# Quantitative Aptitude: Data Sufficiency Questions Set 12

Directions: The following questions are accompanied by three statements I, II and III. You have to determine which statement/s is/are sufficient to answer the question.

1. What is the amount invested by A?
Statement I: Total amount received by B after 3 years is Rs.4800 at compound interest.
Statement II: B and A invested their amount at the rate of 10% per annum.
Statement III: A and B invested their amount at simple interest and compound interest respectively and the difference between the interests received by both after 2 years is Rs.1200.
Only I and II are sufficient
Only II and III are sufficient
Either II alone or I and II together to sufficient
All I, II and III necessary to the answer the question
The question can’t be answered even with all I, II and III
Option E
From statement I,
Let the amount invests by B = x
4800 = x * (1 + R/100)^3
So, Statement I alone is not sufficient to answer the question.
From statement II,
R = 10%
So, Statement II alone is not sufficient to answer the question.
From statement III,
Let the amount invests by A = x
Let amount invests by Bl = y
SI = y * 2 * R/100 = yR/50
CI = x * (1 + R/100)2 – x
CI – SI = 1200
or
SI – CI = 1200
So, Statement III alone is not sufficient to answer the question.

2. What is the sum of the ages of person 1 and 2?
Statement I: Ratio of the ages of 1 to 3 is 4: 5 and the ratio of the ages of 1 to 4 is 1: 3.
Statement II: Sum of the ages of 2,3 and 4 is 125 years and 5 years ago the ratio of the ages of 1 to 4 is 3: 11.
Statement III: 4’s age is 200% more than that of 1’s age and the difference between the ages of 1 and 4 is 40 years.
Only I and II are sufficient
Only II and III are sufficient
Either II alone or I and II together to sufficient
All I, II and III necessary to the answer the question
The question can’t be answered even with all I, II and III
Option A
From statement I,
p1/p3 = 4/5
p1/p4 = 1/3
So, Statement I alone is not sufficient to answer the question
From Statement II,
p2 + p3 + p4 = 125
(p1 – 5)/(p4 – 5) = 3/11
So, Statement II alone is not sufficient to answer the question
From statement III,
p4 = 300/100 * p1
p4: p1 = 3: 1
2x = 40
x = 20
p1= 20 years
p4 = 3 * 20 = 60 years
So, Statement III alone is not sufficient to answer the question
From statement I and II,
p1 and p4’s present age be x and 3x respectively
(p1 – 5)/(p4 – 5) = 3/11
(x – 5)/(3x – 5) = 3/11
= > 11x – 55 = 9x – 15
= > 2x = 40
= > x = 20
Present age of p1 and p4 is 20 and 60 years respectively
p3’s present age = 20/4 * 5 = 25 years
p2’s present age = 125 – (25 + 60) = 125 – 85 = 40 years
Sum of the ages of p1 and p2 = (20 + 40) = 60 years
Hence, statement I and II alone is sufficient to answer the given question.

3. What is the total surface area of the conical box?
Statement I: Ratio of height of the box to height of the cylindricall box is 2: 1.
Statement II: Height of the cylindrical box is equal to the perimeter of the square whose area is 9 cm2.
Statement III: Radius of the cone is equal to length of the rectangle whose perimeter is 20 cm.
Only I and II are sufficient
Only II and III are sufficient
Either II alone or I and II together to sufficient
All I, II and III necessary to the answer the question
The question can’t be answered even with all I, II and III
Option E
Height of cone/height of the cylinder = 2/1
So, Statement II alone is not sufficient to answer the question
From statement II,
Area of the square = 9
Side of the square = 3
Perimeter of the square = 3 * 4 = 12 cm
Height of the cylinder = 12 cm
So, Statement II alone is not sufficient to answer the question
From statement III,
Radius of the cone = length of the rectangle
Perimeter of the rectangle = 2 * (l + b) = 20
So, Statement III alone is not sufficient to answer the question

4. There are four members p1, p2, p3 and p4 partners in the business. What is the profit share of p2?
Statement I: p1 and p2 started the business with investment of Rs.x and Rs.2x respectively and after 6 months p3 and p4 joined them with investment of Rs.(x + 1000) and Rs.3x respectively.
Statement II: At the end of one years and profit Share of p3 is Rs.4000.
Statement III: At the end of one year the profit ratio of p3 and p4 is 2:3.
Only I and II are sufficient
Only II and III are sufficient
Either II alone or I and II together to sufficient
All I, II and III necessary to the answer the question
The question can’t be answered even with all I, II and III
Option D
From statement I,
p1= x
p2 = 2x
p3= (x + 1000)
p4 = 3x
So, Statement I alone is not sufficient to answer the question
From Statement II,
p3’s share = Rs.4000
So, Statement I alone is not sufficient to answer the question
From statement III,
Profit ratio of p3/p4 = 2/3
So, Statement III alone is not sufficient to answer the question
From I, II and III
Profit ratio of p1, p2, p3 and p4 = x * 12: 2x * 12: (x + 1000) * 6: 3x * 6
=12x: 24x: (6x + 6000): 18x
(6x + 6000)/18x = 2/3
6x + 6000 = 12x
x = 1000
Profit ratio = 12000: 24000: 12000: 18000
= 2: 4: 2: 3
p2’s profit share = 4/2 * 4000 = 8000
All the statements are necessary to answer the question.

5. What is the initial quantity of the juice in vessel A?
Statement I: Ratio of the juice and water in vessel A and B is 3: 2 and 4: 3 respectively.
Statement II: 28 liters of the mixture of B is poured into A and then the ratio of the juice and water in vessel A becomes 17: 12.
Statement III: 10 liters of the mixture from vessel C is taken out and is poured into vessel A, then the ratio of the juice to water becomes vessel A is 5: 4.

Only I and II are sufficient
Only II and III are sufficient
Either II alone or I and II together to sufficient
All I, II and III necessary to the answer the question
The question can’t be answered even with all I, II and III
Option A
From statement I,
juice and water in A = 3: 2
juice and water in B = 4: 3
So, Statement I alone is not sufficient to answer the question
From statement II,
Vessel B mixture = 28
Ratio of the juice and water in A = 17: 12
So, Statement II alone is not sufficient to answer the question
From statement III,
Mixture of C = 10
Ratio of juice and water in C = 5: 4
So, Statement III alone is not sufficient to answer the question
From I and II
juice in 28 liters of B = 4/7 * 28 = 16 liters
Water in 28 liters of B = 3/7 * 28 = 12 liters
3x + 16/2x + 12 = 17/12
34x + 204 = 36x + 192
2x = 12
x = 6
juice in vessel A = 3 * 6 = 18 liters
So, Statement I and II are necessary to answer the question.

6. Directions: The following questions are accompanied by three statements I and II. You have to determine which statement/s is/are sufficient to answer the question.

7. What is the difference between the total number of employees from A in all the three years together and the number of males from Company A in three years together?
Statement I: The ratio of the number of males to females from Company A in 2015 is 3:2 and the number of females from company A in 2014 is 20 more than that of the number of males from A in 2016.
Statement II: If the total number of employees from company A in 2014, 2015 and 2016 60%, 40% and 50% respectively are females.
Only I
Only II
Either I or II sufficient
All I and II necessary to the answer the question
The question can’t be answered even with all I and II
Option B
From statement I,
Females from A in 2015 = 2/5 * 250 =100
Males from A in 2015 = 3/5 * 250 =150
So, Statement I alone is not sufficient to answer the question.
From statement II,
Females from A in 2014 = 60/100 * 400 = 240
Males from A in 2014 = 400 – 240 = 160
Females from A in 2015 = 40/100 * 250 = 100
Males from A in 2015 = 250 – 100 = 150
Females from A in 2016 = 50/100 * 300 = 150
Males from A in 2016 = 300 – 150 = 150
Total number of employees from A = 400 + 250 + 300 = 950
Males from A = 150 + 150 + 160 = 460
Difference = 950 – 460 = 490
So, Statement II alone is sufficient to answer the answer.

8. What is the ratio of the males to females from company C in 2014?
Which of the following statement is sufficient to answer the question?
Ratio of the males to females from company A and B in 2014 is 1: 3 and 2: 1 respectively and total employees in 2014 from all the companies together 60% are females.
The number of females from C in 2014 is half of the number of males from B in 2015.
Ratio of the number of males to females from C in all the years together is 3: 2 and the 50% of the employees from C in 2015 is females.
40% of the employees from C in 2014 is left and in this 80% of the employees is girl
Cannot be determine
Option A
From option (A)
Females from A in 2014 = 400 * ¾ =300
Females from B in 2014 = 1/3 * 300 =100
Number of females in 2014 = (400 + 300 + 200) * 60/100 = 540
Number of females from C in 2014 = 540 – 300 – 100 = 140
Number of males from C in 2014 = 200 – 140 = 60
Required ratio = 60: 140 = 3: 7
This satisfied the given condition.
From option (B)
Number of males from B in 2015 is not given
This not satisfied.
From option (C)
Number of females from C in 2015 = 300 * 50/100 = 150
we cannot find the answer of the question.
This not satisfied.
From option (D)
Number of employees left from C in 2014 = 200 * 40/100 = 80
Number of females left from C in 2014 = 80 * 80/100 = 64
This not satisfied the given condition.

9. Number of females from B in all the years together is what percent of the total number of employees from B in all the years together?
Statement I: Total number of employees from B in 2017 is 280 and the ratio of the number of females to males from B in 2017 is 4: 3.
Statement II: 60% of the total number of employees from B in 2014 to 2017 is males.
Only I
Only II
Either I or II sufficient
All I and II necessary to the answer the question
The question can’t be answered even with all I and II
Option D
From statement I,
Number of females from B in 2017 = 4/7 * 280=160
Number of males from B in 2017 = 3/7 * 280=120
So, statement I alone is not sufficient to answer the question.
From statement II,
60% of the total number of employees from B in 2014 to 2017 is males.
So, statement II alone is not sufficient to answer the question.
From I and II,
Total number of employees from B in 2014 to 2017 = 300 + 100 + 350 + 280 = 1030
Number of males from B in 2014 to 2017 = 1030 * 60/100 = 618
Number of males from B in 2014 to 2016 = 618 – 120 = 498
Number of females from B in 2014 to 2016 = (300 + 100 + 350) – 498 = 252
Required percentage = 252/750 * 100 = 33.6%
Both the statements are necessary to answer the question.

10. Ratio of the males to females from A, B and C in 2016 is 7: 8, 4: 3 and 2: 3 respectively and the ratio of total number of males from A, B and C in 2017 to the number of males from A, B and C in 2016 is 1: 2. Total number of employees from A, B and C in 2017 is 360.
From the statement given in the above question which of the following can be determined.
Number of females from A, B and C in 2017
Average number of males from C in 2014 to 2017
Ratio of number of males to females from A, B and C in 2017
Difference between the number of females and males from all the three companys in all the years together (2014, 2015, 2016 and 2017) a) Only A b) Only A and D c) Only A, C and D d) Only A and C e) All A, B, C and D
sum of males and females
Option C
Number of males from A in 2016=7/15 * 300=140
Number of females from A in 2016=8/15 * 300=160
Number of males from B in 2016=4/7 * 350=200
Number of females from B in 2016=3/7 * 350=150
Number of females from C in 2016=3/5 * 150=90
Number of males from C in 2016=2/5 * 150=60
Number of males in 2016=140 + 200 + 60=400
Number of males in 2017=1/2 * 400=200
Number of females in 2017=360 – 200=160
Required ratio males to females in 2017 = 200: 160=5:4

11. 40% of the employees from C in all the years together is females and the number of males from C in 2015 and 2016 is 180 and 80 respectively. What is the ratio of the number of females from C in 2014, 2015 and 2016?
7:12:7
5:14:5
3:17:5
2:17:9
1:7:9
Option A
Number of females from C in 2015 = 300 – 180 = 120
Number of females from C in 2016 = 150 – 80 = 70
Total number of females from C = (200 + 300 + 150) * 40/100 = 260
Number of females from C in 2014 = 260 – 120 – 70 = 70
Required ratio = 70: 120: 70
= 7: 12: 7