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.

     


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