Quant Sectional Test 1 for SBI PO 2019 Prelim Exam

Directions(1-5): Find out the values of x and y and then choose a correct option.

1. I.x^2 + 31x +234 = 0
   II.y^2 – 2y – 195 = 0
   
   x > y
   x >= y
   y > x
   y >= x
   No relation
   Option D
   I.x^2 + 31x +234 = 0
   =>x^2 + 18x + 13x + 234 = 0
   =>(x+18)(x+13) = 0
   =>x = -18,-13
   II.y^2 – 2y – 195 = 0
   =>y^2 – 15y + 13y – 195 = 0
   =>(y-15)(y+13) = 0
   =>y = -13,15
   y >= x
   

    

2. I.3x^2 – 15x + 18 = 0
   II.3y^2 = 4y + 15
   
   x >= y
   y >= x
   x > y
   y > x
   No relation
   Option E
   I.3x^2 – 15x + 18 = 0
   =>3x^2 – 9x – 6x + 18 = 0
   =>(3x-6)(x-3) = 0
   =>x = 2,3
   II.3y^2 = 4y + 15
   =>3y^2 – 9y + 5y – 15 = 0
   =>(3y+5)(y-3) = 0
   =>y = -5/3,3
   No relation
   

    

3. I.x^2 – 16x + 63 = 0
   II.y^2 – 11y + 30 = 0
   
   y >= x
   y > x
   x >= y
   x > y
   No relation
   Option D
   I.x^2 – 16x + 63 = 0
   =>x^2 – 9x – 7x + 63 = 0
   =>(x-9)(x-7) = 0
   =>x = 9,7
   II.y^2 – 11y + 30 = 0
   =>y^2 – 5y – 6y + 30 = 0
   =>(y-5)(y-6) = 0
   =>y = 5,6
   x > y
   

    

4. I.5x^2 – 18x + 16 = 0
   II.3y^2 – 13y + 14 = 0
   
   y > x
   x > y
   x >= y
   y >= x
   No relation
   Option D
   I.5x^2 – 18x + 16 = 0
   =>5x^2 – 10x – 8x + 16 = 0
   =>(x-2)(5x-8)= 0
   =>x = 2,8/5
   II.3y^2 – 13y + 14 = 0
   =>3y^2 – 6y – 7y + 14 = .
   =>(y-2)(3y -7) = 0
   =>y = 7/3,2
   y >= x
   

    

5. I.11x + 9y = 169
   II.13x – 5y = 59
   
   y >= x
   x >= y
   x > y
   y > x
   No relation
   Option D
   Solving both the equations, we get
   x = 8
   y = 9
   y > x
   

    

6. The upstream speed and downstream speed of a boat is 32 km/hr and 40 km/hr resp. Find the time taken by the boat to travel a distance of 240 km upstream when the speed of the stream is 50% more than its usual speed?
   3 hours
   6 hours
   9 hours
   5 hours
   8 hours
   Option E
   Speed of boatman in still water = (32+40)/2 = 36 km/hr.
   Speed of stream = (40-32)/2 = 4 km/hr.
   New upstream speed = 36 – 1.5*4 = 30 km/hr.
   Required time = 240/30 = 8 hours
   

    

7. A and B together can do a piece of work in 12 days. A,B and C together can do the same work in 8 days. In how many days can C alone can do the same piece of work?
   26 days
   24 days
   25 days
   20 days
   28 days
   Option B
   Total work = 24 units
   A and B can do work in one day = 24/12 = 2 units
   A, B and C together in one day = 24/8 = 3 units
   work done by C alone in one day = 3-2 = 1 unit
   Time taken by C alone to complete the work = 24/1 = 24 days
   

    

8. Train A of length 240 m can cross a train B of length 460 m (stationary) in 35 seconds. Find the time taken by both trains to cross each other while moving opposite direction, if train B is moving at a speed 25% less than speed of train A.
   
   25 seconds
   10 seconds
   20 seconds
   15 seconds
   18 seconds
   Option C
   Let the speed of train A be x m/s.
   (240+460)/x = 35
   =>x = 20 m/s
   Speed of train B = 20*0.75 = 15 m/s
   Required time = (240+460)/(20+15) = 20 seconds
   

    

9. Mrs. Sharma invests 15% of her monthly salary, i.e., Rs. 4428 in Mutual Funds. Later she invests 18% of her monthly salary on Pension Policies also she invests another 9% of her salary on Insurance Policies. What is the total monthly amount invested by Mrs. Sharma?
   
   16329
   18520
   14580
   12398
   13125
   Option D
   15% → 4428
   1% → 4428/15
   ( 15 + 18 + 9) = 42% → 4428
   15 × 42 → Rs. 12398.4 == 12398
   

    

10. A trader sells two bullocks for Rs. 8,400 each, neither losing nor gaining in total. If he sold one of the bullocks at a gain of 20%, what is the loss of other sold ?
    17(3/7)%
    13(1/3)%
    12(3/4)%
    14(2/7)%
    11(2/5)%
    Option D
    S.P. of two bullock = 8400 + 8400 = Rs. 16800
    CP of first bullock = 100/120*8400 = 7000
    CP of second bullock =16800 – 7000
    Required % loss = [9800-8400]/9800*100 = 14(2/7)%
    

     

11. The average weight of a class of (x+5) students is 48 kg. If the weight of a student whose weight is 70 kg is excluded, find the average weight of the class decreases by 0.5 kg. Find the value of x.
    30
    60
    40
    50
    80
    Option C
    Total weight = (x+5)
    48(x+5) – 70 = (48 -0.5)*(x+5-1)
    =>x = 40
    

     

12. Out of his total income, Mr. Kapoor spends 20% on house rent and 70% of the rest on house hold expenses. If he saves Rs 1,800 what is his total income (in rupees)?
    
    Rs.6600
    Rs.7000
    Rs.8800
    Rs.7500
    Rs.8100
    Option D
    Saving % = 100 – (20 + 56) = 24%
    24% = 1800
    100% = 1800/24*100 = Rs.7500
    

     

13. A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?
    180
    162
    125
    170
    154
    Option B
    Volume of hemi-sphere = 2/3*pi*27*27*27 cm^3
    Volume of cylindrical bottle = pi*3*3*9
    Required no. of bottles = 162 bottles {Divide hemisphere volume to the cylinder}
    

     

14. A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying. How many days must A now work alone to complete the work?
    9(1/7) days
    8(1/4) days
    7(1/3) days
    5(1/2) days
    6(1/5) days
    Option C
    In 6 days part of the work done by A = 6/8 = ¾
    During 2 days, part of the work destroyed by B = 2/3
    work done = ¾ – 2/3 = 1/12
    Remaining work = 1 – 1/12
    Required no. of days = 11/12 × 8 = 7(1/3) days
    

     

15. Two trains, A and B, start from stations X and Y towards each other, they take 4 hours 48 minutes and 3 hours 20 minutes to reach Y and X respectively after they meet if train A is moving at 45 km/hr., find the speed of the train B.
    54 km/hr.
    38 km/hr.
    44 km/hr.
    61 km/hr.
    50 km/hr.
    Option A
    S2/S1 = (24/5)^1/2/(10/3)^1/2 = (36)^1/2/(25)^1/2 = 6/5
    S2 = 6/5*45 = 54 km/hr.
    

     

Directions(16-20): Find the missing ‘?’ term of the following series.

16. 19,10,11,24,100,?
    
    950
    700
    808
    660
    740
    Option C
    19*0.5+0.5 = 10
    10*1+1 = 11
    11*2+2 = 24
    24*4+4 = 100
    100*8+8 = 808
    

     

17. 21,38,?,174,293,446
    
    77
    80
    95
    89
    65
    Option D
    +17*1
    +17*3
    +17*5
    +17*7
    +17*9
    ? = 89
    

     

18. 563,562,558,549,?,508
    459
    533
    420
    600
    580
    Option B
    -1^2,-2^2,-3^2,-4^2,-5^2
    ?= 533
    

     

19. 21,44,?,104,141,182
    68
    73
    80
    92
    78
    Option B
    +23,+29,+31,+37,+41
    ? = 73
    

     

20. 13,14,16,22,?,166
    40
    46
    38
    59
    64
    Option B
    +1!,+2!,+3!,+4!,+5!
    ? = 46
    

     

Directions(21-25): Answer the questions based on the following information.
The chart given shows the percentage distribution of the number of employees who wear spectacles in five different companies. Total number of employees in five companies together is 4500.


21. If the number of employees who donot wear spectacles in company E is 12.5% more than the number of employees who wear spectacles in the same company. Find the number of employees in the company E.
    477
    385
    459
    562
    440
    Option C
    Number of employees in company E who donot wear spectacles = 112.5% of 216 =243
    Required number of employees in company E = 243+216 = 459
    

     

22. If the respective ratio of the number of male employees to female employees of company D who wear spectacles is 11:7. Find the number of female employees who wear spectacles in company D.
    
    150
    136
    168
    147
    140
    Option D
    Required number of female employees = 7/18*378 = 147

     

23. If the total number of employees in company D was 730. Find the number of employees who donot wear spectacles in the same company.
    
    312
    352
    367
    348
    330
    Option B
    Number of employees who donot wear spectacles = 730 – 378 = 352

     

24. If the ratio of the number of employees who wear spectacles to the number of employees who donot wear spectacles in company B is 3:2 resp. Find the number of employees in company B.
    
    1620
    1350
    1480
    1710
    1220
    Option B
    Number of employees who wear spectacles in company B = 810
    Number of employees who donot wear spectacles in company B = 810*2/3 = 540
    Required number of employees in company B = 810+540 = 1350
    

     

25. Find the difference between the number of employees who wear spectacles in company A and that of the same company C.
    186
    170
    144
    162
    159
    Option D
    Required Difference = 729 – 567 = 162

     

Directions(26-35): What will be the value of question mark ‘?’ in the following questions.

26. 251 + ? + 317 – 469 = 358 – 297 + 343
    315
    258
    296
    305
    385
    Option D
    251 + ? + 317 – 469 = 358 – 297 + 343
    =>? + 568 – 469 = 701 – 297
    =>? + 99 = 404
    =>?= 305
    

     

27. (81^5 / 27^8)* 9^5 = 3^(? – 2)
    9
    10
    8
    12
    4
    Option C
    (81^5 / 27^8)* 9^5 = 3^(? – 2)
    .=> {(3^4)^5 / (3^3)^8 }*(3^2)^5 = 3^(?-2)
    =>? = 8
    

     

28. (484)^1/2 + (784)^1/2 – (361)^1/2 = 25% of ?
    148
    135
    161
    150
    124
    Option E
    (484)^1/2 + (784)^1/2 – (361)^1/2 = 25% of ?
    =>22 + 28 – 19 = 25% of ?
    =>? = 124
    

     

29. 893 + ?^2 – 724 = 18*25 + 16*5
    
    22
    15
    12
    19
    10
    Option D
    893 + ?^2 – 724 = 18*25 + 16*5
    =>?^2 + 169 = 450+80
    =>?^2 = 361
    =>? = 19
    

     

30. (16)^2 + 219.98% of 20 = ?
    500
    400
    100
    200
    300
    Option E
    (16)^2 + 219.98% of 20 = ?
    = >256 + 220% of 20 = ?
    =>? = 300
    

     

31. (600% of 75)/45 = ?^2 – (676)^1/2
    6
    8
    9
    5
    4
    Option A
    (600% of 75)/45 = ?^2 – (676)^1/2
    =>(600% of 75)/45 = ?^2 – 26
    =>450/45 = ?^2 – 26
    =>? = 6
    

     

32. 12% of 375 = 20% of ? + 25% of 140
    20
    25
    35
    50
    45
    Option D
    12% of 375 = 20% of ? + 25% of 140
    =>12^ of 375 = 20% of ? + 25% of 140
    =>? = 50
    

     

33. 7.5% of 140 + 2.5% of 80 = ?
    17.9
    12.5
    18.1
    14.4
    10.8
    Option B
    7.5% of 140 + 2.5% of 80 = ?
    =>7.5/100*140 + 2 = ?
    =>? = 12.5
    

     

34. (1024 – 263 – 233)/( 986 – 764 – 156) = ?
    
    9
    6
    5
    8
    7
    Option D
    (1024 – 263 – 233)/( 986 – 764 – 156) = ?
    =>(1024 – 496)/(986 – 920) = ?
    =>? = 8
    

     

35. [135/15*32]/?= 45*24
    0.160
    0.212
    0.266
    0.125
    0.121
    Option C
    [135/15*32]/?= 45*24
    =>9*32/ ? = 45*24
    =>? = 0.266