Quant : Data Sufficiency for IBPS Clerk Mains 2017 – Set-3

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Data Sufficiency for IBPS Clerk Mains 2017

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Data Sufficiency for IBPS Clerk Mains 2017 will help you learn concepts on important topics in Quant Section.

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Data Sufficiency for IBPS Clerk Mains 2017


1.Rahul owns 75 government securities from Lot -L1 and 120 government securities from Lot -L2. What is the net worth of his government securities from the two lots?
I. The value of each government security from Lot- L1 is twice the value of each government security from Lot -L2.
II. The value of 8 government securities from Lot -L1 and the value of 6 government securities from Lot- L2 is Rs. 4400.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Neither statement I nor statement II is sufficient to answer the question

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D. Both the statements I and II together are necessary to answer the question.

Suppose the value of each government securities from Lot- L1 is Rs. x and value of each government securities from Lot- L2 is Rs. y
From statement I: x = 2y
From statement II: 8x+6y = 4400
Neither statement I nor statement II alone can give the value of x and y
Now, from both the statements
(8*2y) + 6y = 4400
=> 16y + 6y = 4400
=> 22y = 4400
=> y = 4400/22 = 200
So, x = 2*200 = 400
Hence, total worth of government securities of Rahul = 75x + 120y = (75*400) + (120*200) = Rs. (30000+24000) = Rs. 54000
Therefore, both the statements together are necessary to answer the question.

2.Barj worked for 8 days on a project in his village. He was paid Rs. 5.5 more for each day of work as compared to the amount he was paid on the preceding day. How much was he paid for the third day of the work?
I. His total earning after 8 days of work, was Rs. 1200
II. He was paid less than Rs. 78.50 on the first day.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Neither statement I nor statement II is sufficient to answer the question

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A. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question

Let he was paid Rs. x on 1st day,
From statement I:
x+(x+5.5)+(x+11)+(x+16.5)+(x+22)+(x+27.5)+(x+33)+(x+38.5) = 1200
=> 8x+154 = 1200
=> 8x = 1200-154
=> 8x = 1046
=> x = 130.75
He paid for the third day of the work = Rs. (x+11) = Rs. (130.75+11) = Rs. 141.75.
From statement II,
It is not mentioned that how much less than Rs. 78.50 was he paid on the first day. So we can’t determine the amount he was paid on the third day.
Hence, only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question.

3.A bag contains 75 balls out of which at least 15 balls are red. If three balls are picked at random from the bag, what is the probability that one of the balls is not red?
I. Only 35 balls in the bag are blue.
II. When a ball is picked at random from the bag, the probability of the ball being white is 1/5.
III. When two balls are picked at random from the bag, the probability of both the ball being green is 12/925.
a. Any one statement is sufficient to answer the question
b. Any two statements together are sufficient to answer the question
c. Statement I and III together are sufficient to answer the question
d. All three statements together are sufficient to answer the question
e. All three statements together are not sufficient to answer the question

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E. All three statements together are not sufficient to answer the question

From I
We know about 15+35 i.e. 50 balls but we don’t know the color of remaining 25 balls
From II
When a ball is picked at random from the bag, the probability of the ball being white is 1/5 = 15/75
So, the number of white balls = 15
We know about 15+35 i.e. 50 balls but we don’t know the color of remaining 25 balls
Using I and II
We know about 15+35+15 i.e. 65 balls but we don’t know the color of remaining 10 balls
From III
When two balls are picked at random from the bag, the probability of both the ball being green is 12/925
=> nC2/75C2 = 12/925 (where n is number of green balls)
=> n(n-1)/(75*74) = 12/925 => n = 9

Using I and III or II and III or all I, II and III together we cannot determine the exact number of red balls in the bag.

4.A shopkeeper sells sugar at the rate of Rs. 100 per kg to customers. How much profit was earned on every kg of sugar sold?
I. 20% profit would have been earned, if sugar was sold for Rs. 90 per kg.
II. The profit was one-third of the cost price.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Neither statement I nor statement II is sufficient to answer the question

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C. Either statement I or statement II alone is sufficient to answer the question

Let cost price of sugar is Rs. x
From statement I,
Cost price = (90*100)/120 = Rs. 75
Profit = Rs. (100-75) = Rs. 25
From statement II,
Selling price = cost price + profit
=> x + (x/3) = 100
=>4x/3 = 100
=> x = (100*3)/4 = 75
so, profit = cost price/3 = Rs.(75/3) = Rs. 25
Hence, either statement I or statement II alone is sufficient to answer the question.

5.What is the speed of the car?
I. Time taken to cover a distance of 264 km by a truck is 2 hours more than that by the car.
II. The truck’s speed is 22 km/h slower than the car.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Only either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Neither statement I nor statement II is sufficient to answer the question

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D. Both the statements I and II together are necessary to answer the question

From statement I,
Distance = 264 km
Let the time taken by the car be T hours.
Therefore,
Time taken by the truck = (T + 2) hours
From statement II,
Let the speed of the car = SC km/h
Therefore

Speed of the truck = (SC– 22) km/h
From statement I and II,
264/SC= 264/(SC – 22) – 2
264/(SC – 22) – 264/SC = 2
(264SC – 264SC + 5808)/{SC*(SC – 22)} = 2
2(SC)2– 44SC = 5808
(SC)2– 22SC – 2904 = 0
SC= 66 or -44
Neglect the negative value of SC.

Therefore,
Speed of the car = 66 km/h
Therefore, both the statements are necessary to answer the question

6.Virat is a typist in Central secretariat. He types a certain application. How many words are there in the application?
Statement I: He will take 2 minute less to type the application at an average speed of 100 words per minute than the time taken to type the application at an average speed of 70 words per minute.
Statement II: He will take 5 minute to type the first half of the application at an average speed of 55 words per minute.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Only either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Neither statement I nor statement II is sufficient to answer the question

 

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C. Only either statement I or statement II alone is sufficient to answer the question.

Let ‘t’be the number of minutes it takes to type the application at a rate of 70 words per minute then according to statement,
(t – 2)* 100 = t*70 => (100t – 70t) = 200 = > t = 200/30 = 20/3 minutes
So, the total number of words in the application = (20/3)*70 = 467 words (approx)
Hence, statement I alone is sufficient to answer the question.
From statement II
According to question, Work = Rate*Time
Work is half of the application. The rate is 55 words per minute and time is 5 minute.
So, (1/2) work = 55*5 = 275 => work = 2*275 = 550
Thus, total number of words in the application = 550 words
Hence, statement II alone is sufficient to answer the question.
Thus, only either statement I or statement II alone is sufficient to answer the question.

7.What is the probability of picking three green balls from a bag of 49 balls containing 24 red balls?
Statement I: The number of red balls in the bag is twice the number of blue balls in the bag.
Statement II: The number of white balls in the bag is one less than the number of green balls in the bag.
Statement III: There are balls of five different colors in the bag.
Which one of the following is sufficient to answer the question?
a. Statement I
b. Statement I & II together
c. Statement II & III together
d. Statement I, II & III together
e. None of the above

 

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E. None of the above

From Question Number of red balls = 24
From I
Number of blue balls = 24/2 = 12
From II
Number of white balls = Number of green balls -1
From III
There are balls of 5 different colors in the bag
Even after using all the three statement we cannot determine the number of green balls in the bag.

8.Team India can reach Firoz Shah Kotla stadium from a hotel in Connaught Place by one of the two routes. What is the length of the shorter route?
Statement I: When the bus carrying team India drives from hotel to stadium by the shorter route and returns by the longer route, it drives a total of 42 km
Statement II: When the bus carrying team India drives both ways from hotel to stadium and back, by the longer route, it drives a total of 46 km.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Only either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Neither statement I nor statement II is sufficient to answer the question

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D. Both the statements I and II together are necessary to answer the question

Let the length of the shorter route = x km
And the length of the longer route = y km
Then, from statement I, x + y = 42
From statement II, y + y = 46
Or, y = 23
So, from both statements,
x = 42 – y = 42 – 23 = 19
Thus, both the statements I and II together are necessary to answer the question.

9.A Hawk is flying in the blowing wind. What is the Hawk’s speed in still air?
Statement I: The speed of the wind is one-third of the Hawk’s speed in still air.
Statement II: In a given time, the Hawk can fly twice as far with the wind as it can against the wind.
a. Only statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question
b. Only statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question
c. Only either statement I or statement II alone is sufficient to answer the question
d. Both the statements I and II together are necessary to answer the question
e. Both statements I and II together are not sufficient to answer the question

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E. Both statements I and II together are not sufficient to answer the question

Let the speed of Hawk in still air is h and speed of wind is w
From statement I,
3w = h
From statement II,
d/(h-w) = 2d/h+w
=>h = 3w
Both the equations are same and the equation cannot be solved for h or w
Hence, both the statements together are not sufficient to answer the question.

10.There are three pipes A, B and C connected to a tank. Pipe-A fills pure milk which contain 12% cream, Pipe-B fills water in the tank and Pipe-C fills only cream in the tank. If all the pipes are opened together and they fill the tank at their normal capacity, how long will it takeso that the cream content is 8% in the tank?
Statement I: The normal capacity of Pipe-A, Pipe-B and Pipe-C are 50 ltr/hr, 5 ltr/hr and 1 ltr/hr respectively.
Statement II: Initially, there was 10 ltr pure milk in the tank.
Statement III: The volumetric capacity of the tank is 50 ltr.
Which one of the following is sufficient to answer the question?
a. Statement I & II
b. Statement II & III
c. Statement I & III
d. Statement I, II and III
e. None of the above

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D. Statement I, II and III

From I
A = 50 ltr/hr, B = 5 ltr/hr, C = 1 ltr/hr
From II
Initially there was 10 ltr pure milk in the tank
From III
Volume of tank = 50ltr
So, I is necessary to solve the question
From I and II
Let after t hours the cream concentration will be 8%
So, {(50)t(0.12)+(5)(t)(0)+(1)(t)(1)}/{10+(50)t+(5)(t)+(1)(t)} = 8/100
=>7t/(56t+10) = 2/25
=>175t = 112t+20
=>t = 20/63 h

Total volume of liquid in the tank after 20/63 hr = 10+56*20/63 ltr = 27.8 ltr
It is to be noted that Statement III also is necessary to answer the question because sufficient empty space is needed in the tank for the three pipes to be operating until the calculated time.


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