Quant Test for IBPS PO 2018 Prelim Exam Set – 15

Directions(1-5): What will come in place of question mark “?” in the following questions.

1. I. 16x^2 + 20x + 6 = 0
   II. 10y^2 + 38y + 24 = 0
   y>x
   y>=x
   x>=y
   x>y
   x=y or relation cannot be established.
   Option D
   Divide both equations by 2 I. 16x^2 + 20x + 6 = 0
   => 8x^2 + 10x + 3 = 0
   => 8x^2 + 4x + 6x + 3 = 0
   x = -1/2, -3/4
   II. 10y^2 + 38y + 24 = 0
   => 5y^2 + 19y + 12 = 0
   => 5y^2 + 15y + 4y + 12 = 0
   y = -4, -4/5
   x > y

    

2. I. 2x^2 – (2 + 2√5)x + 2√5 = 0
   II. 4y^2 – (6 + 2√2)y + 3√2 = 0
   x>y
   x>=y
   y>x
   y>=x
   x=y or relation cannot be established.
   Option E
   I. 2x^2 – (2 + 2√5)x + 2√5 = 0
   => 2x^2 – 2x – 2√5x + 2√5 = 0
   => 2x (x – 1) – 2√5 (x – 1) = 0
   So, x = 1, √5 (2.2)
   II. 4y^2 – (6 + 2√2)y + 3√2 = 0
   => 4y^2 – 6y – 2√2y + 3√2 = 0
   => 2y (2y – 3) – √2 (2y – 3) = 0
   So, y = 3/2, 1/√2 (0.7)
   x = y or relation cannot be established.

    

3. I. 6x^2 + x – 2 = 0
   II. 3y^2 – 22y + 40 = 0
   y>x
   x>=y
   y>=x
   x=y or relation cannot be established.
   x>y
   Option A
   I. 6x^2 + x – 2 = 0
   => 6x^2 + x – 2 = 0
   => 6x^2 + 4x – 3x – 2 = 0
   x = 1/2, -2/3
   II. 3y^2 – 22y + 40 = 0
   => 3y^2 – 22y + 40 = 0
   => 3y^2 – 12y – 10y + 40 = 0
   y = 10/3, 4
   x < y

    

4. I. x^² – (1+√2)x + √2 = 0
   II. y^² – 3y + 2 = 0
   x=y or relation cannot be established.
   x>y
   y>=x
   x>=y
   y>x
   Option A
   I. x^² – x −√2x + √2 = 0
   =>x(x – 1) – √2(x − 1) = 0
   => (x − √2)(x − 1) = 0
   =>x = √2 or 1
   II. y^² – 3y +2 = 0
   => y^² – 2y – y+ 2 = 0
   =>y (y – 2) – 1 (y – 2) = 0
   => (y – 1) (y – 2) = 0
   => y= 1 or 2
   Relation cannot be established between x and y.

    

5. I. x^ 2 − 19x + 84 = 0
   II. y^ 2 − 25y + 156 = 0
   y>x
   y>=x
   x>y
   x=y or relation cannot be established.
   x>=y
   Option B
   I. x ^2 − 19x + 84 = 0
   => x ^2 − 7x − 12x + 84 = 0
   => (x − 7)(x − 12) = 0
   x = 7, 12
   II. y^ 2 − 25y + 156 = 0
   y ^2 − 13y − 12y + 156 = 0
   => (y − 13)(y − 12) = 0
   => y = 13, 12
   y>=x

    

6. Abhishek took a loan at simple interest rate of 6% in the year with an increase of 0.5% in each subsequent year. He paid interest of Rs. 6125 after 5 year. How much loan did he take?
   Rs. 19900
   Rs. 17500
   Rs. 18200
   Rs. 15500
   Rs. 11400
   Option B
   Total interest = Rs. 6125
   Rate = 6% and increasing by 0.5% every year
   Let total Loan Amount = P
   P = [6125 × 100]/[ 6 × 1 + 6.5 × 1 + 7 × 1 + 7.5 × 1 + 8 × 1] = 612500/35 = Rs. 17500

    

7. A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
   190 km.
   170 km.
   180 km.
   150 km.
   200 km.
   Option C
   Speed in downstream = (14 + 4) km/hr = 18 km/hr
   Speed in upstream = (14 – 4) km/hr = 10 km/hr.
   Let the distance between A and B be x km.
   Then, x/18 + (x/2)/10 = 19
   => x/18 + x/20 = 19
   => x = 180 km.

    

8. Every year before the festive season,a shopkeeper increases the price of the product by 35% and then introduce two successive discount of 10% and 15% respectively.what is percentage loss and percentage gain ?
   3.27%
   2.12%
   5.05%
   4.15%
   2.21%
   Option A
   Let CP = 100
   35 % Increase in SP = 135
   10 % Discount = 135((135*10)/100)=13.5
   So, 1st SP =(135-13.5) = 121.5
   Again,
   15 % Discount in 1st SP = ((121.5*15)/100) = 18.225
   2nd SP = (121.5-18.225) = 103.275
   So,finally CP = 100
   SP = 103.275
   Gain = 103.275 – 100 = 3.27%

    

9. Neha’s father was 38 years of age when she was born while her Mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
   7 years
   5 years
   10 years
   6 years
   8 years
   Option D
   Let Neha’s age = x and her brother’s age = x−4
   Neha’s father’s age = x+38
   Neha’s mother’s age =(x−4)+36 = x+32
   Neha’s father’s age – Neha’s mother’s age = (x+38) − (x+32) = 6 years

    

10. Out of the 35 players attending the opening ceremony of an event there are 12 cricketers, 10 wrestlers, 5 badminton players and 8 hockey players. The management wants a cricketer or a wrestler to lead the group in the parade. In how many ways can this be done?
    18
    20
    15
    12
    22
    Option E
    Required ways = 22 ways