Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.

What is the two-digit number?

I.

Sum of the digits is 7.

II.

Difference between the number and the number obtained by interchanging the digits is 9.

III.

Digit in the ten's place is bigger than the digit in the unit's place by 1.

A.

I and II only

B.

II and III only

C.

I and III only

D.

All I, II and III

E.

None of these

Answer: Option E

Explanation:

Let the tens and units digit be x and y respectively.

I. x + y = 7.

II. (10x + y) - (10y + x) = 9 x - y = 1.

III. x - y = 1.

Thus, I and II as well as I and III give the answer.

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

2.

In how many days can 10 women finish a work?

I.

10 men can complete the work in 6 days.

II.

10 men and 10 women together can complete the work in 3

3

days

7

III.

If 10 men work for 3 days and thereafter 10 women replace them, the remaining work in completed in 4 days.

A.

Any two of the three

B.

I and II only

C.

II and III only

D.

I and III only

E.

None of these

Answer: Option A

Explanation:

I. (10 x 6) men can complete the work in 1 day.

1 man's 1 day's work =

1

60

II.

10 x

24

men +

10 x

24

women can complete the work in 1 day.

7

7

240

men's 1 day work +

240

women's 1 day work = 1.

7

7

240

x

1

+

240

women's 1 day's work = 1.

7

60

7

240

women's 1 day's work =

1 -

4

=

3

7

7

7

10 women's 1 day's work =

3

x

7

x 10

=

1

7

240

8

So, 10 women can finish the work in 8 days.

III. (10 men's work for 3 days) + (10 women's work for 4 days) = 1

(10 x 3) men's 1 day's work + (10 x 4) women's 1 day's work = 1

30 men's 1 day's work + 40 women's 1 day's work = 1

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

A.

5 : 2

B.

7 : 3

C.

9 : 2

D.

13 : 4

Answer: Option B

Explanation:

Let the ages of father and son 10 years ago be 3x and x years respectively.

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A.

173 m

B.

200 m

C.

273 m

D.

300 m

Answer: Option C

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question.

12.

What is the cost painting the two adjacent walls of a hall at Rs. 5 per m^{2} which has no windows or doors?

I.

The area of the hall is 24 sq. m.

II.

The breadth, length and height of the hall are in the ratio of 4 : 6 : 5 respectively.

III.

Area of one wall is 30 sq. m.

A.

I only

B.

II only

C.

III only

D.

Either I or III

E.

All I, II and III are required.

Answer: Option C

Explanation:

From II, let l = 4x, b = 6x and h = 5x.

Then, area of the hall = (24x^{2}) m^{2}.

From I. Area of the hall = 24 m^{2}.

From II and I, we get 24x^{2} = 24 x = 1.

l = 4 m, b = 6 and h = 5 m.

Thus, area of two adjacent walls = [(l x h) + (b x h)] m^{2} can be found out and so the cost of painting two adjacent walls may be found out.

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A.

3 hrs 15 min

B.

3 hrs 45 min

C.

4 hrs

D.

4 hrs 15 min

Answer: Option B

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

A.

9 a.m.

B.

10 a.m.

C.

10.30 a.m.

D.

11 a.m.

Answer: Option B

Explanation:

Suppose they meet x hours after 7 a.m.

Distance covered by A in x hours = 20x km.

Distance covered by B in (x - 1) hours = 25(x - 1) km.

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

A.

4

B.

9

C.

12

D.

49

Answer: Option B

Explanation:

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

17.

In a cricket team, the average age of eleven players in 28 years. What is the age of the captain?

I.

The captain is eleven years older than the youngest player.

II.

The average age of 10 players, other than the captain is 27.3 years.

III.

Leaving aside the captain and the youngest player, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively.

A.

Any two of the three

B.

All I, II and III

C.

II only or I and III only

D.

II and III only

E.

None of these

Answer: Option C

Explanation:

Total age of 11 players = (28 x 11) years = 308 years.

I. C = Y + 11 C - Y = 11 .... (i)

II. Total age of 10 players (excluding captain) = (27.3 x 10) years = 273 years.

Age of captain = (308 - 273) years = 35 years.

Thus, C = 35. .... (ii)

From (i) and (ii), we get Y = 24

III. Total age of 9 players = [ (25 x 3) + (28 x 3) + (30 x 3)] years = 249 years.