Quant Sectional Test 2 for SBI PO 2019 Prelim Exam


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

  1. I.4x^2 – 23x – 6 = 0
    II.4y^2 + 19y + 12 = 0

    y > x
    No relation
    x > y
    y >= x
    x >= y
    Option C
    I.4x^2 – 23x – 6 = 0
    =>4x^2 – 24x + x – 6 = 0
    =>(x-6)(4x + 1) = 0
    =>x = 6,-1/4
    II.4y^2 + 19y + 12 = 0
    =>4y^2 + 16y + 3y + 12 = 0
    =>(y+4)(4y+3) =0
    =>y = -4,-3/4
    x > y

     

  2. I.x^2 -14x + 48= 0
    II.y^2 – 2y – 63 = 0
    x > y
    x >= y
    y > x
    No relation
    y >= x
    Option D
    I.x^2 -14x + 48= 0
    =>x^2 – 8x – 6x + 48 = 0
    =>(x-6)(x-8) = 0
    =>x = 6,8
    II.y^2 – 2y – 63 = 0
    =>y^2 -9y + 7y – 63 = 0
    =>(y+7)(y-9) = 0
    =>y = -7,9
    No relation

     

  3. I.30x^2 – 49x + 20 = 0
    II.63y^2 – 64y + 16 = 0

    x >= y
    x > y
    y > x
    y >= x
    No relation
    Option B
    I.30x^2 – 49x + 20 = 0
    =>30x^2 – 24x – 25x +20 = 0
    =>(6x-5)(5x-4) = 0
    =>x = 5/6,4/5
    II.63y^2 – 64y + 16 = 0
    =>63y^2 -28y – 36y + 16 = 0
    =>(7y-4)(9y -4) = 0
    =>y = 4/9,4/7
    x > y

     

  4. I.35x^2 – 43x + 12 = 0
    II.42y^2 – 65y + 25 = 0
    x>= y
    y >= x
    No relation
    y > x
    x > y
    Option C
    I.35x^2 – 43x + 12 = 0
    =>35x^2 – 15x – 28x + 12 = 0
    =>(5x-4)(7x-3) = 0
    =>x = 4/5,3/7
    II.42y^2 – 65y + 25 = 0
    =>42y^2 – 30y – 35y + 25 = 0
    =>(6y -5)(7y -5) = 0
    =>y = 5/6,5/7
    No relation

     

  5. I.x^2 + x – 42 = 0
    II.y^2 + 15y + 56 = 0
    y >= x
    x >= y
    y > x
    x > y
    No relation
    Option B
    I.x^2 + x – 42 = 0
    =>x^2 + 7x – 6x – 42 = 0
    =>(x-6)(x+7) = 0
    =>x = 6,-7
    II.y^2 + 15y + 56 = 0
    =>y^2 + 8y + 7y + 56 = 0
    =>(y+8)(y+7) = 0
    =>y = -8,-7
    x >= y

     

  6. A vessel contains a mixture of milk and water in the ratio of 14 : 3. Now, 25.5 liters of the mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of pure milk is added to the mixture. If the resultant mixture contains 20% water, what was the initial quantity of mixture in the vessel before the replacement? (in litres)
    75
    60
    90
    68
    80
    Option D
    Let Milk = 14𝑥
    Water =3𝑥
    Now,
    [14𝑥+5]/[3𝑥+2.5]=4/1
    14𝑥+5=12𝑥+10
    =>2𝑥=5
    => 𝑥=2.5
    Initial quantity =17×2.5+25.5=68

     

  7. In a circular race of 900m length, A and B start with speeds 27 km/hr and 36 km/hr starting at the same time from the same point. When will they meet for the first time at the starting point when running in opposite direction?
    8 min.
    4 min.
    6 min.
    9 min.
    5 min.
    Option C
    Time taken by A to reach start point =900/(27×5)×18 = 120 sec
    Time taken by B to reach start point =900/(36×5)×18 =90 sec.
    LCM of 90 and 120 = 30×3×4 = 360 sec.
    Required time =360/60=6 min.

     

  8. After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. The difference between the ages of the replaced and the new members is :
    10
    13
    15
    11
    12
    Option C
    Let present average =𝑥 year
    Total age =5𝑥 years According to questions 5𝑥−𝑦+𝑧=5𝑥−15
    𝑦-> Old member, 𝑧-> New member
    −𝑦+𝑧=−15
    =>𝑦−𝑧=15

     

  9. A watch dealer usually sells watches for Rs.2350 per watch. Once he gave two successive discounts of 15% and 25% while selling a watch to a customer. But he charged an additional 8% on the net sale price from the customer. By what percent is the new selling price less than the original selling price?
    15.15%
    31.15%
    14.27%
    22.40%
    20.25%
    Option B
    Let usually S.P. = 100
    After discounts price =85/100×75/100×108/100×100 = 68.85%
    Requried % = 100−68.85 =31.15%

     

  10. How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27kg of sugar costing Rs.7 per kg so that there may be gain of 10% by selling the mixture at Rs.9.24 per kg?
    48 kg
    55 kg
    60 kg
    50 kg
    63 kg
    Option E
    Mean price =10/110×9.24
    =10×0.84
    = 8.4

    9 ====7
    ===8.4
    1.4===0.6
    Ratio = 1.4/0.6 = 7/3
    Required Quantity = 27*7/3 = 63 kg

     

  11. 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 one book?
    14
    10
    15
    13
    16
    Option E
    Sum of price of the remaining two
    Books = 12 × 10 – 11.75 × 8
    = 26
    Let cost of First book
    => 260𝑥/100=26
    x = 10
    Price of second book = 10 + 6 = 16

     

  12. A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
    7 km
    5 km
    6 km
    4 km
    8 km
    Option C
    Average speed =2×3×2/(2+3)=12/5 km/hr.
    Total time taken =5 hours

    Distance travelled =12/5×5=12 km

    Therefore, distance between his house and office
    =12/2=6 km

     

  13. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
    30(3/10)%
    33(2/13)%
    32(4/12)%
    40(1/13)%
    45(5/11)%
    Option E
    Total runs scored = 110

    Total runs scored from boundaries and sixes
    =3×4+8×6=60
    Total runs scored by running between the wickets
    =110−60=50
    Required percent
    =50/110×100=500/11= 45(5/11)%

     

  14. A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
    9
    7
    8
    6
    4
    Option C
    Let B joined for xx months. Then

    85000×12:42500×x=3:1
    =>850×12:425x=3:1
    =>850×12×1=3×425x
    =>850×4=425x
    =>x=8

     

  15. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increases by:
    1/2
    1/4
    1/6
    1/7
    1/5
    Option D
    Let the cost of the rental car =x

    When 8 persons share equally, share of one person =x/8

    When 1 person withdraws and other 7 persons share equally, share of one person =x/7

    Increase in the share =x/7−x/8=x/56

    Required fraction =(x/56)/(x/8) = 1/7

     


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

  17. 567, 1140, 2290, ?, 9206, 18434

    4320
    4594
    4425
    4105
    4110
    Option B
    ×2 + 6,×2 + 10,× 2 + 14,× 2+ 18
    ? = 4594

     

  18. 17, 38, ?, 508, 2565, 15426

    111
    120
    105
    123
    116
    Option D
    ×2+ 2^2,×3+3^2,× 4 + 4^2
    ? = 123

     

  19. 2, 60 ,10, 120 ,30, ?
    250
    230
    240
    210
    220
    Option D
    1^3+1, 4^3 – 4,2^3+2,5^3 –5,3^3+3,6^3 – 6
    ? = 210

     

  20. 6,15, 45, 157.5, ?, 2835
    630
    600
    619
    635
    616
    Option A
    ×2.5,× 3,× 3.5,× 4
    ? = 630

     

  21. 210, 130, 60, ? ,6, 2
    30
    40
    50
    60
    80
    Option A
    6^3−6,5^3+5,4^3−4,3^3+3,2^3−2,1^3+1
    ? = 30

     

  22. Directions(21-30):approximate value will come in place of question mark ‘?’ in the following questions.

  23. (60% of 40% of 3250 – 23*24) = ?
    241
    228
    230
    212
    200
    Option B
    (60% of 40% of 3250 – 23*24) = ?
    =>60% of 1300 – 552 = ?
    =>780 – 552 = ?
    =>? = 228

     

  24. [(872/32+12)*4 – (774/43)] = ?
    120
    144
    125
    139
    110
    Option D
    [(872/32+12)*4 – (774/43)] = ?
    =>[(27.25+12)*4 – 18] = ?
    =>39.25*4 – 18 = ?
    =>? = 139

     

  25. (26*7 + 29*4 – 32*5) = ?
    156
    138
    152
    160
    144
    Option B
    (26*7 + 29*4 – 32*5) = ?
    =>182 + 116 – 160 = ?
    =>? = 138

     

  26. 16 of 19 – 702/26 – 17*14 = ?
    40
    45
    42
    39
    30
    Option D
    16 of 19 – 702/26 – 17*14 = ?
    =>304 – 27 -238 = ?
    =>? = 39

     

  27. 228/12 + 16*7 + 75 = ?
    212
    200
    220
    206
    215
    Option D
    228/12 + 16*7 + 75 = ?
    =>19 + 112 + 75 = ?
    =>? = 206

     

  28. 20% of 150 + 323 /17 + (?)^1/2 = 27% of 300
    1010
    1024
    1122
    1325
    1440
    Option B
    20% of 150 + 323 /17 + (?)^1/2 = 27% of 300
    =>30+19 + (?)^1/2 = 81
    =>(?)^1/2 = 81 -49
    =>(?)^1/2 = 32
    =>? = 1024

     

  29. (81)^1/2 *(625)^1/2 + 1225 = (?)^2 – 150
    50
    40
    60
    30
    70
    Option B
    (81)^1/2 *(625)^1/2 + 1225 = (?)^2 – 150
    =>9*25 + 1225 = (?^2 ) – 150
    =>?^2 – 150 = 225+1225
    =>?^2 = 1450+150
    =>? = 40

     

  30. [(256)^1/2 + 192 /8 ]% of 500 = ?^2 of 8
    8
    7
    6
    5
    4
    Option D
    [(256)^1/2 + 192 /8 ]% of 500 = ?^2 of 8
    =>?^2 * 8 = (16+24)% * 500
    =>?^2 * 8 = 40% of 500
    =>?^2 = 200/8
    =>?^2 = 25
    =>? = 5

     

  31. (576)^1/2 + (676)^1/2 *8 = ?% of 250
    130
    100
    150
    160
    140
    Option D
    (576)^1/2 + (676)^1/2 *8 = ?% of 250
    =>?*2.5 = (24+26)*8
    =>?*2.5 = 50*8
    =>? = 400/2.5
    =>? = 160

     

  32. 60% of 250 + 14^2 = ?^2 – (225)^1/2
    15
    19
    17
    18
    16
    Option B
    60% of 250 + 14^2 = ?^2 – (225)^1/2
    =>?^2 – 15 = 0.6*250 + 196
    =>?^ 2= 150+196 +15
    =>?^2 = 361
    =>? = 19

     


  33. Directions(31-35):
    Answer the following questions based on the given information given below:
    The graph represents the number of Amul store opened in different quarters in different years.

  34. The total number of Amul stores opened in 2010 in first quarter and third quarter combined was what percentage of the total number of Amul stores opened in 2011 in first quarter and third quarter combined?
    75%
    65%
    81%
    92%
    70%
    Option C
    Total number of Amul stores opened in 2010 in first and third quarter = 140+160 = 300
    Total number of Amul stores opened in 2011 in first and third quarter = 180+190 = 370
    Required% = 300/370*100 = 81.08% == 81%

     

  35. 30% of the total number of Amul stores opened in 2013 were about to shut down. What was the total number of Amul store opened in 2013 that were about to shut down?
    255
    222
    220
    235
    240
    Option A
    Total number of stores opened in 2013 = 260+150+230+210 = 850
    Total number of stores about to shut down = 0.3*850 = 255

     

  36. What was the ratio of the total number of Amul store opened in third quarter in the given years combined and the total number of Amul store opened in fourth quarter in the given years combined ?
    35:36
    33:38
    32:35
    39:34
    31:29
    Option D
    Total number of Amul stores opened in third quarter in 4 years = 160+190+ 200+230 = 780
    Total number of Amul stores opened in fourth quarter in 4 years = 120+160+190+210 = 680
    Required ratio = 780:680 = 39:34

     

  37. What was the difference between the average of the number of Amul store opened in first quarter in 2010 and 2012 together and the average of the number of Amul store opened in fourth quarter in 2011 and 2013 together?
    16
    14
    12
    10
    18
    Option D
    Average number of Amul store opened in first quarter in 2010 and 2012 together = (140+250)/2 = 195
    Average number of Amul store opened in first quarter in 2011 and 2013 together = (160+210)/2 = 185
    Required Difference = 195-185 = 10

     

  38. Find the total number of Amul stores opened 2009, if the number of Amul stores opened increased by % in 2010
    as compared to the previous year.
    395
    410
    400
    350
    448
    Option C
    Total number of Amul stores opened in 2010 = 140+80+160+120 = 500
    Total number of Amul stores opened in 2009 = 500/1.25 = 400

     


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