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Data Sufficiency
Directions (Q. 1 – 5): The following questions are accompanied by two statements I and II. You have to determine which statement is/are sufficient to answer the questions.
1) Find the perimeter of circle?
I) The ratio of length and breadth of a rectangle is 7 : 5 and the area is 875 sq m. The radius of the circle is equal to the length of the rectangle.
II) The perimeter of the square is 140 m and the side of the square is equal to the radius of the circle.
a) Neither Statement I alone or Statement II alone is sufficient
b) Both the Statement I and II are sufficient
c) Statement I alone is sufficient
d) Statement II alone is sufficient
e) Either Statement I alone or Statement II alone is sufficient
2) Find the present age of R, if the age of Q, 5 years ago is 17 years?
I) 5 years ago, the age of P and 8 years hence, the age of Q is in the ratio of 2: 3.
II) The average present age of P, Q and R, after 10 years is 35 years.
a) Statement I alone is sufficient
b) Neither Statement I alone or Statement II alone is sufficient
c) Either Statement I alone or Statement II alone is sufficient
d) Statement II alone is sufficient
e) Both the Statement I and II are sufficient
3) Find the perimeter of the square, if the side of the square is equal to the radius of the cylinder?
I) The surface area of cylinder is 3080 cm and the height of the cylinder is 21 cm.
II) The volume of the cylinder is 12936 sq cm and height of the cylinder is 7 cm more than the radius of the cylinder.
a) Statement I alone is sufficient
b) Either Statement I alone or Statement II alone is sufficient
c) Both the Statement I and II are sufficient
d) Neither Statement I alone or Statement II alone is sufficient
e) Statement II alone is sufficient
4) How long will 12 women and 6 men take to do the work?
I) 8 women and 4 men can complete the work in 10 days.
II) 10 women and 8 men can complete the same work in 6 days.
a) Neither Statement I alone or Statement II alone is sufficient
b) Statement II alone is sufficient
c) Either Statement I alone or Statement II alone is sufficient
d) Both the Statement I and II are sufficient
e) Statement I alone is sufficient
5) Find the cost price of an item, if the profit earned is Rs. 560?
I) A shopkeeper allows a discount of 20 % on the marked price of an item and sells it for Rs. 2400.
II) The shopkeeper allows a discount of 25 % on the marked price. The marked price of the item is Rs. 3200.
a) Statement I alone is sufficient
b) Neither Statement I alone or Statement II alone is sufficient
c) Both the Statement I and II are sufficient
d) Either Statement I alone or Statement II alone is sufficient
e) Statement II alone is sufficient
Data Interpretation
Directions (Q. 6 – 10): Study the following information carefully and answer the given questions?
The given line graph shows the speed of the boat in still water on 5 different days.
6) If the boat on Friday travelled 30 km upstream in 72 minutes which is 20% more than that of the travelling time of boat in downstream, then what is the distance travelled by boat in downstream?
a) 28 km
b) 30 km
c) 31 km
d) 32 km
e) None of these
7) On Tuesday, the distance travelled by a boat is 75 km and the time taken by boat to cover that distance in downstream to upstream is in the ratio of 3:5. What is the speed of stream?
a) 2 kmph
b) 5 kmph
c) 8 kmph
d) 10 kmph
e) None of these
8) If on Wednesday, the speed of upstream is 20 kmph, then what is speed of downstream?
a) 24 kmph
b) 28 kmph
c) 32 kmph
d) 36 kmph
e) None of these
9) If on Thursday, the ratio of the speed of the stream to the speed of the boat in still water is 1:4, the time taken by boat to travel x km in upstream is 2 hours more than that of the boat travels the same distance in downstream, then find the distance ?
a) 60 km
b) 48 km
c) 36 km
d) 24 km
e) None of these
10) On Monday, the boat takes 10 hours to travel 120 km in upstream and the boat covers the same distance in downstream in x hours. Find the value of x?
a) 3 hours
b) 5 hours
c) 7 hours
d) 9 hours
e) None of these
Answers :
Directions (1-5) :
1) Answer: E
From statement I,
The ratio of length and breadth of a rectangle = 7 : 5 (7x, 5x)
Given,
7x * 5x = 875
35x2 = 875
x2 = 875 / 35 = 25
x = 5
The length of the rectangle = The radius of circle = 35 m
Perimeter of circle = 2 * (22/7) * 35 = 220 m
Statement I alone is sufficient to answer the question.
From statement II,
The perimeter of the square = 4a = 140 m
Side (a) = 140 / 4 = 35 m = The radius of circle
Perimeter of circle = 2 * (22/7) * 35 = 220 m
Statement II alone is sufficient to answer the question.
2) Answer: E
From statement I and II,
5 years ago, the age of P and 8 years hence, the age of Q is in the ratio = 2: 3
The present age of P and Q = 2x + 5, 3x – 8
The age of Q, 5 years ago = 17 years
The present age of Q = 22 years
3x – 8 = 22
3x = 30
x = 10
The present age of P = 25 years
The average present age of P, Q and R, after 10 years = 35 years
25 + 22 + R + 30 = 35 * 3
77 + R = 105
R = 28
The present age of R = 28 years
Both the Statement I and II are sufficient to answer the question.
3) Answer: A
From statement I,
The height of the cylinder = 21 cm
The surface area of cylinder = 3080 cm
= > 2Ï€r (r + h) = 3080
= > 2 * (22/7) * r * (r + 21) = 3080
= > r2 + 21r = 3080 * (7/44)
= > r2 + 21r = 490
= > r2 + 21r – 490 = 0
= > (r + 35) (r – 14) = 0
= > r = 14, -35 (Negative value will be eliminated)
Side of the square (a) = 14 cm
Perimeter of square = 4a = 4 * 14 = 56 cm
Statement I alone is sufficient to answer the question.
From statement II,
The height of the cylinder = (r + 7) cm
The volume of the cylinder = 12936 sq cm
= > πr2h = 12936
= > (22/7) * r2 * (r + h) = 12936
Statement II alone is not sufficient to answer the question.
4) Answer: D
From statement I and II,
(8 w + 4 m) * 10 = (10 w + 8 m) * 6
40 w + 20 m = 30 w + 24 m
10 w = 4 m
5 w = 2 m
8 w + 4 m = 8 w + 10 w = 18 w
12 w + 6 m = 12 w + 15 w = 27 w
Women     days
18Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10
27Â Â Â Â Â Â Â Â Â Â Â Â Â Â ?
Required days = (18 * 10) / 27 = 20/3 = 6 2/3 days
Both the Statement I and II are sufficient to answer the question.
5) Answer: D
From statement I,
CP = 2400 – 560 = Rs. 1840
Statement I alone is sufficient to answer the question.
From statement II,
SP = 3200 * (75/100) = Rs. 2400
CP = 2400 – 560 = Rs. 1840
Statement II alone is sufficient to answer the question.
Directions (6-10) :
6) Answer: C
Upstream speed=30/(72/60) =25 kmph
Speed of the Boat in still water=28 kmph
Speed of the stream=28 – 25 =3 kmph
Downstream Speed=28 + 3 =31 kmph
The travelling time of boat in downstream = (72 * 100) / 120 = 60 minutes
Distance travelled in downstream=31 * 1=31 km
7) Answer: B
Consider the speed of stream = W
Time taken by boat to cover 75 km in downstream = 75 / (20+ W)
Time taken by boat to cover that distance in upstream =75 / (20 – W)
So ,
(75/(20 + W)) / (75 / (20 –W)) =3/5
(20 – W) / (20 + W) = 3/5
60 + 3W = 100 – 5W
40 = 8W
W=5 kmph
8) Answer: B
Speed of steam=24 – 20 =4 kmph
Speed of downstream=24 + 4 =28 kmph
9) Answer: A
Speed of the boat in still water = 16 kmph
Speed of stream = (1/4) * 16 = 4 kmph
Speed of boat in downstream = 16 + 4 = 20 kmph
Speed of boat in upstream = 16 – 4 = 12 kmph
(x/12) – (x/20) = 2
5x – 3x=120
X=60 km
10) Answer: B
Speed of boat in upstream=120/10=12 kmph
Speed of stream = 18 – 12 = 6 kmph
Speed of boat in downstream=18 + 6 =24 kmph
Time taken by the boat in downstream = 120/24 = 5 hours
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