Data Sufficiency Questions - 1

# Directions (Q 1 to Q 40): In each of the following questions, a question is asked followed by statements. While answering you may or may not require the data provided in the statements. The answer number bearing the combinations of statements or single statement which is sufficient to answer the question is your answer.

How Reema is related to Seema ?


I. Seema’s brothers father’s brother is Jai.

II. Jai’s sisters mother is Reema.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

From I => Seema’s brother’s father brother is Jai = Jai is uncle of Seema [fathers brother]

From II => Jai’s sister = [Seema fathers sister’s] => mother => Reema => Grandmother.

Reema is Grandmother of Seema.

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What is the share of B in a profit of Rs.10, 000 ?


I. There are three partners in the business.

II. Share of B is 20% of the amount received by A and C together.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

From I => Providing information regarding the number of partners in the business.

From II => Share of B is 20% of the share of A and C together = 1/6th of the total profit.

Therefore share of B in the profit of Rs.10, 000 is = 10, 000 x 1/6 = 1666.66

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Who is the winner in an election ?


I. A defeated B by 10,000 votes.

II. B defeated C by 5,000 votes.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

None of the statements, as information regarding the number of contestants is not given.

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What is the sum of two numbers ?


I. Difference between the squares of that numbers is 32.

II. Difference between the numbers is 2.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

Both I and II are required:

Sum of two numbers = Difference between the squares of the numbers / Difference between the numbers

Let the numbers be ‘a’ and ‘b’

From the rule = a + b =

$$ \frac{a^2 \ - \ b^2}{a \ - \ b} \ = \ \frac{32}{2} \ = \ 16 $$

the numbers are = 9 and 7

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What is the sum of two numbers ?


I. Difference between the squares of the numbers is 81.

II. They are consecutive numbers.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

From both I and II

Difference between the squares of any two consecutive numbers is equal to the sum of that numbers.

The numbers are 40 and 41 => 412 = 1681, 402 = 1600 => 1681 – 1600 = 81

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What is the speed of a train ?


I. It covers a bridge of 300 meters in 15 seconds.

II. Time taken by the train to cross a pole is 5 seconds.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

From both I and II

Time taken to cross only the length of the bridge [300m] is

Time taken to cross the bridge – time taken to cover length of the train.

15 – 5 = 10 seconds. Therefore the train takes 10 seconds to cover 300 m

Speed of the train = 300/10 = 30 m/sec.

Speed of the train per hour = 30 x 18/5 = 108 km/hr

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In how many days 5 men can complete a work ?


I. 8 women who are as capable as 7 men, can complete the same work in 10 days.

II. 10 boys who are as capable as 7 men, can complete the work in 12 days.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

Convert the capacity into men and

$$ From \ I \ => \ \frac{7 \ X \ 10}{5} \ = \ \frac{70}{5} \ = \ 14 \ days $$

OR

$$ From \ II \ => \ \frac{7 \ X \ 12}{5} \ = \ \frac{84}{5} \ = \ 16.8 \ days $$

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What is the area of a circle ?


I. Its diameter is 14 cm.

II. Its circumference is 132 cms.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

Area of a circle = πr2

From I => radius = Diameter/2 = 14/2 = 7 cm

$$ => \ area \ = \ \frac{22}{7} \ X \ 7 \ X \ 7 \ = \ 22 \ X \ 7 \ = \ 154 \ sqcm $$

From II => Circumference of a circle = 2πr = 132 cm

$$ 2 \ X \ \frac{22}{7} \ X \ r \ = \ 132cm \ => \ r \ = \frac{132 \ X \ 7}{2 \ X \ 22} \ = \ 21 \ cm $$

$$ Area \ = \ 2 \ X \ \frac{22}{7} \ X \ 21 \ X \ 21^3 $$

= 2 x 22 x 21 x 3 = 1386 sqcm

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The total distance covered by a man in 6 hours is ?


I. He travelled to the place at 4 Km/hr and returned at 6 Km/hr.

II. Average speed was 9 Km/hr.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

From I => Let distance be ‘x’ =

$$ \frac{x}{4} \ + \ \frac{x}{6} \ = \ 6 \ => \ \frac{3x \ + \ 2x}{12} \ = \ 6hrs $$

5x = 72 => x or distance = 14.4 km

From II => Distance covered [Speed x Time] = 9 km/hr x 6hrs = 54km

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What is the rate of interest ?


I. Amount payable after 3 years will be Rs.15, 000.

II. Amount payable after 5 years will be Rs.17, 000, and after 6 years will be Rs.18000.

  • I only
  • II only
  • Both I and II
  • Either I or II
  • Neither of the statements
Explanation   

Though it is not mentioned whether it is simple interest or compound interest.

From I and II total amount payable after 3 years is 15000, after 5 years it is 17000, after 6 years it is 18000.

Every year amount payable is increasing by Rs.1000 constantly.

Therefore we can conclude that interest payable according to Simple Interest.

Principal = 18000 – 6000 [interest for 6 years] = 12000

$$ Rate \ of \ interest \ = \ \frac{1000}{12000} \ X \ 100 \ = \ 8.33\% $$

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