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We have come up with Sectional Tests for upcoming LIC AAO 2019 Prelim Exam. Practice the questions to ace the exam.

**Directions(1-4):** Compare both the equations and choose a correct option.

- I.6x^2 – 25x + 14 = 0

II.2y^2 – 13y + 6 = 0x>=yx > yy>=xy > xNo relationOption E

I.6x^2 – 25x + 14 = 0

=>6x^2 -21x – 4x + 14 = 0

=>(2x-7)(3x – 2) = 0

=> x = 7/2, 2/3

II.2y^2 – 13y + 6 = 0

=>2y^2 – 12y – y + 6 = 0

=>(y-6)(2y – 1) = 0

=> y = 6, ½

No relation. - I.5x^2 – 27x + 10 = 0

II.y^2 – 14y + 48 = 0

y > xNo relationy>=xx > yx>=yOption A

I.5x^2 – 27x + 10 = 0

=>5x^2 – 25x – 2x + 10 = 0

=>(x-5)(5x-2) = 0

=>x = 5,2/5

II.y^2 – 14y + 48 = 0

=>y^2 – 8y – 6y + 48 = 0

=>(y-8)(y-6) = 0

=> y = 8,6

y > x - I.x^2 + 12x + 32 = 0

II.y^2 + 10y + 16 = 0

x > yy>=xNo relationx>=yy > xOption C

I.x^2 + 12x + 32 = 0

=>x^2 + 8x + 4x + 32 = 0

=>(x+4)(x+8) = 0

=>x = -4,-8

II.y^2 + 10y + 16 = 0

=>y^2 + 2y + 8 y + 16 = 0

=>(y+2)(y+8) = 0

=> y = -2,-8

No relation. - I.2x^2 – 18x + 36 = 0

II.2y^2 – 30y + 108 = 0

No relationx > yy > xy>=xx>=yOption D

I.2x^2 – 18x + 36 = 0

=>2x^2 – 12x – 6x + 36 = 0

=>(2x-6)(x – 6) = 0

=> x = 3,6

II.2y^2 – 30y + 108 = 0

=>2y^2 – 12y – 18u + 108 = 0

=>(2y – 18)(y-6) = 0

=> y = 6,9

y>=x - 750 *(10.24)^1/2 = ?% of 480
500440320400510Option A

750 *(10.24)^1/2 = ?% of 480

=>750*3.2 = ?*4.8

=>? = 500 - (75% of 1820) – 25^2 = ?^2 -25% of 176
2018112817Option D

75% of 1820) – 25^2 = ?^2 -25% of 176

=>?^2 – ¼*176 = 0.75*1820 – 625

=>?^2 – 44 = 1365- 625

=>?^2 = 740 + 44

=>? = 28 - {(484)^1/2 + 224 / 2^3 }% of 960 = ?% of 640
6681707590Option D

{(484)^1/2 + 224 / 2^3 }% of 960 = ?% of 640

=>?% of 640 = (22+28)% of 960

=>? * 6.4 = 480

=>? = 75 - (600/24)*25 + 25^2 + 125% of 280 = ?^2
3340254153Option B

(600/24)*25 + 25^2 + 125% of 280 = ?^2

=>?^ 2 = 25*25 +625 + 350

=>?^2 = 1250 + 350

=> ? = 40 - 15*8 + ? – 9 * 11 = 12*18
195152170164175Option A

15*8 + ? – 9 * 11 = 12*18

=> 120 + ? – 99 = 216

=>? + 21 = 216

=>? = 195 - 16% of 1750 -20% of 1150 =25% of ?
110100200324220Option C

16% of 1750 -20% of 1150 =25% of ?

=>0.25*? = 0.16*1750 – 0.20*1150

=>0.25*? = 280 – 230

=>? = 200 - 244 – 156 + ?^2 -13^2 = 15*14 + 25*22
2016142919Option D

244 – 156 + ?^2 -13^2 = 15*14 + 25*22

=>88 + ?^2 – 169 = 210 + 550

=>?^2 – 81 = 760

=>?^2 = 841

=> ? = 29 - {(3072/16)/8)/4}+ 14^2 = ?
195174166202188Option D

{(3072/16)/8)/4}+ 14^2 = ?

=>? = {(192/8)/4} + 14^2

=> ? = 24/4 +196

=>? = 202 - 648/9 + 18^2 – 20% of 630 = ?*6
4122303545Option E

648/9 + 18^2 – 20% of 630 = ?*6

=>?*6 = 72 + 324 – 0.20*630

=>?*6 = 396 – 126

=>?*6 = 270

=> ? = 45 - 613 + 762 + ? – 981 = 549 – 375 + 817
660597500495510Option B

613 + 762 + ? – 981 = 549 – 375 + 817

=>1375 + ? – 981 = 991

=>394 + ? = 991

=>? = 597 - 84^2 – 79^2 + (1936)^1/2 – 20% of 980 = ?
740600548663875Option D

84^2 – 79^2 + (1936)^1/2 – 20% of 980 = ?

=>815 + 44 – 196 = ?

=>? = 663 - 958, 833, 733, 658, 608, (?)

448415583574545Option C

958, 833, 733, 658, 608, (?)

958 – 833 = 125

833 – 733 = 100

733 – 658 = 75

658 – 608 = 50

? = 608 – 25 = 583 - 11, 10, 18, 51, 200, (?)
900880995745717Option C

11 × 1 – 1 = 10

10 × 2 – 2 = 18

18 × 3 – 3 = 51

51 × 4 – 4 = 200

200 × 5 – 5 = 995 - 25, 48, 94, 186, 370, (?)
695687770712738Option E

25 × 2 – 2 = 50 – 2 = 48

48 × 2 – 2 = 96 – 2 = 94

94 × 2 – 2 = 188 – 2 = 186

186 × 2 – 2 = 372 – 2 = 370

370 × 2 – 2 = 740 – 2 = 738 - 14, 24, 43, 71, 108, (?)

154140125136118Option A

14 + 10 = 24

24 + 19 (=10 + 9) = 43

43 + 28 (= 19 + 9) = 71

71 + 37 (= 28 + 9) = 108

108 + 46 (=37 + 9) = 154 - 144, 173, 140, 169, 136, (?)
140165157125133Option B

144 + 29 = 173

173 – 33 = 140

140 + 29 = 169

169 – 33 = 136

136 + 29 = 165 - The respective ratio of number of Passenger trains to the number of Express trains passing through platform number 7 is 5:7. If the total number of trains passing through platform number 7 is 50% more than the total number of trains passing through platform number 2. Find the number of Passenger trains passing through platform number 7.

7152456084Option D

Total number of trains passing through platform number 2 = 56+40 = 96

Total number of trains passing through platform number 7 = 96*1.5 = 144

Total number of Passenger trains passing through platform number 7 = 5/12*144 = 60 - The number of passenger trains passing through platform number 6 to the number of passenger trains passing through platform number 5 are in the ratio 4:5 resp. and the number of Express trains passing through platform number 6 are 25% more than number of Express trains passing through platform number 5 . Find the total number of trains passing through platform number 6.

125111108114117Option A

Total number of Passenger trains passing through platform number 6 = 50/5*4 = 40

Total number of Express trains passing through platform number 6 = 68*1.25 = 85

Total number of trains passing through platform number 6 = 40+85 = 125 - Find the ratio of number of trains passing through platform number 2 to the total number of trains passing through platform number 3?
1:33:24:55:73:4Option C

Total number of trains passing through platform number 2 = 56+40 = 96

Total number of trains passing through platform number 3 = 48+72 = 120

Required ratio = 4:5 - Total number of trains passing through platform number 4 is what percentage more or less than the number of Express trains passing through platform number 3?
32%10%18%25%20%Option D

Total number of trains passing through platform number 4 = 36+54 = 90

Required% = (90-72)/72*100 = 25% - Find the average of the number of passenger trains passing through platform number 1,2 and 3 taken together.
3038445647Option D

Required average = (64+56+48)/3 = 56 - Prakash borrowed some money at the rate of 3 percent per annum for the first 4 years, 7 percent per annum for the next 5 years and at the rate of 9 percent per annum for the next 7 years. If the total interest paid by him at the end of 16 years is 4400. Find the money borrowed by Prakash?

Rs.3000Rs.2000Rs.4000Rs.6000Rs.5000Option C

Let the sum be Rs.x.

(3*4*x)/100 + (7*5*x)/100 + (9*7*x)/100 = 4400

=>x = 440000/110 = Rs.4000 - Prabir invests an amount of Rs.15860 in the names of her three daughters A,B and C in such a way that they get the same interest after 2,3 and 4 years resp. If the rate of interest is 5% p.a. Find the ratio of the amounts invested among A,B and C.
1:4:25:3:73:7:25:1:46:4:3Option E

(P1*2*5)/100 : (P2*3*5)/100 : (P3*4*5)/100

=> 10P1 : 15P2 : 20P3

=>P1:P2:P3 =30:20:15 = 6:4:3 - If numerical value of percentage markup price, marked price per kg and percentage discount offered on marked price of a product are in the ratio 20:12:9. Find the percentage profit on the product.

7.7%9.2%5.8%6.5%8.3%Option B

MP = 12

SP = (100-9)/100*12 = 10.92

Let CP be x.

(100+20)/100*x = 12

=> x= 10

Profit% = 0.92/10*100 = 9.2% - Sahil buys wheat at Rs.10 per kg and puts a price tag on it so as to earn a profit of 30%. However his faculty shows 1 kg when it is actually 700 gm. What is his actual profit percent?

613/2%600/7%515/4%623/8%551/5%Option B

CP of 1 kg = Rs.10

CP of 1 gm = 1/100

SP of 700 gm = Rs.13

SP of 1 gm = 13/700

Profit% = {[13/700 – 1/100]/[1/100]}*100 = 600/7% - To do a certain work A is 100/3% more efficient than B. They started to work alternatively on the same work starting from A on one day and B on day two and finished 60% of work in 30 days. Find the time taken by A alone to finish the whole work?
163/5 days157/2 days166/5 days175/4 days171/3 daysOption D

Ratio of efficiency of A and B is 4:3.

Let in one day A does 4x unit of work and in one day B does 3x unit of work.

In 30 days 60% work is completed.

So, in 50 days whole work will be completed.

In 2 days 7x unit is completed so in 50 days.

= 50*7x/2 unit done

Whole work is completed by A in = (50*7x)/(4x*2) = 175/4 days - A car covered 48 km less in T hours than a train, if speed of train is 25% more than the speed of car, which is 64 km/hr. and speed of an aircraft is 62(1/2)% more than the sum of speed of car and train. Find how much distance will be covered by aircraft in (T-1/4) hour?
873.7 km741.6 km555.5 km643.5 km612.4 kmOption D

Speed of train = 64*5/4

= 80 km/hr.

Now,

80T – 64T = 48

=>T = 3 hours

Speed of Aircraft = (144*13/8) = 234 km/hr.

Required distance = 234*(3 – 1/4) = 643.5 km - Sam invested some amount in scheme P which offers 20% C.I. p.a. while some amount in scheme Q which offers 8% S.I. p.a. After 2 years, ratio of interest earn from P to Q is 11:6. Amount invested by Sam in scheme P is what percent of the amount invested by him in scheme Q.
53(4/5)%66(2/3)%44(2/7)%50(1/2)%61(3/5)%Option B

Let the amount invested in scheme P and Q be x and y resp.

x*[(120/100)^2 – 1]/(y*8*2/100) = 11/6

=>(x*0.44)/(y*0.16) = 11/6

=>x / y = 2/3

Required% = 2/3*100 = 66(2/3)% - There are two vessels A and B which contains mixture of sulphuric acid and nitrous oxide in the ratio of 7:2 and 3:4 resp. Mixture of both vessels are mixed to obtain a mixture of 390 ml, in which quantity of nitrous oxide is 160 ml. Find the ratio of quantity of mixture in vessel A to quantity of mixture in vessel B ?
3:42:56:77:83:5Option C

Let the total mixture of sulphuric acid and nitorus oxide in vessel A and vessel B be x and y resp.

x + y = 390 – (1)

2x/9 + 4y/7 = 160

14x+36y = 10080 –(2)

On solving these two equations, we get

x = 180 ml

y = 210 ml

Required ratio = 6:7 - The surface of sphere is 423.5 cm^2 less than total surface area of a hemisphere. If ratio between radius of hemisphere and sphere is 3:2. Find the radius of hemisphere?
8.4 cm12.3 cm13.7 cm7.4 cm10.5 cmOption E

3*pi*r*r*r – 4*pi*r*r = 423.5

=>x = 3.5 cm

Radius of hemisphere = 21/2 = 10.5 cm - In first bucket there are five apples, Y oranges and 7 bananas. Probability of drawing one orange from bucket is 2/5. In second bucket there are (Y-3) apples, (Y-4) oranges and 6 bananas, if two fruits are drawn from second bucket. Find the probability that both are apples?

1/174/272/214/233/19Option C

Probability of drawing one orange = Y/(12+Y) = 2/5

=> Y = 8

Required Probability = 5C2/15C2 = 2/21

**Directions(5-20): **What will be the approximate value come in place of question mark ‘?’ in the following questions.

**Directions(21-25):** Answer the following questions based on the following graph.

The given chart shows the number of Passenger trains and Express trains passing through different platforms of a railway station on a particular day.