21. What is the length of the train?

Statement I: The train crosses a man is running in opposite direction at the speed of 20 kmph in 14.4 seconds and the speed of the train is 60 kmph.

Statement II: The train crosses a 200 m long platform in 54 seconds and also crosses a pole in 18 seconds.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “C” is correct.

Answer: C

From statement I,

Length of train = (60 + 20) *5/18* 14.4

= 320 m

So, Statement I alone is sufficient to the answer the question.

From statement II,

Speed of train = y

Length of train = x

x + 200 = y * 5/18 * 54

x + 200 = 15y

x = y * 5/18 * 18

x = 5y

10y = 200

y = 20

x = 100 m

So, Statement II alone is sufficient to the answer the question.

22. Ratio between the length and breadth of the rectangle A is 7 : 5. Find the area of the square B.

Statement I: Length of the rectangle A is same as the diameter of the circle, whose area is 1386 cm2.

Statement II: The perimeter of the rectangle A is 44 cm more than the perimeter of the square B.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “E” is correct.

Answer: E

Let length of the rectangle = 7x

And breadth of the rectangle = 5x

From Statement I:

We have given that,

πr= 1386

r= 1386 × 7/22

r = 21 cm

So, the length of the rectangle = 21 × 2 = 42 cm

And the breadth of the rectangle = 42/7 × 5 = 30 cm

From Statement I and II:

 2 × (l + b) – 4a = 44

 2 × (42 + 30) – 4a = 44

144 – 4a = 44

 4a = 100

 a = 25

So, the area of the square B= (25)= 625 cm2

Hence, Both Statement I and Statement II are necessary to answer the question.

23. Find the amount invested at the rate of 20%?

Statement I: A person invested in two schemes X and Y in the ratio of 2 : 1. Scheme X offered simple interest at 20% per annum and scheme Y offered compound interest at 30% per annum. Person got a total interest of Rs. 2711.8 after two years from both schemes.

Statement II: Total amount of Rs. 6000 invested in two different schemes at the rate of 30% and 20% per annum for two years. Simple interest received from both schemes are equal.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data given in both statements I and II together are necessary to answer the question.
C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
D. The data given in both statements I and II together are not sufficient to answer the question.
E. The data either in statement I alone or in statement II alone is sufficient to answer the question.

Option “E” is correct.

Answer: E

From Statement I:

Let person invested = Rs. 3x

Now, compound interest of 2 years on 30%.

= 30 + 30 + (30 × 30)/100

= 69%

So, according to the question,

 [(2x × 20 × 2)/100] + (x × 69/100) = 2711.8

4x/5 + 69x/100 = 2711.8

 (80x + 69x)/100 = 2711.8

149x/100 = 2711.8

x = 2711.8 × 100/149

x = 1820

So, the amount invested on 20% = 1820 × 2 = Rs. 3640.

From Statement II:

Let amount invested on 30% = Rs. x

And amount invested on 20% = Rs. (6000 – x)

So, according to the question,

(x × 30 × 2)/100 = [(6000 – x) × 2 × 20]/100

60x = (6000 – x) × 40

60x = 2,40,000 – 40x

100x = 2,40,000

x = 2400

So, the amount invested on 20% = (6000 – 2400) = Rs. 3600.

Hence, Either Statement I alone or Statement II alone are sufficient to answer the question.

24. Find the score of c.

Statement I: The average score of a,b,c is 10. The score of c is 4 more than b and 4 less than a.

Statement II: The average score of a,b,c is 10.The ratio of a and b is 7:3 and the difference between a and b is 8.

A. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. The data in statements II alone is sufficient to answer the question, while the data in 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. The data in both the statements I and II is not sufficient to answer the question.
E. The data in both the statements I and II together is necessary to answer the question.

Option “C” is correct.

Answer: C

Statement I:

c= b+4

= > b= c-4

c= a-4

= > a=c+4

a+b+c = 10*3=30

= >(c+4)+(c-4)+c =30

= > 3c = 30

= > c= 10

Statement II:

a:b = 7:3

a-b = 8

= > 4’s = 8

= > 1’s =2

= > 7’s = 14

= > 3’s = 6

14+6+c = 10*3=30

c = 10

25. Find the time taken by the boat covers 360 km along with stream?

Statement I: The speed of the boat along with stream is 25% more than the speed of the boat in still water.

Statement II: The boat covers 240 km against stream in 16 hours.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “E” is correct.

Answer: E

From statement I,

Speed of boat = x

Speed of downstream = x * 125/100 = 5x/4

So, Statement I alone is not sufficient to answer the question.

From statement II,

Speed of upstream = 240/16 = 15 kmph

So, Statement II alone is not sufficient to answer the question.

From Statement I and II,

x – y = 15

x + y = 5x/4

y = x/4

x – x/4 = 15

3x = 15 * 4

x = 20

y = 20/4 = 5

Required time = 360/(20 + 5) = 14.4 seconds

Both statements are necessary to answer the question.

26. A company has two different departments IT and HR and the total number of employees in the company is 3300. Find the total number of female employees in HR department?

Statement I: The ratio of the number of male to female employees in IT department is 4:3 and the ratio of the number of male to female employees in HR department is 9:10.

Statement II: Total number of employees in IT departments is 1400 and the number of male employees in HR department is 100 less than the number of female employees in HR department.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “B” is correct.

Answer: B

From Statement I,

Number of male employees in IT = 4x

Number of female employees in IT = 3x

Number of male employees in HR = 9y

Number of female employees in HR = 10y

So, Statement I alone is not sufficient to answer the question.

From Statement II,

Number of female employees in HR = x

Number of male employees in HR = x – 100

Total number of employees in HR = 3300 – 1400 = 1900

x + x – 100 = 1900

2x = 2000

x = 1000

So, Statement II alone is sufficient to answer the question.

27. Find the selling price of the book?

Statement I: If the marked price of the book is 15% more than its cost price and the shopkeeper offer a discount of 10% on marked price of the book.

Statement II: If the book sold at the profit of 3.5% and the discount offered by the book is Rs.20.7.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “E” is correct.

Answer: E

From statement I,

CP of book = x

MP of book = x * 115/100 = 1.15x

SP of book = 1.15x * 90/100 = 1.035x

So, Statement I alone is not sufficient to answer the question.

From statement II,

Profit of book = 3.5%

Discount = Rs.20.7

So, Statement II alone is not sufficient to answer the question.

From statement I and II,

1.15x – 20.7 = 1.035x

x = 180

SP of book = 1.035 * 180 = Rs.186.3

Both statements are necessary to answer the question.

28. A box contains certain number of red, blue and yellow balls. Find the total number of balls in the box?

Statement I: Ratio of the number of red, blue and yellow balls in the box is 3:2:4 respectively. If two balls are drawn at random, then the probability of that ball being a red and a blue ball is 16/105.

Statement II: Number of red balls in the box is 10 and the ratio of the number of blue and yellow balls is 3:4. If one ball is drawn at random, then the probability of that ball being red is 5/12.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “C” is correct.

Answer: C

From statement I,

3xC1 * 2xC1/9xC2 = 16/105

3x * 2x * 2/9x * (9x – 1) = 16/105

4x * 105 = 48x * (9x – 1)

420x = 432x – 48

x = 4

Total number of balls = 9 * 4 = 36

So, Statement I alone is sufficient to answer the question.

From statement II,

10C1/(7x + 10)C1 = 5/12

35x + 50 = 120

x = 2

Total number of balls = 14 + 10 = 24

So, Statement II alone is sufficient to answer the question.

29. Two mobile shops are selling same model of mobile phone. Then find the cost price of a mobile, if cost price of mobile on both shops is same.

Statement I: Marked price of mobile on two shops A and B is same. Shops A allows 20% discount and shop B allows 25% discount on mobile. A man purchased mobile from shop B, if man spend Rs 640 more, he could purchase the same mobile from shop A.

Statement II: Marked price of mobile is 52 (8/21)% more than its cost price. If discount of 30% allows on MP of mobile, shopkeeper made a profit of Rs. 560.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “B” is correct.

Answer: B

From Statement I:

Let marked price of mobile on both shops = 100X

According to statement,

100X x (80/100) = 100X x (75/100) +640

5X = 640

X = 128

MP = 12800 Rs

From statement I we could not determine the cost price.

From Statement II:

Let cost price of mobile = 100X

Marked price of mobile = 100X +100X x (11/21) = (3200X/21)

SP of mobile = (3200X/21) x (70/100) = 320X/3

According to statement,

(320X/3) – 100X =560

X = 560 x  (3/20) = 84

Cost price of mobile = 8400

Only Statement II is sufficient to answer.

30. Find Rakesh’s age four years hence from present.

Statement I: Ratio between Rakesh’s age and Rahul’s age, three years ago was 8:9, while rakesh is two years younger than Rahul.

Statement II: Ratio between present age of Rahul and Rakesh is 21:19, while five year hence average age of Rahul and Rakesh will be 25 years.

A. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
B. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
C. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “C” is correct.

Answer: C

From Statement I:

Let the age of Rakesh and Rahul three years ago be 8X and 9X respectively.

According to statement,

(9X+3) – (8X+3) = 2

X = 2 years

Rakesh age after four years = (2 x 8 +7) = 23 years

From statement II:

Let present age of Rahul and Rakesh be 21X and 19X year respectively.

According to statement,

((21X+19X)+ 10)/2 = 25

40X = 50 – 10

X = 1 year

Present age of Rakesh = 19 years

Four years hence Rakesh age = 19 + 4 = 23

Hence, either statement I or II alone is sufficient to answer.

238 thoughts on “Data Sufficiency”

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