# Quantitative Aptitude: Data Sufficiency Questions Set 4

Directions (1-5): In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and answer accordingly.

1. What is the principal amount?
Statement I: The Simple Interest obtained on the principal after 2 years at 8% rate of interest is Rs 450 less than the compound interest obtained on the same principal after 2 years at 8% per annum.
Statement II: The sum becomes double in 10 years at 6% per annum rate of simple interest.
Statement III: The compound interest obtained on the principal amount is Rs 4540 after 2 years at the rate of 8% compounded annually.
A) Only I
B) All I, II and III together
C) II and III together
D) Only I or III
E) I or II and III
Option D
Explanation
:
From I : Pr^2/100^2 = 450. So P can be found.
From III: using the compound interest formula, P can be find out
2. What is the speed of boat in still water?
Statement I: The boat can cover 12 km downstream distance in 2 hours.
Statement II: Speed of the stream is three-fourth the speed of boat in still water.
Statement III: The boat can cover 12 km upstream distance in 4 hours.

A) I and III together
B) Only II
C) I and II together
D) I and either II or III
E) Any combination of 2 statements can give the required result
Option E
Explanation
:
Let speed of boat = u, and stream = v
From I: u + v= 12/2 = 6 km/hr
From II: v = 3u/4
From III: u – v = 12/4 = 3
So solving I and II ‘u’ can be found. Similarly by solving II and III and by solving I and III
3. A person borrowed some money at compound interest for 2 years. What will be the amount required to return after 2 years?
Statement I: If the amount was borrowed at simple interest, then after 5 years Rs 600 was required to pay as simple interest.
Statement II
: The rate of interest is 6% per annum
Statement III: The sum of money borrowed is 10 times the amount required to be paid as simple interest after 2 years.

A) II and I or III
B) Even all statements together cannot answer the question
C) II and III together
D) I and III together
E) All I , II and III
Option E
Explanation
:
From I: SI after 5 yrs is rs 600, so after 1 yr = 600/5 = Rs 120
So after 2 years is 120*2 = Rs 240
From III: P = 10*SI after 2 years
So from I and III, P = 10*240 = Rs 2400
Now P = 2400 and from statement II, r = 6%, so CI formula can be used to find the required amount
4. Shopkeeper gained how much by selling his products in November 2016?
Statement I: He earned 40% more profit in December 2016 as compared to October 2016.
Statement II
: In December 2016 he earned 10% more profit than in November 2016.

Statement III: The total profit earned in November 2016 and October 2016 was Rs 55,000.
A) Only I and III

B) Only II and III
C) Only I and II
D) All I, II and III
E) Even all statements together cannot answer the question
Option D
Explanation
:
Using all statements:
Let profit earned in Oct and Nov is Rs x and Rs y resp.
So in Dec = 140/100 *x = 1.4x
Given x + y = 55000
From II – 1.4x = 110/100 * y
So we have 2 equations in 2 variables, y can be found
5. In how many days 6 men and 5 women can complete the work working together?
Statement I: The ratio of efficiency of man to woman is 2 : 1
Statement II
: 9 Women can complete three-five of the work in 15 days.
Statement III: 6 Men and a child together can complete 1/4th work in 12 days while 6 women and the child together can complete two-third of the work in 16 days
A) I and either II or III

B) Any combination of 2 statements can give the required result
C) Only I and II
D) All I, II and III
E) None of these
Option B
Explanation
:
From I and II: we have number of days in which 9 women can complete the work. So using efficiency we can find the number of days required by man to complete the work and then the required answer
From II and III: we have number of days in which 9 women can complete the work. So days required by child can be find out, and then by men.
From I and III: We get 3 equations in 3 variables – man, woman and child. So can be found.

Directions (6-10): In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly.

1. What is the age of A in a group of 6 students – A, B, C, D, E and F who average age is 16 years?
Statement I: Total age of B and D is 30 years
Statement II: Total age of E and F is 31 years.

A) If the data in statement I alone is sufficient to answer the question.
B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option D
Explanation
:
From both statements also we do not know the age of both A and C. So of A cant be found
2. A person lent Rs 5000. At what rate percent per annum he lent the money?
Statement I: The difference between the simple interest and compound interest on same money is Rs 60.
Statement II
:  The simple interest obtained after 4 years is Rs 300
A) If the data in statement I alone is sufficient to answer the question.

B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option B
Explanation
:
In I, time is not given, so cannot be fount from I
In II: P = 5000, t = 4 years and SI = 300
3. How much discount percent is offered on the article?
Statement I: Profit earned by selling the article for Rs 230 after giving discount is Rs 30
Statement II
: Had there been no discount the, 20% would be the profit.
A) If the data in statement I alone is sufficient to answer the question.

B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option E
Explanation
:
From I: SP = 230, profit = 30, so CP = 200
From II: when there is no discount, profit = 20%
So profit = 20/100 * 200 = Rs 40
So MP = 200+40 = Rs 240
Now MP = 240, and SP = 230, so discount% can be found out
4. What is the speed of the train?
Statement I: The train another train running in the same direction in 12 minutes.
Statement II
: The train crosses a signal in 8 minutes.
A) If the data in statement I alone is sufficient to answer the question.

B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.
Option D
Explanation
:
In I, length and speed of second train is required which is not given
5. A sum of money is invested. What is the compound interest obtained after 2 years?
Statement I: The different between the simple and compound interest on a sum of Rs 1200 is Rs 30 after 2 years
Statement II
: The interest obtained after 1 year on Rs 1200 is Rs 100
A) If the data in statement I alone is sufficient to answer the question.

B) If the data in statement II alone is sufficient to answer the question.
C) If the data either in statement I alone or statement II alone are sufficient to answer the question.
D) If the data given in both I and II together are not sufficient to answer the question.
E) If the data in both the statements I and II together are necessary to answer the question.