Quadratic Equations Quiz for IBPS PO / SBI PO 2017

Directions (1-5): In these questions two equations numbered I and II are given. You have to solve both the equations and mark answer.

(a) X > Y

(b) X ≤ Y

(c) X < Y

(d) X ≥ Y

(e) Relationship between X and Y cannot be established

(a) X ≥ Y

(b) X ≤ Y

(c) X < Y

(d) X > Y

(e) Relationship between X and Y cannot be established

(a) X ≥ Y

(b) X > Y

(c) X ≤ Y

(d) X < Y

(e) Relationship between X and Y cannot be established

(a) X ≥ Y

(b) X > Y

(c) X ≤ Y

(d) X < Y

(e) Relationship between X and Y cannot be established

(a) X ≥ Y

(b) X < Y

(c) X > Y

(d) X ≤ Y

(e) Relationship between X and Y cannot be established

Directions (6-10): In each of these questions, two equations I and II are given. You have to solve both the equations and give answer.

(a) x < y

(b) x > y

(c) x = y

(d) x ≥ y

(e) x ≤ y or no relationship can be established between x and y

Directions (11-15): In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer.

(a) If x > y

(b) If x ≥ y

(c) If x < y

(d) If x ≤ y

(e) x = y or relationship cannot be established

Solutions

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Quadratic Equations Quiz for IBPS PO / SBI PO 2017

Directions (Q. 1–4): In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer

a) if x > y 

b) if x >= y 

c) if x < y

d) if x <= y 

e) if x = y or relationship between x and y cannot be determined.

1. 

I. x^2 + x – 20 = 0

II. y^2 + 13y + 40 = 0

1. b

I. x^2 + 5x – 4x – 20 = 0

(x – 4) (x + 5) = 0

x = 4, – 5

II. y^2 + 8y + 5y + 40 = 0

(y + 8) (y + 5) = 0

y = –8, – 5

x >= y

2. 

I. x^2 – 11x + 30 = 0

II. y^2 – 13y + 40 = 0

2. e

I. x^2 – 6x – 5x + 30 = 0

(x – 5) (x – 6) = 0

x = 5, 6

II. y^2 – 8y – 5y + 40 = 0

(y – 8) (y – 5) = 0

y = 8, 5

No relationship between ‘x’ and ‘y’ exits.

3. 

I. x^2 + 10x + 25 = 0

II. 5y^2– √60 y + 3 = 0

3. c

I. (x + 5)^2 = 0

x = –5

II. (√5y – √3)^2 = 0

y = √3/√5

y>x

4. 

I. 10x^2 – 29x – 21 = 0

II. y^2 + 13y – 68 = 0

4. e

I. 10x^2 – 35x + 6x – 21 = 0

(5x + 3) (2x – 7) = 0

x = -3/5, 7/2

II. y^2 + 17y – 4y – 68 = 0

(y – 4) (y + 17) = 0

y = 4, –17

No relationship between x and y exists.

Directions (Q. 5–7): What value should come in the place of question mark (?) in the following number series?

5. 362, 452, 550, 656, ?

a) 770 

b) 772 

c) 670 

d) 870 

e) 790

5. a

 

6. 25, 28, 26, ?, 27, 30

a) 28 

b) 32 

c) 34 

d) 29 

e) 36

6. d

7. 9, 12, 30, 99, ?

a) 406 

b) 418 

c) 408 

d) 416 

e) 424

7. c

Directions (Q. 8–10): What value should come in the place of question mark (?) in the following questions?

8. 168.781 – 112.412 – 8.409 – 1.150 = ?

a) 44.81 

b) 46.81 

c) 40.81 

d) 47.81 

e) 46.61

8. b

? = 46.81

9. 2.01*8.96 + 128.12/(2.05*1.97) = ?

a) 50 

b) 11 

c) 21 

d) 44 

e) 23

9. a

2.01*8.96 + 128.12/(2.05*1.97) = ?

Or, 2*9 + 128/(2*2) = 18 + 32 = 50 (approx.)

10. 8.5% of 160 – 0.42% of 750 = ?

a) 11.45 

b) 12.45 

c) 13.45 

d) 9.45 

e) 10.45

10. e

? = 8.5/100 * 160 - 0.42/100 * 750

= 13.6 - 3.15 = 10.45

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RBI Assistant Prelims 2016-17 (Important Questions-13)

Directions(1-5): What should come in place of question mark (?) in the following series:

1. 8, 13, 5, 10, 2, ?

A. 5
B. 6
C. 7
D. 8
E. None of these

Sol. 8 + 5 = 13
    13 - 8 = 5
     5 + 5 = 10
    10 - 8 = 2
     2 + 5 = 7

2. 9, 21, 45, 93, 189, ?

A. 361
B. 389
C. 381
D. 379
E. None of these

Sol. 9 + 6*(2^1) = 21
    21 + 6*(2^2) = 45
    45 + 6*(2^3) = 93
    93 + 6*(2^4) = 189
   189 + 6*(2^5) = 381

3. 16, 24, 60, 210, 945, ?

A. 5197.5
B. 5200
C. 5215.5
D. 5205.5
E. None of these

Sol. *1.5, *2.5, *3.5, *4.5, *5.5

4. 31, 34, 71, 216, 867, ?

A. 4338
B. 4348
C. 4368
D. 4388
E. None of these

Sol. *1 + 3, *2 + 3, *3 + 3, *4 + 3, *5 + 3

5. 3, 10, 18, 28, ?

A. 43
B. 41
C. 42
D. 46
E. None of these

Sol. Difference of the difference is : 1, 2, 3.
Thus, answer is 41.

6. The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

(a)8 : 3
(b)7 : 5
(c)4 : 3
(d)2 : 3
(e)none of these

Sol. (1/2-2/5) / (4/7 - 1/2)
Required Ratio = 14/10
= 7 : 5

7. The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

(a)Rs. 5, Rs.7.50
(b)Rs. 8, Rs. 12
(c)Rs. 10, Rs. 16
(d)Rs. 12, Rs. 14
(e)None of these

Sol. Sum of price of the remaining two
Books = (12 * 10) – (11.75 * 8)
= 26
Let cost of First book be x
x + 160x/100 = 26
260x/100 = 26
x = 10
Price of second book = 10 + 6 = 16.

8. Simple interest on the sum of money of Rs.2600 for 2 years at X% per annum is 832. Then what is the interest on Rs.3600 for 3 years at X+3% per annum ?

A. 2000
B. 2068
C. 2052
D. 2130
E. None of these

Sol. As given,

832 = 2600*2*X/100

Thus, X = 16

Now, S.I. = [3600*(16+3)*3]/100

Solving, S.I. = Rs 2052.

9. A sum of Rs 4600 is invested in two different schemes. Scheme A offers 8% rate of interest per annum for 3 years and scheme B offers 10% rate of interest compounded annually for 2 years. If after investing the amount in both schemes, the difference in interests received is Rs 24, find the amount invested in scheme B ?

A. 2100
B. 2400
C. 2500
D. 2600
E. None of these

Sol. (4600-x)*8*3/100 – [x (1 + 10/100)^2 – x] = 24
Solve, x = 2400.

10. The ratio of X’s 3 years hence and Y’s age 3 years ago is 4 : 3. After 7 years from now X’s age will be 10 less than twice Y’s present age. Find the difference between the ages of both ?

A. 3
B. 4
C. 5
D. 2
E. None of these

Sol. (X+3)/(Y-3) = 4/3
so, 3X – 4Y = -21
Also (X+7) = 2Y – 10, so X – 2Y = -17
Solve, both equations, X = 13, Y = 15
Thus, difference = 15 - 13 = 2.

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RBI Assistant Prelims 2016-17 (Important Questions-12)

RBI Assistant Prelims 2016-17 (Important Questions-12)

Directions(1-5): What should come in place of (_) in the following series:

1. 15, 19, 23, 24, 33, 31, 45, _

A. 48
B. 45
C. 40
D. 42
E. None of these

Sol. C) 40.
Two alternating series,
23 - 15 = 8
33 - 23 = 10
45 - 24 = 12

24 - 19 = 5
31 - 24 = 7
Thus, 31 + 9 = 40. 

2. 2, 10, 26, 50, 82, _

A. 120
B. 124
C. 122
D. 125
E. None of these

Sol. 2 + 1*8 = 10
    10 + 2*8 = 26.....

Thus, 82 + 5*8 = 122. 

3. 23, 17, 29, 11, 35, _

A. 25
B. 15
C. 5
D. 0
E. None of these

Sol. 17 - 23 = -6
     29 - 17 = 12
     11 - 29 = -18
     35 - 11 = 24

Thus, 35 - 30 = 5.

4. 3, 7, 31, 191, 1535, _

A. 15390
B. 15350
C. 15359
D. 15345
E. None of these

Sol. 3*2 + 1 = 7
     7*4 + 3 = 31
    31*6 + 5 = 191....

Thus, 1535*10 + 9 = 15359.

5. 5, 6, 35, 88, 161, _

A. 280
B. 250
C. 200
D. 180
E. None of these

Sol. B) 250. 
Difference of the difference is in A.P. of 28, 24, 20, 16.

6. Rajesh has 2 sons. He gave 20% of his income to 1st son and 30% of remaining to 2nd son. He gave 10% of the remaining balance to the charity. He is left with Rs 10,080. Find his income ?

A. 10,000
B. 20,000
C. 30,000
D. 40,000
E. None of these

Sol. Let the income be x.
Balance after giving to 1st son,
= x - 0.2x
= 0.8x
Balance after giving to 2nd son,
= 0.8x - 0.3*0.8x
= 0.56x
Balance after giving to charity,
= 0.56x - 0.1*0.56x
= 0.504x

Thus, 0.504x = 10080
Solving, x = Rs 20,000.

7. The Cost Price of 40 articles is same as the Selling Price of 25 articles. Find the gain per cent.

A. 60%
B. 50%
C. 40%
D. 45%
E. None of these

Sol. Gain(%) = [(40-25)/25]*100 = 60%.

8. A jet covers a certain distance at a speed of 240 km/hr in 5 hrs. To cover the same distance in 1.5 hrs, it must travel at a speed of ?

A. 720
B. 640
C. 580
D. 800
E. None of these

Sol. Let the speed be v km/hr.
Then, 240*5 = 1.5v
Solving, v = 800 km/hr.

9. Out of 5 women and 3 men, a committee of 3 members is to be formed in such a way that atleast 1 member is man. How many ways this can be done ?

A. 45
B. 46
C. 47
D. 48
E. None of these

Sol. 5c2 * 3c1 + 5c1 * 3c2 + 3c3
= 30 + 15 + 1
= 46.

10. 2 coins are tossed simultaneously. Find the probability that both outcomes are head ?

A. 1/4
B. 2/5
C. 1/2
D. 3/5
E. None of these

Sol. Total cases = 4
Favorable cases = 1
Required Prob. = 1/4.

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RBI Assistant Prelims 2016-17 (Important Questions-11)

RBI Assistant Prelims 2016-17 (Important Questions-11)

1. Normally it takes 6 hrs for tap A to fill a tank but accidently tap B was opened due to which tank was filled 2 hrs earlier. If the tank is emptied completely and tap B is opened then how long will it take to fill the tank ?

A. 10 hrs
B. 12 hrs
C. 13 hrs
D. 11 hrs
E. None of these

Sol. Lets assume it takes 'x' hrs for tap B to fill the tank.
Then, 1/6 + 1/x = 1/4
Solving, x = 12 hrs.

2. The length of the rectangle is 20cm and the breadth is 8cm more than twice the length of the rectangle. The area of the square is 15 times the area of rectangle. Find the perimeter of square ?

A. 400
B. 450
C. 480
D. 460
E. None of these

Sol. Breadth = 2*20 + 8 = 48cm
Area of rectangle = 20*48
As given, area of square = 15*20*48 = 14400
Thus, side of the square = 120cm
Perimeter of square = 4*120 = 480cm.

3. Suresh purchased a phone at Rs 5000 and sold it at a gain of 20%. From this amount he purchased another phone and sold it at 10% loss. Find its overaall loss/gain ?

A. 500
B. 400
C. 300
D. 600
E. None of these

Sol. Second S.P. = 5000*(120/100)*(90/100) = Rs 5400
Total Gain = 5400 - 5000 = Rs 400.

4. The present age ratio of Rajesh and Mahesh is 3:8. Mahesh's present age is 12 yrs less than Rohan's present age. Rohan's age will be 50 yrs after 6 yrs. Find Rajesh's present age ?

A. 15
B. 12
C. 30
D. 28
E. None of these

Sol. R/M = 3/8     (where Rajesh's age is R and Mahesh's age is M)
Also, M = Ro -12 (where Rohan's age is Ro)
Also, Rohan's age is = Ro = 50 - 6 = 44 yrs.
Thus, solving, we get, R = 12 yrs.

5. In an election there were only two candidates . One of the candidates secured 40% of votes and is defeated by other candidate by 300 votes. The total number of votes polled is ?

A. 1200
B. 1500
C. 1250
D. 1350
E. None of these

Sol. Lets assume the total number of votes is 'x'.
Thus, x(60-40)/100 = 300
Solving, x = 1500 votes.

Directions(6-10): What should come in place of (_) in the following series:

6. 13,14,30,93, _

A. 382
B. 376
C. 366
D. 327
E. 380

Sol. B.376
13 * 1 + 1 = 14
14 * 2 + 2 = 30
30 * 3 + 3 = 93

7. 9,11,16,33,98,_

A. 326
B. 336
C. 331
D. 340
E. 355  

Sol. E.355
11 – 9 = 2
16 – 11 = 5
33 – 16 = 17;( 5 – 2 = 3; 17 – 5 = 12(3*4))

8. 8,14,25,46,82,_

A. 138
B. 153
C. 166
D. 139
E. 135

Sol. A.138
14 – 8 = 6
25 – 14 = 11
46 – 25 = 21; 11 – 6 = 5, 21 – 11 = 10

9. 65, 70, 63, 74, 61, _

A. 76
B. 78
C. 71
D. 76
E. 73 

Sol. B.78
65 – 63 = 2
74 – 70 = 4
63 – 61 = 2

10. 14, 8, 7, 11.5, 22, _

A. 54
B. 59
C. 56
D. 58
E. 51

Sol. C.56
14 * 0.5 + 1 = 8
8 * 1 – 1 = 7

7 * 1.5 + 1 = 11.5 

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RBI Assistant Prelims 2016-17 (Important Questions-10)

RBI Assistant Prelims 2016-17 (Important Questions-10)

1. 5 years ago, the ratio of age of Rajesh and his son was 12:5. 5 years hence, Rajesh's age is 10 years more than double his son's age. Find present Rajesh's age ?

A. 60
B. 65
C. 70
D. 75
E. None of these

Sol. Lets assume Rajeesh's present age to be 'x'
And his son's present age to be 'y'

According to the question, 
(x-5)/(y-5) = 12/5

and 

(x+5) = 2(y+5) + 10

Solving these, we get,
x = 65 years.

2. Two cards are drawn from a peck of 52 cars, one after another without replacement, such that if 1st card drawn is honour card then 2nd card will also be a honour card. Find the probability of getting atleast 1 honour card ?

A. (36*35)/(52*51)
B. (16*15)/(52*51)
C. 1 - (36*35)/(52*51)
D. 1 - (16*15)/(52*51)
E. None of these

Sol. Probability of having atleast one honour card = 1 - probability of drawing none honour card.
Thus, Probability of drawing no honour card = (36/52)*(35*51)
Therefore, required prob. = 1 - (36*35)/(52*51).

3. Rajesh sells two maachines each of Rs 8400 to Mahesh such that no profit or loss is made. If he sold 1st one for 20% gains then what loss% he sold the 2nd one ?

A. 15%
B. 20%
C. 25%
D. 10%
E. None of these

Sol. As cost of both product is same thus to negate the 20% gain it should be 20% loss.

4. Ashish spends 20% in rent, 70% of the rest in house-hold expenses and saves Rs 1800. Find his income ?

A. 6000
B. 7000
C. 7500
D. 6500
E. None of these

Sol. Lets assume Ashish's income to be 'x'
Then, Rent = 20x/100 = 0.2x
House-hold expenses = (70/100)*(80x/100) = 0.56x

According to the question,
x - (0.2x + 0.56x) = 1800
Solving, x = Rs 7,500.

5. X and Y invested in a business in the ratio of 5:6. At the end of 8 months X withdraws from it. If the profit is in the ratio of 5:9. For how long Y's investment was used ?

A. 10 months
B. 11 months
C. 12 months
D. 15 months
E. None of these

Sol. Lets assume the number of months Y made his investment be 'y'.
Then, (5*8)/(6*y) = 5/9
Solving, y = 12 months.

Directions(6-10): What should come in place of (_) in th following series:

6. 14, 6, 4, 4, 8, _

A. 26
B. 32
C. 46
D. 27
E. None of these

Sol. B.32
     14 * 1 – 8 = 6
      6 * 2 – 8 = 4
      4 * 3 – 8 = 4

7. 6, 16, 45, 184, 917, _

A. 5506
B. 4756
C. 5786
D. 5686
E. None of these 

Sol. A.5506
     6 * 2 + 4 = 16
    16 * 3 – 3 = 45
    45 * 4 + 4 = 184

8. 24, 28, 19, 35, 10, _

A. 46
B. 56
C. 66
D. 65
E. None of these

Sol. A.46 
    24 + 4 = 28
    28 – 9 = 19
    19 + 16 = 35 

9. 15, 22, 36, 64, _, 232

A. 120
B. 140
C. 180
D. 150
E. None of these

Sol. A.120
     22 – 15 = 7
     36 – 22 = 14
     64 – 36 = 28

10. 12, 8, 16, 48, 184, _

A. 560
B. 420
C. 860
D. 550
E. None of these

Sol. C.860
     12 * 0.5 + 2 = 8
      8 * 1.5 + 4 = 16

     16 * 2.5 + 8 = 48

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RBI Assistant Prelims 2016-17 (Important Questions-8)

RBI Assistant Prelims 2016-17 (Important Questions-8)

1. A boy multiplied a number by 3/5 instead of 5/3, what is the percentage error in the calculation ?

A. 65%
B. 64%
C. 60%
D. 68%
E. None of these

Sol. Lets assume the number be 'x'.
Difference in result = 5x/3 - 3x/5

Percentage error = [(5x/3 - 3x/5)/(5x/3)]*100 = 64%.

2. The average weights of 3 groups of friends of 50, 30 and 20 members respectively are 50kg, 52kg and 55kg. What is the average weight of all friends taken together ?

A. 51
B. 51.6
C. 52.6
D. 55.3
E. None of these

Sol. = [(50*50)+(30*52)+(20*55)]/100
= 51.6 kg.

3. Present ages of father and the son are in the ratio of 6:! respectively. 4 yrs hence the ratio of their ages will become 4:! respectively, what is the son's present age ?

A. 6
B. 8
C. 9
D. 4
E. None of these

Sol. Son's age = x
     Father's age = 6x

According to the question, (6x+4)/(x+4) = 4/1
Solving, x = 6 years.

4. P is twice as good a workman as Q and Q is twice as good a workman as R. If P and Q can together finish a piece of work in 4 days, then R can do it by himself in ?

A. 20
B. 24
C. 28
D. 32
E. None of these

Sol. R completes the work in 'y' days
     Q completes the work in 'y/2' days
     P completes the work in 'y/4' days

In 1 day P and Q working together, 
= 4/y + 2/y 
= 6/y
Thus, complete the work in 'y/6' days.
y/6 = 4
y = 24 days.

5. A boy has 6 friends to invite . In how many ways can he send the invitation cards to them, if he has three servants to carry the cards ?

A. 216
B. 729
C. 243
D. 256
E. None of these

Sol. Number of ways = 3^6 = 729 ways.

Directions(6-10): What approximate value should come in place of the question mark (?) in the following questions ?

6. 25.675% of 1321 + 64.328% of 4001= ___?__

A. 2912
B. 3016
C. 3126
D. 3254
E. 3348

Sol. A. 2912

7. 11.001 × ? × 25.875 = 678543

A. 2380
B. 2381
C. 2382
D. 2383
E. None of these

Sol. D : 2383
    ? =678543 / (11.001 ×25.875)
    ? = 678543 / 284.7
    ? = 2383

8. 118.07 × 13.49 + 169.8% of 784 = ?

A. 2870
B. 2760
C. 2930
D. 2650
E. 2860

Sol. C: 2930
    ? nearly equals to 118 × 13.5 + (170 * 785)/100
    = 1593 + 1334.5 = 2927.5 nearly equals to 2930

9. 49.80 % of 750.08 ÷ 11.02 = 56.09 –  ?

A.34
B.16
C.22
D.27
E.None of these

Sol. C : 22
     50% of 750÷11 = 56 – x
     375/11 = 56 – x
     34.09 = 56 – x
     X = 56 – 34.09 = 21.91 = 22

10. 17.38% of 1557 – 21.012 × 8.97 = ?

A. 100
B. 175
C. 95
D. 80
E. 150

Sol. D : 80
    ? nearly equals to (17.4*1550)/100 - 21/9

    = 269.7 - 189 = 80.7 nearly equals to 80. 

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