Quant Test for SBI PO Prelims Exam set – 09

Banya
  1. 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(1/2) days
    4(1/6) days
    7(1/3) days
    8(1/2) days
    3(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

     

  2. 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.8100
    Rs.7500
    Rs.9000
    Rs.6200
    Rs.7000
    Option B
    Saving % = 100 – (20 + 56) = 24%
    24% = 1800
    100% = 1800/24*100 = Rs.7500

     

  3. A and B are partners in a business. They invest in the ratio 5 : 6, at the end of 8 months A withdraws. If they receive profits in the ratio of 5 : 9, find how long B’s investment was used?
    14
    8
    10
    16
    12
    Option E
    5x : 6x, Let B investment was used for y months
    8*5 x : 6x *y = 5 : 9
    =>y= 12

     

  4. A train is moving at a speed at a speed of 132 km/hour. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?
    7.5 seconds
    9.1 seconds
    8.6 seconds
    3.3 seconds
    4.2 seconds
    Option A
    132*5/18 = (100+165)/x
    =>x = 7.5 seconds

     

  5. A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has atleast one woman?
    5/14
    9/10
    6/13
    7/12
    8/11
    Option B
    Probability = (2C1*3c2 + 2c2*3c1)/5c3 = 9/10

     

    6. Directions(6-10): Find the values of x and y and then compare them and choose a correct option.

  6. I. 4x + 7y = 42
    II. 3x – 11y = – 1

    y >x
    y>=x
    x>=y
    x > y
    No relation
    Option D
    On solving both the equations, we get x = 7
    y = 2
    x > y

     

  7. I. 3x^2 – 19x – 14 = 0
    II. 2y^2 + 5y + 3 = 0

    x>=y
    x > y
    y >x
    No relation
    y>=x
    Option B
    I. 3x^2 – 19x – 14 = 0
    =>3x^2 -21 x + 2x – 14 = 0
    =>3x (x -7) +2(x -7) = 0
    =>(x-7)(3x+2) = 0
    =>x = 7, -3/2
    II. 2y^2 + 5y + 3 = 0
    =>2y^2 +2y +3y + 3 = 0
    =>2y (y+1) + 3(y+1) = 0
    =>(y+1)(2y+3) = 0
    =>y = -1, -3/2
    x > y

     

  8. I. x^2 + 14x + 49 = 0
    II. y^2 + 9y = 0

    x>=y
    y>=x
    No relation
    x > y
    y >x
    Option C
    I. x^2 + 14x + 49 = 0
    =>X^2 + 7X+7X + 49 = 0 =>x(x+7)+7(x+7) = 0
    =>(x+7)(x+7) = 0
    =>x = -7,-7
    II. y^2 + 9y = 0
    =>y = -9,0
    No relation

     

  9. I. 3x^2 – 4x – 32 = 0
    II. 2y^2 – 17y + 36 = 0

    x>=y
    No relation
    y>=x
    y >x
    x > y
    Option C
    I. 3x^2 – 4x – 32 = 0
    =>3x^2 – 12x + 8x – 32 = 0
    => 3x(x – 4) + 8(x -4) = 0
    =>(x-4)(3x+8) = 0
    =>x = 4,-8/3
    II. 2y^2 – 17y + 36 = 0
    =>2y^2 – 8y – 9y + 36 = 0
    =>2y(y- 4) -9(y-4) = 0
    =>(y-4)(2y-9) = 0
    =>y = 4,4.5
    y>=x

     

  10. I. 9x^2 – 29x + 22 = 0
    II. y^2 – 7y + 12 = 0

    No relation
    x > y
    y>=x
    y >x
    x>=y
    Option D
    I. 9x^2 – 29x + 22 = 0
    =>9x^2 – 18x – 11 x + 22 = 0
    =>9x (x-2) -11(x-2) = 0
    =>(x-2)(9x-11) = 0
    =>x = 2,11/9
    II. y^2 – 7y + 12 = 0
    =>y^2 -4y -3y + 12 = 0
    =>y(y-4) -3 (y -4) = 0
    =>(y-4)(y-3) = 0
    =>y = 4,3
    y >x

     



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