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Data sufficiency
Direction (1 – 5): The following questions are accompanied by three statements I and II. You have to determine which statement is/are sufficient to answer the question.
1) Written in digit form, 24x82y. If the digit is divisible by 9, what is the value of x and y?
Statement I: Difference between x and y is 1.
Statement II: x * y = 30
a) Only I
b) Only II
c) Either I or II sufficient
d) All I and II necessary to the answer the question
e) The question can’t be answered even with all I and II
2) What is the volume of the cylinder?
Statement I: Surface area of the sphere is equal to the curved surface area of the cone and the radius of the cylinder is equal to the radius of the sphere.
Statement II: Radius of the sphere is equal to the radius of the cylinder and the radius and height of the cone is 7 cm and 24 cm respectively.
a) Only I
b) Only II
c) Either I or II sufficient
d) All I and II necessary to the answer the question
e) The question can’t be answered even with all I and II
3) Find the value of x?
Statement I: If A’s age is x% of more than that of B’s age and D’s age is 30% more than C.
Statement II: B’s age is 20% more than C and A’s age is 50% more than D.
a) Only I
b) Only II
c) Either I or II sufficient
d) All I and II necessary to the answer the question
e) The question can’t be answered even with all I and II
4) A, B and C started the business. What is C’s profit share?
Statement I: A and B invests Rs.6000 and Rs.8000 respectively and after 6 months C joined with them with the investment of Rs.6000.
Statement II: Total profit is Rs.28000 and the B’s investment period is 8 months.
a) Only I
b) Only II
c) Either I or II sufficient
d) All I and II necessary to the answer the question
e) The question can’t be answered even with all I and II
5) A bag contains x red balls and y blue balls. Find the value of x?
Statement I: The probability of two red balls selected randomly is 1/6.
Statement II: The probability of two blue balls is selected at randomly is 5/18.
a) Only I
b) Only II
c) Either I or II sufficient
d) All I and II necessary to the answer the question
e) The question can’t be answered even with all I and II

6. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
A.2 hours
B.3 hours
C.4 hours
D.5 hours


7. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
A.8.5 km/hr
B.9 km/hr
C.10 km/hr
D.12.5 km/hr

8. 
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A.4
B.5
C.6
D.10

9. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
A.3 km/hr
B.5 km/hr
C.8 km/hr
D.9 km/hr

10.  Agrocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
A.Rs. 4991
B.Rs. 5991
C.Rs. 6001
D.Rs. 6991
Solution-
Answers:
Directions (1-5):
1) Answer: E
From statement I,
Sum of the digits = 2 + 4 + x + 8 + 2 + y = 16 + x + y
The number is divisible by 9, so sum of the digits is divisible by 9.
So, x + y = 2 or 11
x – y = 1 or y – x = 1
So, statement I alone is not sufficient to answer the question.
From statement II,
Sum of the digits = 2 + 4 + x + 8 + 2 + y = 16 + x + y
The number is divisible by 9, so sum of the digits is divisible by 9.
So, x + y = 2 or 11
x * y = 30
So, x + y = 2 is not possible.
x + y = 11
x = 11 – x
x * (11 – x) = 30
11x – x= 30
x2– 11x + 30 = 0
(x – 5) (x – 6) = 0
x = 5, 6
If x = 5 means y = 6 and if x = 6 means y = 5
So the number forms, 24x82y = 245826 or 246825
So, statement II alone is not sufficient answer the question.
2) Answer: E
From statement I,
Surface area of the sphere = 4πr2 = 4 * 22/7 * r2
CSA of cone = πrl = 22/7 * r * l
So, Statement I alone is not sufficient to answer the question.
From statement I,
Radius of the cone = 7 cm
Height of the cone = 24 cm
So, Statement II alone is not sufficient to answer the question.
3) Answer: D
From statement I,
A = [(100 + x)/100] * B
D = 130/100 * C
So, Statement I alone is not sufficient to answer the question.
From statement II,
B = 120/100 * C
A = 150/100 * D
So, Statement II alone is not sufficient to answer the question.
From I and II,
A = [(100 + x)/100] * B
D = 130/100 * C
B = 120/100 * C
A = 150/100 * D
2A/3 = D
2A/3 = 13/10 * C
20A/39 = C
B = 6/5 * 20A/39
B = 8A/13
A = (100 + x)/100 * 8A/13
1300 = 800 + 8x
500 = 8x
x = 62.5
Both the statements are necessary to answer the question.
4) Answer: E
From statement I,
A’s investment = Rs.6000
B’s investment = Rs.8000
C’s investment = Rs.6000
So, Statement I alone is not sufficient to answer the question.
From statement II,
Total profit = Rs.28000
B’s investment period = 8 months
So, Statement II alone is not sufficient to answer the question.
From I and II,
A and C’s investment period is not given.
Both the statements are not necessary to answer the question.
5) Answer: E
From statement I,
1/6 = x * (X – 1)/(x + y) * (x + y – 1)
1/6 = (x2 – x)/(x2 + xy – x + xy + y2 –y)
6(x2 – x) = x2 + xy – x + xy + y2 –y
6x2 – 6x = x2 + xy – x + xy + y2 –y
5x2 – 2xy – 5x – y2 +y = 0
So, Statement I alone is not sufficient to answer the question.
From statement II,
5/18 = y * (y – 1)/(x + y) * (x + y – 1)
18(y2 – y) = 5(x2 + xy – x + xy + y2 –y)
18y2 – 18y = 5x2 + 10xy – 5x + 5y2 –5y
13y2 – 13y – 5x2 – 10xy + 5x = 0
So, Statement II alone is not sufficient to answer the question.

6. C

7. Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.

8. Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
30+30= 41
(15 + x)(15 - x)2
900=9
225 - x22
 9x2 = 225
 x2 = 25
 x = 5 km/hr.

9. 
Speed in still water =1/2(11 + 5) kmph = 8 kmph.

10. Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
 Required sale = Rs. [ (6500 x 6) - 34009 ]
   = Rs. (39000 - 34009)
   = Rs. 4991.