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Data sufficiency
Direction (1-5): The following questions are accompanied by two/three statements I, II and III. You have to determine which statement is/are sufficient to answer the question.
1) What is the perimeter of square?
Statement I: Area of the circle is 420 square cm more than that of the area of the square.
Statement II: Circumference of the circle is 88 cm
Statement III: Area of the rectangle is 55 cm2 more than that of the area of the square. Ratio of the length and breadth of the rectangle is 6:5.
A) Only I and II are sufficient
B) Only II and III are sufficient
C) Either I or III and II are sufficient
D) All I, II and III necessary to answer the question
E) The question can’t be answered even with all I, II and III
2) If A, B and C three pipes open together, then how much time taken to fill the tank completely?
Statement I: Pipe A can fill the tank in 4 hours and Pipe B can empty the tank in 8 hours.
Statement II: Pipe C can fill the tank in 12 hours.
A) Only I
B) Only II
C) Either I or II are sufficient
D) Both I and II sufficient to the answer the question
E) The question can’t be answered even with all I and II
3) What is the speed of the stream?
Statement I: Speed of boat in still water is four times the speed of stream
Statement II: Downstream speed is 8kmph and upstream speed is 4kmph.
Statement III: The boat goes 40km and comes back in 8 hours.
A) Only I and II are sufficient
B) Only II and III are sufficient
C) Either II or III and I is sufficient
D) All I, II and III necessary to answer the question
E) The question can’t be answered even with all I, II and III
4) Find the CP of the article?
Statement I: Shopkeeper sells the article at the profit of 20%. If he had bought it at 20% less and sold it for Rs.20 less he would have gained 25%.
Statement II: If an article sold at 30% profit instead of 30% loss, it would have bought Rs.45.
A) Only I
B) Only II
C) Either I or II is sufficient
D) All I and II necessary to answer the question
E) The question can’t be answered even with all I and II
5) What is the sum of the initial investment of A and B?
Statement I: A, B and C enter into the business by investing in the ratio of 4:5:6. After three months A and B withdrew half of his investment.
Statement II: At the end certain period, C got a profit share of Rs.12000 out of the total profit of Rs. 28000.
A) Only I
B) Only II
C) Either I or II are 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
Application Sums
6) A bike travelled first x km at 10kmph faster than the usual speed but it returned the same distance at 10kmph slower than the usual speed, If the total time taken by the bike is 12 hours and the faster speed is y kmph. Then Find the value of x and y?
A) 50km, 25kmph
B) 25km, 15kmph
C) 20km, 18kmph
D) 30km, 20kmph
E) None of these
7) (x-6) men can do a piece of work in x days and (x+6) men can do one-fourth of the same work in (x-11) days. Then in how many days can (x+12) men finish the work?
A) 5 days
B) 3 days
C) 2 days
D) 4 days
E) None of these
8) The radius of the sphere is 25% more than the length of the rectangle. The breadth of the rectangle is 22cm. If the area of the rectangle is equal to the curved surface area of the sphere, then what will be the curved surface area of the sphere?
A) 24.64
B) 30.64
C) 28.64
D) 32.64
E) None of these
9) A, B and C can complete the work in 8 days, 12 days and 24 days respectively. How many days does it need to complete the work if A start the work, every second day B joined with A and every third day C joined with A?
A) 6 days
B) 8 days
C) 4 days
D) 9 days
E) None of these
10) Boat can travel 5 times distance down the stream then up the stream in the same time. If the speed of the boat in still water is 18kmph, and then find the speed of the current?
A) 10kmph
B) 15kmph
C) 12kmph
D) 8kmph
E) None of these
Answers :
Directions (1-5) :
1) Answer: A
From Statement I,
(∏*r*r) – (a*a) = 420
So, statement I alone is not sufficient to answer the question.
From Statement II,
2*∏*r=88
r=88*7/22*2
r=14 cm
So, statement II alone is not sufficient to answer the question.
From Statement III,
(l*b) – (a*a) =55
Length and breadth=6:5
So, statement III alone is not sufficient to answer the question.
From I and II,
22/7*14*14-a*a=420
616-420=a*a
a=14
Perimeter=4*14=56
2) Answer: D
From Statement I,
A=1/4
B=1/8
So, statement I alone is not sufficient to answer the question.
From Statement II,
C=1/12
So, statement II alone is not sufficient to answer the question.
From I and II,
Time taken =1/4+1/12-1/8
=5/24
Time=4.8 hours
3) Answer: C
From Statement I,
Speed of boat=w
Speed of water=b
b=4w
So, statement I alone is not sufficient to answer the question.
From Statement II,
Speed of water=(8-4)/2=4/2=2kmph
So, statement II alone is sufficient to answer the question.
From Statement III,
40/(b+w)+40/(b-w)=8
So, statement III alone is not sufficient to answer the question.
From I and III
40/5w+40/3w=8
1/w+5/3w=1
3+5=3w
8=3w
w=8/3kmph
4) Answer: C
From Statement I,
120x/100-80x/100*125/100=20
120x-100x=2000
20x=2000
X=100
So, statement I alone is sufficient to answer the question.
From statement II,
130x/100-70x/100=45
60x=4500
X=75.
So, statement II alone is sufficient to answer the question.
5) Answer: E
From Statement I,
Investment ratio of A, B and C=4:5:6
After 3 months profit ratio, there is no information about C’s investment
So, statement I alone is not sufficient to the answer the question.
From statement II,
C’s share=12000
Total profit=28000
There is no information about the period of investment.
So, statement II alone is not sufficient to the answer the question.
Directions (6-10) :
6) Answer: A
From Option (A)
s=usual speed
50/(s+10)+50/(s-10)=12
(50(s-10)+50(s-10))/(s2-100)=12
100s=12s2-1200
3s2-25s-300=0
s=15
Faster speed y=15+10=25kmph
7) Answer: B
(x-6)x=((x+6)*(x-11))/1/4
X2-6x=4(x2-11x+6x-66)
3x2-14x-264=0
3x2-36x+22x-264=0
3x(x-12)+22(x-12)=0
(x-12)(3x+22)=0
x=12 and negative value neglect.
(12+12)*d=(12-6)*12
24d=6*12
d=3
8) Answer: A
Let the length of the rectangle=x
Radius of the sphere=125x/100=5x/4
4*22/7*(5x/4)(5x/4)=22*x
X=28/25
Radius=5/4*28/25=7/5
CSA of sphere=4*22/7*7/5*7/5=24.64
9) Answer: A
A=1/8
B=1/12
C=1/24
First day A is complete 1/8 of the work.
Second day B joined with A=1/8+1/12=5/24
Second day 1/8+5/24=8/24=1/3
Second day (A+B) complete 1/3 of the work
Third day (A+C)=1/8+1/24=4/24=1/6
Third day total work completed by=1/6+1/3=1/2
Remaining ½ work completed by another 3 days.
Total time=3+3=6 days
10) Answer: C
Downstream speed=5 upstream speed
Speed of the boat in still water=25kmph
(18+W)=5(18-W)
18+W=90-5w
6w=72
W=12kmph
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