BANK & INSURANCE (DATA SUFFICIENCY) PART 2

Total Questions: 30

1. Three Statement Based Questions:

Ques: Following question consists of three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer:

Find the HCF of three numbers p, q, and r (p, q, and r are positive integers).

Statement I: LCM and product of p and q is 144 and 3456 respectively.
Statement II: HCF of q and r is 12 and r is 60 more than q. (r < 110)
Statement III: LCM of all the three numbers is 432.

Correct Answer: (a) Statement I and II together are sufficient.
Solution:

From I:
LCM of p and q = 144
Product of p and q = 3456

HCF of p and q = (Product of p and q)/(LCM of p and q)
= 3456/144 = 24

Statement I alone is not sufficient.

From II:
HCF of q and r = 12
Let q = 12a and r = 12b [a and b are co-prime]

r - q = 12b - 12a = 60
b - a = 5

Possible pair of values of (a, b) = (1, 6), (2, 7), (3, 8), (4, 9), and so on.

Possible pair of values of (q, r) = (12, 72), (24, 84), (36, 96), and (48, 108)

Statement II alone is not sufficient.

From III:
LCM of p, q and r = 432

Statement III alone is not sufficient.

From I and II:
Possible pair of values of (q, r) = (12, 72), (24, 84), (36, 96), and (48, 108)
Possible pair of values of p = 288, 144, 96, and 72
Possible LCM of p and q = 288, 144, 288, and 144

Case 1: When p = 144, q = 24, and r = 84
HCF of p and q = 24
HCF of three numbers p, q, and r = 12

Case 2: When p = 72, q = 48, and r = 108
HCF of p and q = 24
HCF of three numbers p, q, and r = 12

In both the cases we are getting the same HCF.
Statements I and II together are sufficient.

From I and III:
Let p = 24m and q = 24n [m and n are co-prime.]
LCM of p and q = 24mn = 144
mn = 6
Possible value of (m, n) = (1, 6), (6, 1), (2, 3), and (3, 2)
Statements I and III together are not sufficient.

From II and III:
Possible pair of values of (q, r) = (12, 60), (24, 84), (36, 96), and (48, 108)
LCM of p, q, and r = 432
Statements II and III together are not sufficient.

2. The given question is followed by three statements. You have to determine whether the data given in the statements are sufficient for answering the question. Choose the most appropriate option as your answer.

Three partners A, B and C entered into a business by investing capital in ratio 12 : 5 : 3 respectively for initial 2 years. Find the total profit obtained from the business after 4 years.

Statement I: 25% of the profit that is received by A is Rs.375.
Statement II: After 2 years, they made an additional investment in the ratio of 6 : 3 : 1 respectively.
Statement III: After 4 years, the profit ratio between A, B and C is 3 : 1 : 1 respectively and the difference between the profit received by A and B is Rs.1000.

Correct Answer: (d) Either I and II together or only III.
Solution:

Let the initial amount invested by A, B and C are Rs.12X, Rs.5X and Rs.3X respectively.

From statement I and II together:
Profit received by A = 375 × 100/25 = Rs.1500

Let additional amounts invested by A, B and C are Rs.6Y, Rs.3Y and Rs. Y respectively.

Ratio of profit received by A, B and C =
(12X + 12X + 6Y + 6Y) : (5X + 5X + 3Y + 3Y) : (3X + 3X + Y + Y)
= (24X + 12Y) : (10X + 6Y) : (6X + 2Y)

Let the total profit = Rs. Z

Then,
[(24X + 12Y) / (40X + 20Y)] × Z = 1500

12/20 × Z = 1500
Z = 2500

From statement III:
Ratio of profit received by A, B and C = 3 : 1 : 1

Given,
3 - 1 = 2 units = Rs.1000
1 unit = Rs.500

So, 3 + 1 + 1 = 5 units = 500 × 5 = Rs.2500

3. In the following questions, which of the given statement(s) are necessary for determining the answer?

If X, B, A, and Z are integers, find the value of (X - B) - (Z - A).

I. X³ + Z³ = 91, given X > Z
II. A³ + B³ = 91, given B > A
III. Sum of X and Z is 1 and the sum of A and B is 7.

Correct Answer: (a) All three I, II, and III together are sufficient.
Solution:

From I and II together,
Not enough information given about the exact values of X, B, A and Z. We cannot find the value of (X - B) - (Z - A).

From I and III together,
Given,
X + Z = 1 ..........(1)

Cube both sides,
X³ + Z³ + 3XZ (X + Z) = 1
91 + 3XZ = 1
XZ = -30

From equation (1),
-30/Z + Z = 1
Z² - Z - 30 = 0

(Z - 6)(Z + 5) = 0
Z = 6 or -5

So, X = -5 or 6

Given X > Z,
So X = 6 and Z = -5

Given, A + B = 7

There are lots of possible values for A and B, so we cannot find the exact values of A, and B from I and III together. So, we cannot find the value of (X - B) - (Z - A).

From I, II and III together,
X + Z = 1 ..........(1)

Cube both sides,
X³ + Z³ + 3XZ (X + Z) = 1
91 + 3XZ = 1
XZ = -30

From equation (1),
-30/Z + Z = 1
Z² - Z - 30 = 0
(Z - 6)(Z + 5) = 0

Z = 6 or -5
So, X = -5 or 6

Given X > Z, so X = 6 and Z = -5

Given,
A + B = 7 ..........(2)

Cube both sides,
A³ + B³ + 3AB (A + B) = 343
91 + 21AB = 343
AB = 12

From equation (2),
12/B + B = 7
B² - 7B + 12 = 0
(B - 4)(B - 3) = 0

B = 4 or 3
Given B > A, so B = 4 and A = 3

Hence values of (X - B) - (Z - A) = (2 + 8) = 10

4. Following question consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.

There are x engineers, y doctors and z teachers in a society. A committee of 5 members is to be formed such that the committee contains 2 engineers, 2 doctors and 1 teacher. Find the total number of engineers, doctors and teachers in the society.

Statement I: x = y + 2
Statement II: Number of ways in which the required committee can be formed = 270
Statement III: z = x/2, z < 5

Correct Answer: (b) All I, II and III
Solution:

From I and II:
x = y + 2
Number of ways in which the required committee can be formed = 270

From I and III:
x = y + 2
⇒ y = x - 2
z = x/2, z < 5
⇒ x = 2z

From II and III:
Number of ways in which the required committee can be formed = 270
z = x/2, z < 5

From I, II and III:
x = 2z
y = 2z - 2

Number of ways in which the committee can be formed =
= ²zC₂ × (²z - 2)C₂ × zC₁
= [2z × (2z - 1) × (2z - 2)!] / [(2z - 2)! × 2!]
× [(2z - 2) × (2z - 3) × (2z - 4)!] / [(2z - 4)! × 2!]
× [z × (z - 1)!] / [(z - 1)! × 1!] = 270

=> [2z × (2z - 1)]/2 × [(2z - 2) × (2z - 3)]/2 × z
= 270

⇒ z × (2z - 1) × (z - 1) × (2z - 3) × z = 270
⇒ z² × (z - 1) × (2z - 1) × (2z - 3) = 270 ...(i)

Putting z = 1 in equation (i)
LHS = 1 × 0 × 1 × (-1) = 0
RHS = 270
LHS ≠ RHS

Putting z = 2 in equation (i)
LHS = 4 × 1 × 3 × 1 = 12
RHS = 270
LHS ≠ RHS

Putting z = 3 in equation (i)
LHS = 9 × 2 × 5 × 3 = 270
RHS = 270
LHS = RHS

Hence, z = 3
x = 2 × 3 = 6
y = 6 - 2 = 4

Total number of engineers, doctors and teachers in the society = 6 + 4 + 3 = 13

Hence, all I, II and III together are sufficient.

5. Following question consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the statements and give answer:

How many people did not like any movie out of three movies A, B, and C if total persons are 120?

I: Total persons who like either A or B or both is 70 and total persons who like only C is 35.
II: Total persons who like movie C is 60 and total persons who like either A or B or both but not C is 45.
III: Total persons who like only one movie and at least two movies are 75 and 30, respectively.

Correct Answer: (d) Either I alone or II alone is sufficient.
Solution:

a + b + c + d + e + f + g + h = 120 ...(1)

From I:
Total persons who like either A or B or both is 70
and total persons who like only C is 35.

a + b + c + d + e + f = 70 ...(2)
g = 35 ...(3)

From (1), (2) and (3):
70 + 35 + h = 120
h = 15

Total persons who did not like any movie = h = 15
Statement I alone is sufficient.

From II:
Total persons who like movie C is 60 and total persons who like either A or B or both but not C is 45.

d + e + f + g = 60 ...(4)
a + b + c = 45 ...(5)

From (1), (4) and (5):
45 + 60 + h = 120
h = 15

Total persons who did not like any movie = h = 15
Statement II alone is sufficient.

From III:
Total persons who like only one movie and at least two movies are 75 and 30 respectively.

a + c + g = 75 ...(5)
b + d + e + f = 30 ...(6)

From (1), (5) and (6):
75 + 30 + h = 120
h = 15

Total persons who did not like any movie = h = 15
Statement III alone is sufficient.

6. A, B and C invested different amounts in a business. What is the amount invested by C if A, B and C invested a fixed amount for 5 years and profit is distributed annually?

I. Amount invested by A and B are in the ratio 3: 4. C received the profit of Rs.7000 for the 2nd year.
II. Amount invested by B is Rs.60,000 and B received profit of Rs.12,000 in the first 2 years together (i.e. at the end of 1st and 2nd year together).
III. A received the profit of Rs.6000 at the end of 1st year.

Correct Answer: (e) All I, II and III together are sufficient
Solution:

No statement alone provides enough data to determine the amount invested by C.

From I and II together:
Amount invested by B = Rs.60,000
Amount invested by A and B are in the ratio 3 : 4
Amount invested by A = Rs.45,000

Profit received by B for 1st and 2nd year together = Rs.12,000

So, Profit received by A for 1st and 2nd year together = Rs.9,000
(Since, the profit will be divided in the proportion of investment for same investment period)

Profit received by C for the 2nd year (i.e. only for 2nd year) = Rs.7,000

Since the profit received by C for the 1st year is unknown, we cannot determine the answer.

From I and III together:
Since, the investment of neither one is given in the statement I and III together, we cannot determine the required answer.

From II and III together:
Investment of B = Rs.60,000
Profit received by B for 1st and 2nd year together = Rs.12,000
Profit of A for first year only = Rs.6000

This information is clearly not sufficient to answer the question.

From I, II and III together:
Profit received by B for 1st and 2nd year together = Rs.12,000

So, profit received by A for 1st and 2nd year together = Rs.9,000

Profit received by A for 1st year only = Rs.6,000
Profit received by A for 2nd year only = Rs.3,000

Profit received by B for 1st year only = Rs.8,000
And, profit received by B only for 2nd year only = Rs.4,000

Profit received by C for the 2nd year (i.e. for 2nd year only) = Rs.7,000

Investment of B = Rs.60,000

Investment of B / investment of C = profit of B / Profit of C (for same period of investment)

60,000 / Investment of C = 4000 / 7000

Investment of C = Rs.1,05,000

So, all three statements together are sufficient to answer the question.

7. Following question consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answers.

Average of weights of four persons A, B, D and E is 40 kg, then what is the weight of person C?

I: Ratio of weights of A to that of B is 38 : 45 and the difference between the weights of C and D is 4 kg. Ratio of weights of E to D is 37 : 40 and weight of E is 1 kg less than that of A.
II: Ratio of weights of C, D and E is 36 : 40 : 37 respectively and average of weights of A and B is 41.5 kg.
III: Difference between the weights of persons B and C is 9 kg.

Correct Answer: (e) Either II alone or I and III together are sufficient.
Solution:

From I:
Let the weights of A and B is 38x and 45x respectively.
Let the weight of D and E is 40y and 37y respectively

Weight of C = (40y - 4) kg or (40y + 4) kg

According to question-
38x - 37y = 1 ...(1)

(38x + 45x + 40y + 37y)/4 = 40
(83x + 77y) = 160 ...(2)

From (1) and (2)
x = y = 1

Weight of C = 44 kg or 36 kg.
Statement I alone is not sufficient.

From II:
Let the weight of C, D and E is 36x, 40x and 37x respectively.
Sum of weights of A and B = 41.5 × 2 = 83

According to question-
(83 + 40x + 37x)/4 = 40
77x = 77
x = 1

Weight of C = 36x = 36 kg
Statement II alone is sufficient.

From III:
We are not given the weight of B. So, we can’t calculate the weight of C.
Statement III alone is not sufficient.

From I and III:
From statement I we get:
Weight of C = 44 kg or 36 kg
Weight of B = 45x = 45 kg

Possible weights of C = (45 + 9) kg or (45 - 9) kg
= 54 kg or 36 kg

After combining both the statements together-
Weight of C = 36 kg

Statements I and III together are sufficient.

8. Following question consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answers.

Two cars A and B are initially a certain distance apart and car A meets car B after 12 minutes and 1.2 hours when travelling in opposite direction and same direction respectively. What is the initial distance between them?

I: Car A crosses a train of length 350 metres running in opposite direction with speed 45 km/h in 15.75 seconds.
II: Speed of car A is 40% more than the speed of car B.
III: Car B can cross a 490 metres long bridge in 70.56 seconds.

Correct Answer: (d) Either I alone or III alone is sufficient.
Solution:

Let the distance between cars A and B be ‘D’ km.
Let the speeds of cars A and B be ‘A’ and ‘B’ respectively.

According to question-
D/(A + B) = (12/60)
D = 0.2(A + B) ...(1)

D/(A - B) = 1.2
D = 1.2(A - B) ...(2)

From (1) and (2)-
0.2A + 0.2B = 1.2A - 1.2B
5A = 7B ...(3)

From I:
According to question-
(350/1000) = (A + 45) × (15.75/3600)
(A + 45) = 80
A = 35 km/h

From equation (3)
B = 25 km/h

From equation (1)
D = 0.2(35 + 25)
D = 12 km

Statement I alone is sufficient.

From II:
According to question-
A = 140% of B
5A = 7B ...(4)

Since, equations (3) and (4) are same. So, we can’t calculate the speed of either of the cars.

Statement II alone is not sufficient.

From III:
According to question-
(490/1000) = B × (70.56/3600)
B = 25 km/h

From equation (3):
A = 35 km/h

From equation (1):
D = 0.2(35 + 25)
D = 12 km

Statement III alone is sufficient

9. The below question is followed by three statements. You have to determine whether the data given in the statement(s) is/are sufficient for answering the question.

In a bag, there are 30 marbles of four colours - red, green, blue, and black. If two marbles are drawn one by one without replacement, then find the probability of drawing a green marble and then a black marble.

Statement I: The ratio of the number of red marbles to the number of green marbles is 2:1 and the number of green marbles is 1 more than the number of blue marbles. Number of black marbles is 2 more than the number of blue marbles.

Statement II: Probability of drawing two red marbles with replacement is 4/25 and probability of drawing two blue marbles with replacement is 1/36.

Statement III: Probability of drawing two green marbles without replacement is 1/29.

Correct Answer: (c) Either only I or both II and III together are sufficient
Solution:

Total number of marbles = 30

From statement I:
Let number of red marbles = 2X
Then number of green marbles = X
Number of blue marbles = X - 1
And number of black marbles = X + 1

Now, 2X + X + X - 1 + X + 1 = 30
5X = 30
X = 6

So, Red marbles = 12, Green marbles = 6, Blue marbles = 5, Black marbles = 7

Probability of drawing a green marble first = 6/30 = 1/5

Now total marbles left = 30 - 1 = 29

Probability of drawing a black marble = 7/29

Required probability = 1/5 × 7/29 = 7/145

Hence, statement I alone is sufficient.

From II and III together:
Probability of drawing two red marbles with replacement = 4/25

Let number of red marbles = X

So, X/30 × X/30 = 4/25
X² = 4 × 900/25
X = 2 × 30/5
X = 12

Probability of drawing two blue marbles with replacement = 1/36

Let number of blue marbles = Y

So, Y/30 × Y/30 = 1/36
Y = 30/6
Y = 5

Probability of drawing two green marbles without replacement = 1/29

Let number of green marbles = Z

So, Z/30 × (Z - 1)/29 = 1/29
Z² - Z - 30 = 0
(Z - 6)(Z + 5) = 0

Z = 6 or -5
Z cannot be negative, So Z = 6

Number of black marbles = 30 - (12 + 6 + 5) = 7

Now,
Probability of drawing a green marble first = 6/30 = 1/5

Now total marbles left = 30 - 1 = 29

Probability of drawing a black marble = 7/29

Required probability = 1/5 × 7/29 = 7/145

Hence, statements II and III together are sufficient.

10. In the following question, the question is followed by three statements. Read all the statements carefully and find which of the following statement(s) is/are sufficient to answer the question.

Respective ratio of speed of boat A in still water and upstream speed of boat B is 3:2. What is the difference between upstream and downstream distance covered by boat B in 3 hours?

Statement I: Boat A covers 220 km downstream in ‘t’ hours and the respective ratio of upstream speed of boat A and stream speed is 7:2.

Statement II: Respective ratio of speed of boat A and B in still water is 9:8 and the stream is flowing with speed (t + 3) km/hr.

Statement III: The difference between speed of boat A and B is 4 km/hr.

Correct Answer: (b) Any two statements together are sufficient.
Solution:

Let ‘a’ km/hr and ‘b’ km/hr are speeds of boat A and B in still water and speed of stream is ‘s’ km/hr.

Then, upstream speed of boat A = a - s
Upstream speed of boat B = b - s

Downstream speed of boat A = a + s
Downstream speed of boat B = b + s

Respective ratio of speed of boat A in still water and upstream speed of boat B is 3 : 2. Then,
a : (b - s) = 3 : 2
s = (3b - 2a)/3

From statement I: Boat A covers 220 km downstream in ‘t’ hours and the respective ratio of upstream speed of boat A and stream speed is 7 : 2.

(a + s) = 220/t
(a - s) : s = 7 : 2
s = 2a/9

(a + 2a/9) = 220/t
t = 180/a

(3b - 2a)/3 = 2a/9 ⇒ a(b) = 9 : 8

From statement II: Respective ratio of speed of boat A and B in still water is 9 : 8 and the stream is flowing with speed (t + 3) km/hr.

a(b) = 9 : 8
s = t + 3

From statement III: The difference between speed of boat A and B is 4 km/hr.

From statement I and II:
t + 3 = s = 2a/9
t = 2a/9 - 3 = 180/a
a = 36, b = 36 × 8/9 = 32
s = 2 × 36/9 = 8

Therefore, difference between upstream and downstream distance covered by boat B in 3 hours
= 3 × (32 + 8) - 3 × (32 - 8) = 48 km

From statement II and III:
a(b) = 9 : 8
a = b + 4

Then, (b + 4)(b) = 9 : 8 ⇒ b = 32
a = 32 + 4 = 36
s = (3b - 2a)/3 = (3 × 32 - 2 × 36)/3 = 8

Therefore, difference between upstream and downstream distance covered by boat B in 3 hours
= 3 × (32 + 8) - 3 × (32 - 8) = 48 km

From statement I and III:
a(b) = 9 : 8
a = b + 4

Then, (b + 4)(b) = 9 : 8 ⇒ b = 32
a = 32 + 4 = 36
s = (3b - 2a)/3 = (3 × 32 - 2 × 36)/3 = 8

Therefore, difference between upstream and downstream distance covered by boat B in 3 hours
= 3 × (32 + 8) - 3 × (32 - 8) = 48 km

Hence, any two statements together are sufficient.