Quant Test for LIC AAO Prelims Exam Set – 1

Directions(1-10): The following questions consists of two statements,you have to decide whether the data provided in the statements are sufficient to answer.

1. Nik invested certain amount of money in a scheme offering 10% compound interest compounded annually. Kim invested Rs.1000 more than Nik in another scheme offering 9% simple interest. Find the amount invested by Nik.
   Statement I: Difference in the interests earned by Nik and Kim after two years is Rs.90
   Statement II: Difference in the interests earned by Nik and Kim after three years is Rs.279.
   II alone is sufficient.
   Both together necessary.
   I alone is sufficient.
   Either I or II.
   Both are not sufficient.
   Option A
   Let the amount invested by Nik and Kim be Rs. x and Rs.(x+1000) resp.
   From I: Interest earned by Nik after two years = x*{(1+0.10)^2 – 1} = Rs.0.21x
   Interest earned by Kim after two years = (x+1000)*0.09*2 = Rs.0.18x+180
   Either == 0.21x – 0.18x – 180 = 90
   =>x = 9000
   Or == 0.18x + 180 – 0.21x = 90
   =>x = 3000
   value of x cannot be determined exactly.
   Statement II: Interest earned by Nik after three years = x * {(1+0.10)^3 -1} = Rs.0.331x
   Interest earned by Kim after three years = (x+1000)*0.09*3 = Rs.0.27x+270
   Here ,0.061x = 549
   => x = 9000
   II alone is sufficient.

    

2. A shopkeeper bought an article and sold it. What is the cost of the article?
   Statement I: Profit earned by the shopkeeper is Rs.250 and selling price of the article is 30% less than the marked price of the article.
   Statement II: Marked price of the article is 25% above the selling price. Shopkeeper marked the price of article Rs.2000 and profit percent earned is 60%.
   I alone is sufficient.
   Either I or II.
   Both are not sufficient.
   II alone is sufficient.
   Both together necessary.
   Option D
   From I: Let the MP be Rs.x
   SP = 70% of x = Rs.7x/10 Profit = Rs.250
   Let CP be Rs.y.
   So, y + 250 = 7x/10
   I alone is not sufficient.
   From II: Let SP be Rs.x
   P = (2000/125)*100 = Rs.1600
   CP = (1600*100)/160 = Rs.1000
   II alone is sufficient.

    

3. After 3 years, ratio of age of P and Q will become 17:15. Find the difference between the age of P and Q.
   Statement I: 3 years ago, the ratio of the age of P and age of Q was 7:6.
   Statement II: The ratio of age P after 5 years and age of Q 7 years ago is 9:5.
   Both together necessary.
   II alone is sufficient.
   Either I or II.
   Both are not sufficient.
   I alone is sufficient.
   Option C
   Let the present age of P and Q be x and y years.
   So,(x+3)/(y+3) = 17/15 =>x = (6+17y)/15
   From I: (x-3)/(y-3)= 7/6
   =>y = 27
   Then x = 31
   Required Difference = 31 – 27 = 4 years
   I alone is sufficient.
   From II: (x+5)/(y-7) = 9/5
   =>y = 27
   x = 31
   Required Difference = 31 – 27 = 4 years
   II alone is sufficient.
   Either I or II.

    

4. If an item is sold at 25% discount. Then it gives a profit of 25%. Find the selling price of the item.
   Statement I: If it is sold for Rs.45 more, then the profit percentage is 40%.
   Statement II: If the marked price of the item is increased by 10% and discount rate remains the same, then the profit percentage is 37.5%.
   Either I or II.
   Both are not sufficient.
   II alone is sufficient.
   I alone is sufficient.
   Both together necessary.
   Option D
   Let CP be Rs.x
   SP = Rs.1.25x
   MP = 1.25x/0.75 = Rs.(5/3)x
   From I: (1.25x + 45) = 1.4x
   => x = Rs.300
   I alone is sufficient.
   From II: New MP = (5/3)x*1.1 = Rs.(5.5/3)x
   Now, (5.5/3)x *0.75 =1.375x
   II is not sufficient.

    

5. Four persons A,B, C and D are hired to do a work. A,C and D can complete the task in 16 days while working together. Find the number of days taken by B alone to complete the task.
   Statement I: C and D can complete the work in 24 days. B is 100% more efficient than A.
   Statement II: A alone can complete the work in 48 days, and ratio of efficiency of C and D is 1:2 resp.
   Both together necessary.
   I alone is sufficient.
   Both are not sufficient.
   Either I or II.
   II alone is sufficient.
   Option B
   From I: Let the total work LCM(16,24) = 48 units
   Number of units of work done by A,C and D in one day = 48/16 = 3 units
   Number of units of work done by C and D in one day = 48/24 = 2 units
   Number of days taken by A to complete the work in one day = 3-2 = 1 units
   Therefore, number of days taken by A to complete the work = 48/1 = 48 days
   So, time taken by B to complete the work = 48/2 = 24 days
   I alone is sufficient.
   From II: Let the efficiency of C and D be x and 2x resp.
   1/48 + x + 2x = 1/16
   => x = 1/72
   II alone is not sufficient.

    

6. Find the marks obtained by Simran in half-yearly exam, if the sum of marks obtained by Simran and Raj in half-yearly exam is 1410.
   Statement I: The ratio of marks obtained by Simran and Raj in quarterly exam was 9:8 resp.
   Statement II: The ratio of marks obtained by Simran in quarterly exam to the half-yearly exam is 2:3 resp. while ratio of marks by Raj in quarterly exam to the half-yearly exam is 4:5 resp.
   I alone is sufficient.
   Both together necessary.
   Both are not sufficient.
   Either I or II.
   II alone is sufficient.
   Option B
   From I: Let the marks obtained by Simran and Raj in quarterly exam be 9x and 8x resp.
   This alone is not sufficient.
   From II: Let the marks obtained by Simran in quarterly and half-yearly exam be 2y and 3y resp.
   Let the marks obtained by Raj in quarterly and half-yearly exam by 4z and 5z resp.
   This alone is not sufficient.
   Combining these two equations,we get 9x*3/2 + 8x*5/4 = 1410
   => x = 60
   Marks obtained by Simran in half-yearly exam = 9x*3/2 = 810
   Both together necessary.

    

7. A bag contains a total of (x+6) balls of three colors like White,Black and Brown such that the ratio of number of White and Brown balls is 3:4 resp. and the probability of drawing a Black ball is 1/3. Find the number of balls in the bag.
   Statement I: Probability of drawing a white ball is 2/7.
   Statemnet II: The number of black balls in the bag is 2 less than the number of brown balls .
   Either I or II.
   I alone is sufficient.
   II alone is sufficient.
   Both are not sufficient.
   Both together necessary.
   Option C
   Let the number of White and Brown color balls be 3x and 4x resp.
   So, the number of Black balls = (y+6)- (3x+4x) = (y – 7x +6)
   Probability of drawing the Black ball = 1/3 (y – 7x + 6)/(y+6) = 1/3
   =>21x = 2y + 12 —-(1)
   From I: Probability of drawing the White ball = 2/7
   3x/(y+6) = 2/7
   21x = (2y+12) —-(2)
   Both the equations are same, so this can’t be solved using Statement I.
   From II: (y – 7x + 6) = 4x – 2
   => y = 11x – 8 —-(3)
   From equations (1) and (2), we get
   21x – 12 = 22x – 16
   => x = 4
   So, y = 11*4 – 8 = 36
   Total number of balls in the bag = 36+6 = 42
   II is alone sufficient.

    

8. Find the time taken by 3 males and 5 females to plough the field while working together.
   Statement I: 1 male can plough half of the field in 12 days, 2 females can plough two fields of the same area and same type in 20 days.
   Statement II: 2 males can plough a field in 12 days and 2 females can plough the same field in 10 days.
   Both are not sufficient.
   I alone is sufficient.
   Either I or II.
   Both together necessary.
   II alone is sufficient.
   Option C
   From I: Time taken by 3 male t plough the field = 12/(3/2) = 8 days
   Time taken by 5 female to plough the field = (20*2)/(5*2 ) = 4 days
   So, the time taken by 3 male and 5 female to plough the field while working together
   = (8*4)/(8+4) = (8/3) days
   I alone is sufficient.
   From II: Time taken by 3 male t plough the field = 12/(3/2) = 8 days
   Time taken by 5 female to plough the field = (10*2)/(5 ) = 4 days
   So, the time taken by 3 male and 5 female to plough the field while working together = (8*4)/(8+4)
   = (8/3) days
   Either I or II.

    

9. A container contains ‘x’ litres of a mixture of water and alcohol in the ratio 7:22 resp. A man takes out ‘y’ litres of the mixture from the container and then mixes 28 litres of a mixture of water and alcohol in the ratio of 6:1 resp. in that container.
   Find the value of x.
   Statement I: The ratio of water and alcohol becomes 3:8 resp. after mixing 28 litres of a mixture of water and alcohol in the ratio of 6:1 resp.
   Statement II: The amount of water in the container becomes 150 litres after mixing 28 litres of a mixture of water and alcohol in the ratio 6:1 resp.
   Both together necessary.
   Both are not sufficient.
   II alone is sufficient.
   Either I or II.
   I alone is sufficient.
   Option B
   Initially amount of water and alcohol be 7x and 22x resp. Amount of water and alcohol taken out be 7y and 22y resp.
   Statement I: (7x – 7y + 24)/(22x – 22y + 4) = 3/8
   =>x – y = 18
   I alone is not sufficient.
   From II: 7x – 7y + 24 = 150
   => x –y = 18
   II alone is not sufficient.
   Combining both the equations, we get
   (7x – 7y + 24)/(22x – 22y + 4 ) = 3/8
   =>x – y = 18
   And 7x – 7y + 24 = 150
   =>x – y = 18
   Both are not sufficient.

    

10. A bag contains red,blue and green balls in the ratio of 4:5:3 resp. Find the total number of balls in the bag.
    Statement I: Probability of drawing two blue balls from the bag is 1/6.
    Statement II: Probability of drawing a green ball from the bag is ¼.
    Either I or II.
    Both are not sufficient.
    I alone is sufficient.
    II alone is sufficient.
    Both together necessary.
    Option C
    From I: Probability of choosing two blue ball from the bag = 5xC2/12xC2 = 1/6
    =>x = 3
    Total number of balls = 12*3 = 36
    I alone is sufficient.
    From II: Probability of drawing a green ball = 3xC1/12xC1 = ¼
    => ¼ = ¼
    II is not sufficient.