Quant Test for IBPS PO 2018 Prelim Exam Set – 21

Directions(1-5): Find the relation between I and II and choose a correct option.

1. I. 4x^2 – 25x + 36 = 0
   II. 2x^2 – 19x + 44 = 0
   I>=II
   II>=I
   II>I
   I = II or relation cannot be established.
   I>II
   Option B
   I. 4x^2 – 25x + 36 = 0
   => 4x^2 – 16x – 9x + 36 = 0
   => x = 9/4,4
   II. 2x^2 – 19x + 44 = 0
   => 2x^2 – 8x – 11x + 44 = 0
   => x = 11/2,4
   II >= I

    

2. I.3x + 5y = 32
   II.8x – 4y = 16
   I>II
   I = II or relation cannot be established.
   II>I
   I>=II
   II>=I
   Option B
   I = II = 4

    

3. I.x^2 – 27x + 180 = 0
   II.y^2 – 20y + 96 = 0
   I>II
   I = II or relation cannot be established.
   II>=I
   II>I
   I>=II
   Option E
   I.x^2 – 27x + 180 = 0
   => x^2 – 15x – 12x + 180 = 0
   => x = 15, 12
   II.y^2 – 20y + 96 = 0
   => y^2 – 12y -8y + 96 = 0
   => y = 12, 8
   I >= II

    

4. I.3x^2 – 17x + 10 = 0
   II.y^2 – 11y + 30 = 0
   I = II or relation cannot be established.
   II>I
   I>=II
   I>II
   II>=I
   Option E
   I.3x^2 – 17x + 10 = 0
   => 3x^2 – 2x – 15x + 10 = 0
   => x = 2/3,5
   II.y^2 – 11y + 30 = 0
   => y^2 – 6y – 5y + 30 = 0
   => y = 6,5
   II >= I

    

5. I.x^2 –x – 6 = 0
   II.y^2 + 7y + 12 = 0
   I>=II
   II>=I
   I>II
   II>I
   I = II or relation cannot be established.
   Option C
   I.x^2 –x – 6 = 0
   => x^2 – 3x + 2x – 6 = 0
   => x = 3, -2
   II.y^2 + 7y + 12 = 0
   => y^2 +3y + 4y + 12 = 0
   => y = – 3 , – 4
   I>II

    

6. 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?
   100 bottles
   162 bottles
   150 bottles
   174 bottles
   181 bottles
   Option B
   Volume of hemi-sphere = 2/3*pi*(27)^3 cm^3
   Volume of cylindrical bottle = pi*(3)^2*9 cm^3
   Required No. of bottles = Volume of hemi-sphere/ Volume of cylindrical bottle
   = 162 bottles

    

7. According to a new plan rolled out by HISP Bank, the rate of simple interest on a sum of money is 8% p.a. for the first two years, 10% p.a. for the next three years and 6% p.a. for the period beyond the first five years. Simple interest accrued on a sum for a period of eight years is Rs. 12,800. Find the sum.
   Rs. 30000
   Rs. 25000
   Rs. 40000
   Rs. 50000
   Rs. 20000
   Option E
   Let the sum be Rs. ‘x’.
   [x*8*2]/100 + [x*10*3]/100 + [x*6*3]/100 =12800
   => 64x/100 = 12800
   => x = Rs. 20000

    

8. 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?
   18
   12
   20
   8
   14
   Option B
   5x : 6x Let B investment was used for y months
   8 * 5x : 6x * y = 5 : 9
   => 40x/60xy = 5/9
   Y = 12

    

9. 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., then find the speed of the train B.
   60 km/hr.
   58 km/hr.
   52 km/hr.
   54 km/hr.
   44 km/hr.
   Option D
   S2/S1 = (24/5/10/3)^1/2
   => S2 = 45*6/5 = 54 km/hr.

    

10. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
    1100
    1212
    1260
    1242
    1990
    Option C
    A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.
    Now, the captain can be selected from these 6 players in 6 ways.
    Therefore, total ways the selection can be made is 210×6 = 1260