 # Quantitative Aptitude: Data Sufficiency Questions Set 11

Directions(1-10): Decide whether the data provided in the statements are sufficient to answer the question.

1. Mrinal invested Rs.(x+500) in two different schemes A and B partially. Find the amount invested in scheme A.
Statement I: The amount invested in scheme A and B is 5:4 resp. and the rate of simple interest offered by scheme A and B is 8% and 10% per annum resp.
Statement II: After two years, Mrinal received equal amount as interest from both the schemes.

Only Statement I
Either I or II
Both are necessary
Both are not sufficient
Only Statement II
Option D
Combining these two Statement I and II, we get
(5/9)*(x+500)*8% * 2 = (4/9)*(x+500)*10% * 2
=> 80% = 80%
Both are not sufficient to answer.

2. 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 profit percentage is 37.5%.

Both are necessary
Both are not sufficient
Either I or II
Only Statement II
Only Statement I
Option E
Let the CP be Rs.x.
SP = Rs.1.25
MP = Rs.1.25x/0.75 = Rs.(5/3)x
From I: (1.25x + 45) = 1.4x
=> x = Rs.300
This statement is alone sufficient.
From II: New MP = (5/3)x*1.1 = Rs.(5.5/3)x
(5.5/3)x*0.75 = 1.375x
This statement is not sufficient to answer.

3. 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 same field in 10 days.

Both are not sufficient
Only Statement I
Both are necessary
Only Statement II
Either I or II
Option E
From I: Let the efficiency of each male and each female be ‘m’ and ‘f’ resp.
Time taken by 3 male to plough the field = 12*(2/3) = 8 days
Time taken by 5 female to plough the field = (20*2)/(5*2) = 4 days
So, the time taken by 3 males and 5 female = (8*4)/(8+4) = 8/3 days
This statement is alone sufficient.
From II: Let the efficiency of each male and each female be ‘m’ and ‘f’ resp.
Time taken by 3 male to plough the field = 12*2/3 = 8 days
Time taken by 5 female to plough the field = (10*2)/5 = 4 days
So, the time taken by 3 males and 5 female = (8*4)/(8+4) = 8/3 days
This statement is alone sufficient.
Either I or II

4. Distance between Lucknow and Bareilly is 360 km. Find the speed of boat in still water.
Statement I: Time taken by boat to travel from Lucknow to Bareilly downstream and come back is 30 hours.
Statement II: Time taken by boat from Lucknow to Bareilly and come back is 28.8 hours if the water is still.

Both are necessary
Only Statement I
Only Statement II
Either I or II
Both are not sufficient
Option C
From I: 360/(b+s) + 360/(b-s) = 30
=> 240b = (b^2 – s^2)
This cannot solve alone.
From II: 360/b + 360/b = 28.8
=> b = 25 km/hr
This statement alone is sufficient.

5. The age of three friends Amar, Akbar and Anthony is (x-8) years, (x+4) years and (x+6) years resp. Find the age of Akbar.
Statement I: The average age of Amar and Akbar taken together is (x-17) years less than the average age of Akbar and Anthony taken together.
Statement II: The average age of Amar and Akbar taken together is 7 years less than the average age Akbar and Anthony taken together.

Both are necessary
Both are not sufficient
Either I or II
Only Statement II
Only Statement I
Option E
From I: [(x-8) + (x+4)]/2 = [(x+4) + (x+6)]/2 – (x-17)
=> x = 24
Average age of Akbar = 24 + 4 = 28 years
This statement alone is sufficient.
From II: [(x-8) + (x+4)]/2 = [(x+4) + (x+6)]/2 – 7
This cannot solve the question.

6. There are three pipes A,B and C, where A and B are inlet pipes while C is outlet pipe. Find the time taken to fill or empty the tank if A and C are opened.
Statement I: Pipes A and B are opened together can fill the tank in 24 min. while and pipe C is 50% less efficient than pipe B.
Statement II: Capacity of tank is 960 litres and rate of flow of pipe B is 24 litres/min.

Both are necessary
Only Statement II
Either I or II
Both are not sufficient
Only Statement I
Option A
Combining these two Statement I and II, we get
1/A + 1/B = 1/24
=> 1/A + 1/40 = 1/24
=> A = 60 minutes
Time taken by pipe C to fill the tank = 40/0.5 = 80 min.
Required time = (60*80)/(80 – 60) = 240 minutes
Both the statements are necessary.

7. Four persons A,B,C and D are hired to do 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 task 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.
Either I or II
Only Statement I
Both are not sufficient
Only Statement II
Both are necessary
Option B
From I: Let the total work lcm(16,24) = 48 units Work done by A,C and D in one day = 48/16 = 3 units Work done by C and D in one day = 48/24 = 2 units
Work done by A in one day = 3-2 = 1 unit
Therefore, number of days taken by A to complete the work = 48/1 = 48 days
The time taken by B to complete the work = 48/2 = 24 days
This statement is alone sufficient.
From II: Let the efficiency of C and D be x and 2x resp.
1/48 + x + 2x = 1/16
=>x = 1/72
This statement is not sufficient to answer.

8. Find the number of factors of the two digit number. Statement I: The two-digit number is 27 more than the two-digit number obtained by reversing the digits of the number.
Statement II: The number is multiple of 9.

Only Statement I
Either I or II
Both are not sufficient
Only Statement II
Both are necessary
Option E
From I: Let the required number be (10x+y).
Now, 10x + y = 10y + x + 27
=> (x – y) = 3
So, the possible values of x and y are 96,85,74,63,52 and 41.
We cannot find an unique solution.
So, this statement is not alone to solve the question.
From II: Two-digit numbers which are multiple of 9 = 18,27,36,45,54,63,72,81,90,99
We cannot find unique solution.
So, this statement alone is not sufficient.
Combining both the equations. Let the required number be (10x+y).
10x + y = 10y + x + 27
=> (x – y) = 3
So, the possible values of x and y are 96,85,74,63,52 and 41.
Two-digit numbers which are multiple of 9 = 18,27,36,45,54,63,72,81,90,99.
So, 63 is the required two-digit number.
So, the factors of 63 are 1,3,7,9 21,63.

9. A bag contains a total of (x+6) balls of three colors of Black, White 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).
Statement II: The number of Black balls in the bag is 2 less than the number of Brown balls.

Both are necessary
Only Statement I
Only Statement II
Both are not sufficient
Either I or II
Option C
Let the number of White and Brown color balls be 3k and 4k resp.
So, the number of Black balls = (x+6) – (3k+4k) = (x – 7k +6)
Probability of drawing Black balls = 1/3 (x – 7k +6)/(x+6) = 1/3
=> 21k = 2x+12 –(1)
From I: Probability of drawing a white ball = 2/7 3k/(x+6) = 2/7
=> 21k = 2x+12 –(2)
Both the equations are same.
So, this statement is not sufficient.
From II: (x – 7k + 6) = 4k – 2
=> x = 11k – 8 –(3)
From (1) and (3), we get
21k – 12 = 22k – 16
=> k = 4
So, x = 11*4 – 8 = 36
Therefore, the total number of balls = 36 + 6 = 42
Hence, this statement is sufficient alone.

10. Find the marks obtained by Sushma in half-yearly exam, if the sum of marks obtained by Sushma and Suraj is half-yearly exam is 1410.
Statement I: The ratio of marks obtained by Sushma and Suraj in quarterly exam was 9:8 resp. Statement II: The ratio of marks obtained by Sushma in quarterly exam to the half-yearly exam is 2:3 resp. while ratio of marks obtained by Suraj in quarterly exam to the half-yearly exam is 4:5 resp.

Both are not sufficient
Only Statement II
Either I or II
Only Statement I
Both are necessary
Option E
From I: Let the marks obtained by Sushma and Suraj in quarterly exam be 9x and 8x resp.
Nothing is known about their marks in half-yearly exam.
So, this statement is not sufficient alone.
From II: Let the marks obtained by Sushma in quarterly exam and half-yearly exam be 2y and 3y resp.
Also, let the marks obtained by Suraj in quarterly exam and half-yearly exam be 4z and 5z resp.
So, this is also not sufficient alone.
Combining both the equations, we get
Let the marks obtained by Sushma and Suraj in quarterly exam be 9x and 8x resp.
Now, 9x*(3/2) + 8x *(5/4) = 1410
=> x = 60
So, the marks obtained by Sushma in half-yearly exam = 9x*(3/2) = 810