 (d) None
Q-23 (400 ´5) -3
(a) 402 (b) 403 (c) 408 (d) None
Q-24 1400 ´10 ¸2 -5
(a) 1400 (b) 1300 (c) 1800 (d) None
Q-25 1300 +15 -10 ¸2
(a) 1305 (b) 1310 (c) 1308 (d) None

### Answers with Reasons : -

1(a) 25!
2(b) 3
3´2+x+6´4 = x+15
18
3(b) 64
4(b) 4/3
100/100 ´8/6
8/6
4/3
5(b) 4900
6(b) 125
1000/8 =125
7(b) 11
7! /6! ´4
7.6! /6! +4
7´4 =11
8(b) -1
7a ´8 =9´8a
-1 =a
9(a) -440/3
5 ´-8/40 =11
-3´ =440
x = -440/3
10(b) .1690
.1690
11(b) 13
Subtract 11y =22
y =2 - ´ = -1
12(a) 0.1
13(c) .0000121
14(b) .315
15(a) 1315 ´102
16(c) ¥
17(c) 13
18(b) 15
19(a) 1
20(b) Rational no
21(c) 413
22(b) 85
23(a) 402
24(b) 1300
25(b) 1310

## Quanta Test 9

Q-1 Under root of(0 ´5) =?
(a) 1 (b) 0 (c) 3 (d) 9
Q-2 under root of25 under root of100 under root of36
(a) 350 (b) 360 (c) 300 (d) 310
Q-3 under root of 729/81 = under root of 441/x Find x
(a) 64 (b) 63 (c) 61 (d) 65
Q-4 Find under root of15 – 1 / under root of15 + 1
(a) (8 – under root of 15)/7 (b) (8 + under root of15)/7 (c) (8 – under root of15)/7 (d) None
Q-5 Find 1/under root of6 – under root of5
(a) under root of 6 + under root of 5 (b) under root of 6 + under root of 7 (c) under root of 5 + under root of 6 (d) None
Q-6 Find the following which is perfect square
(a) 431 (b) 411 (c) 451 (d) 441
Q-7 From the following which is a perfect cube
(a) 216 (b) 226 (c) 156 (d) 286
Q-8 under root of x/100 = 1/10
(a) 101 (b) 100 (c) 104 (d) None
Q-9 under root of 19 + under root of 15/under root of 19 – under root of 15 =?
(a) (17 under root of 285) /2 (b) (17 – under root of 285)/3 (c) 17 + under root of 285 (d) None
Q-10 (27)3 = 3x/3 , Find x
26 (b) 27 (c) 28 (d) 29
Q-11 under root of 729/x = 27/5, find the value of x
(a) 5 (b) 6 (c) 7 (d) 8
Q-12 Which four digit No. is a perfect square
(a) 2500 (b) 2600 (c) 2700 (d) 2800
Q-13 From the following which four digit No. is a perfect cube.
(a) 2000 (b) 1000 (c) 3000 (d) 3500
Q-14 under root of 17 ´ under root of 18
(a) 17.46 (b) 17.49 (c) 17.89 (d) 17.50
Q-15 LCM of 22, 6 is
(a) 2 (b) 4 (c) 6 (d) 12
Q-16 LCM of 45, 46, 47, 48, 411is
(a) 411 (b) 48 (c) 45 (d) None
Q-17 15 & 20 are two No. & HCF is
(a) 21 (b) 20 (c) 23 (d) 24
Q-18 HCF (11-1, 11-5, 11-9, 11-12)
(a) 1112 (b) 11-9 (c) 11-5 (d) 11-1
Q-19 HCF of 12, 12, 12 is
(a) 12 (b) 122 (c) 123 (d) None
Q-20 HCF of 25, 50, 100, 125
(a) 120 (b) 125 (c) 25 (d) None

1. b 0
2. c 300
3. b 63
4. a (8 – under root of 15) /7
5. a under root of 6 + under root of 5
6. d 441
7. a 216
8. b 100
9. a (17 + under root of 285)/2
10. b 27
11. a 5
12. a 2500
13. b 1000
14. b 17.49
15. d 12
16. a 411
17. b 20
18. a 11-12
19. a 12
20. c 25

#### Reasons:

3 27/81 = 27/x, x = 63
4 under root of 15 – 1/under root of 15 + 1 = under root of 15 – 1 / under root of 15 + 1´ under root of 15 – 1/under root of 15 – 1
(under root of 15 – 1)2/ (under root of 15)2 – 1 = 15 + 1 – 2 under root of 15/15 – 1
16 – 2under root of 15 /14 = 2 (8 –under root of 15)/14 = 8 –under root of 15 /7
5 1/under root of 6 – under root of 5 = 1/ under root of 6 – under root of 5 ´ under root of 6 + under root of5/under root of6 + under root of5 = under root of 6 + under root of 5/(under root of 6)2 – (under root of 5)2
under root of 6 + under root of 5/ 6 – 5 = under root of 6 + under root of 5 /1 = under root of 6 + under root of 5
8 under root of x/100 = 1/10 = under root of x = 10, x = 100
9 under root of 19 + under root of 15/under root of 19 – under root of 15 ´ under root of 19 + under root of 15/under root of 19 + under root of15
(under root of19 + under root of15)2 / (19) – (15) = (under root of19 + under root of 15)2/4
(19 + 15 + 2under root of 19 under root of15)/4 = 34 + 2 under root of 285/ 4 = 17 + under root of 285 /2
10 (33)3 = 3x/3 = 39 = 3x/3
9 = x/3, x = 27
14 under root of17 ´under root of 18 = under root of 306 = 17.49
17 L.C.M. ´ HCF = Product of two No.
L.C.M. ´ 15 = 15 ´20
LCM = 300 /15 = 20
18 Take the least power