# Last minute tips and tricks for Cracking XAT 2014 - Great Lakes toppers

This thread would provide some last minute inputs to the candidates which would help them in cracking XAT Gaurav Singh Great Lakes Institute of Management PGPM - 2014 XAT Percentile - 93.66(2013), 96(2012) For official admission…

This thread would provide some last minute inputs to the candidates which would help them in cracking XAT

Gaurav Singh
Great Lakes Institute of Management
PGPM - 2014
XAT Percentile - 93.66(2013), 96(2012)

Posting some questions ...

1 In a society, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?

A. 56 B. 73 C. 80 D. 120 E. None of the above

2 Let an = 1111111.....1, where 1 occurs n number of times. Then,

i. a741 is not a prime.

ii. a534 is not a prime.

iii. a123 is not a prime.

iv. a77 is not a prime.

A. (i) is correct.

B. (i) and (ii) are correct.

C. (ii) and (iii) are correct.

D. All of them are correct.

E. None of them is correct.

3. What is the maximum possible value of (21 sin X + 72 cos X)?

A. 21 B. 57 C. 63 D. 75 E. None of the above

4. A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.

a. The height of the light house above the sea level is:

A. 90 meters B. 94 meters C. 96 meters

D. 100 meters E. 106 meters

b. What is the horizontal distance of the man from the light house in the second position?

A. 300 meters B. 400 meters C. 500 meters D. 600 meters E. None of the above

5. A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:

A. (2, 7) B. (5, 8) C. (9, 10) D. (3, 7) E. None of the above

6. There are four machines in a factory. At 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

A. 0 B. 1/6 C. 1/4 D. 1/3 E. 1

7 The football league of a country is played according to the following rules:

· Each team plays exactly one game against each of the other teams.

· The winning team of each game is awarded 1 point and the losing team gets 0 point.

· If a match ends in a draw, both the teams get 1/2 point.

After the league was over, the teams were ranked according to the points that they earned at the end of the tournament. Analysis of the points table revealed the following:

· Exactly half of the points earned by each team were earned in games against the ten teams which finished at the bottom of the table.

· Each of the bottom ten teams earned half of their total points against the other nine teams in the bottom ten.

How many teams participated in the league?

A. 16 B. 18 C. 19 D. 25 E. 30

8. In a city, there is a circular park. There are 4 points of entry into the park, namely - P, Q, R and S. Three paths were constructed which connected the points PQ, RS, and PS. The length of the path PQ is 10 units, and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS past Q and R respectively, and they meet at a point T on the main road outside the park. The path from Q to T measures 8 units, and it was found that the angle PTS is 60°. Find the area (in square units) enclosed by the paths PT, TS, and PS.

A. 36 B. 54 C. 72 D. 90 E. None of the above

9. In the country of Twenty, there are twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:

· Each candidate must visit each of the other cities exactly once.

· Each candidate must use only the direct roads between two cities for going from one city to another.

· The candidate must return to his own city at the end of the campaign.

· No direct road between two cities would be used by more than one candidate.

The maximum possible number of candidates is

A. 5 B. 6 C. 7 D. 8 E. 9

10. The micromanometer in a factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?

A. 2201 B. 2202 C. 2600 D. 2960 E. None of the above options

Just keep in mind that it is more about accuracy then speed in XAT. There are plenty of sitters. So please ensure you don't get stuck in questions which are there to waste your time. In last year's XAT all the easy questions were there in the beginning. They might follow the same pattern this year also.

Solutions for questions 1 - 10

1. In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?

A. 56 B. 73 C. 80 D. 120 E. None of the above

Explanation:

There are 10 houses in a row, say 1 to 10. If the first house to be selected is i, i + 1 is not available (as a target). If the second house to be selected is j, j + 1 is not available. No matter how the houses are selected, in any one way, 2 houses are not available.

\ The number of ways of selecting the houses is 8C3 = 56. Choice (A)

2. Let an = 1111111.....1, where 1 occurs n number of times. Then,

i. a741 is not a prime.

ii. a534 is not a prime.

iii. a123 is not a prime.

iv. a77 is not a prime.

A. (i) is correct.

B. (i) and (ii) are correct.

C. (ii) and (iii) are correct.

D. All of them are correct.

E. None of them is correct.

i has 741 ones, ii has 534 ones and iii has 123 ones.

Sum of the digits of each of i, ii, and iii is divisible by 3 \ i, ii, iii are all divisible by 3 and hence not prime. Choice (D) follows since only this supports that all these three are not prime.

Choice (D)

3. What is the maximum possible value of (21 sin X + 72 cos X)?

A. 21 B. 57 C. 63 D. 75 E. None of the above

Explanation:

The maximum value of E = a cosx + b sinx is Proof:

E =

(

Let sinq = \ cosq =

E = (sinq cosx + cosq sinx)

= sin(q + x)

\ The maximum/minimum values of E are

±

In the given question a = 72 = 3(24)

b = 21 = 3(7)

\ = 3(25) = 75 Choice (D)

A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.

4a. The height of the light house above the sea level is:

A. 90 meters B. 94 meters C. 96 meters D. 100 meters E. 106 meters

Explanation:

AB = DE = 6

KL represents the light-house. Initially, the man is at BA. His shadow is BC. Then he walks 300 m to the east. He is at DE. His shadow is EF.

From similar triangles, and

As AB = DE,

\ LC is 4 parts(say 4x), LF is 5x or LB is 4 parts (say 4y) and LE is 5y.

As DLBE is right angled at B and E = 300, it follows that LB = 400, LE = 500. Also KL = = = 106 Choice (E)

4b. What is the horizontal distance of the man from the light house in the second position?

A. 300 meters B. 400 meters C. 500 meters D. 600 meters E. None of the above

Explanation:

The horizontal distance of the man in the second position from the light house LE = 500 m Choice (C)

5 A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range:

A. (2, 7) B. (5, 8) C. (9, 10) D. (3, 7) E. None of the above

Explanation:

Let the initial position of the ladder be AC. The base C is drawn out, by 2x to E. As a result the top A comes down by x to D.

Also BC = 7. AC = 25 ∴ AB = 24.

In Δ DBE, DB2 + BE2 = DE2

i.e.,

Þ

Þ (∵ x ≠ 0)

∴ EC = 8.

The interval (5, 8) doesn't include 8.

∴ We have to select Choice (E)

6 There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?

A. 0 B. 1/6 C. 1/4 D. 1/3 E. 1

Explanation:

The mechanic can check two machines. The possible outcomes and the corresponding probabilities are tabulated below. A defective machine is denoted as d and a non-defective as n

Outcome

Probability

1.

d d

2.

d n

3.

n d

4.

n n

In the first and the last cases, the mechanic would have identified the defective machines in time to catch the bus.

\ The probability that he is able to catch the last bus is Choice (D)

Let the initial position of the ladder be AC. The base C is drawn out, by 2x to E. As a result the top A comes down by x to D.

Also BC = 7. AC = 25 ∴ AB = 24.

In Δ DBE, DB2 + BE2 = DE2

i.e.,

Þ

Þ (∵ x ≠ 0)

∴ EC = 8.

The interval (5, 8) doesn't include 8.

∴ We have to select Choice (E)

7. The football league of a country is played according to the following rules:

· Each team plays exactly one game against each of the other teams.

· The winning team of each game is awarded 1 point and the losing team gets 0 point.

· If a match ends in a draw, both the teams get 1/2 point.

After the league was over, the teams were ranked according to the points that they earned at the end of the tournament. Analysis of the points table revealed the following:

· Exactly half of the points earned by each team were earned in games against the ten teams which finished at the bottom of the table.

· Each of the bottom ten teams earned half of their total points against the other nine teams in the bottom ten.

How many teams participated in the league?

A. 16 B. 18 C. 19 D. 25 E. 30

Explanation:

There are 10 teams in the bottom group and say n teams in the top group. The bottom group gets 45 points (there are 45 matches and 1 point per match) playing amongst themselves. Therefore they should get 45 points from their matches against the top group i.e., 45 out of the 10n points. The top group get nC2 points from the matches among themselves. They also get 10n – 45 points against the bottom group, which is half their total points.

\ nC2 = 10n – 45

Þ n(n + 1) = 20n – 90

Þ n2 – 21n + 90 = 0

Þ (n – 6) (n – 15) = 0

If n = 6, the top group would get nC2 + 10n – 45 = nC2 + 10(6) – 45 = 30 points, or an average of 5 points per team, while the bottom group would get (45 + 45)/10 or an average of 9. This is not possible. \ n = 15

The total number of teams is 10 + 15 or 25. Choice (D)

8 In a city, there is a circular park. There are four points of entry into the park, namely - P, Q, R and S. Three paths were constructed which connected the points PQ, RS, and PS. The length of the path PQ is 10 units, and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS past Q and R respectively, and they meet at a point T on the main road outside the park. The path from Q to T measures 8 units, and it was found that the angle PTS is 60°. Find the area (in square units) enclosed by the paths PT, TS, and PS.

A. 36 B. 54 C. 72 D. 90 E. None of the above

Explanation:

Area of Δ PTS = (PT) (SU) = (18) (16) = 72 Choice (C)

9 In the country of Twenty, there are exactly twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:

· Each candidate must visit each of the other cities exactly once.

· Each candidate must use only the direct roads between two cities for going from one city to another.

· The candidate must return to his own city at the end of the campaign.

· No direct road between two cities would be used by more than one candidate.

The maximum possible number of candidates is

A. 5 B. 6 C. 7 D. 8 E. 9

Explanation:

If we consider the distance between any two cities as paths, there were a total of 20C2= 190 paths.

Now each candidate needed to visit all the cities and then come back to the city he started from i.e. each candidate needed to take 20 paths.

Let the maximum number of candidates be n.

Now, 20n

n

Since n is an integer, the maximum value of n is 9. Choice (E)

10. The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?

A. 2201 B. 2202 C. 2600 D. 2960 E. None of the above options

Explanation:

The meter skips all the numbers in which there is a 5.

From 0000 to 0099, 5 occurs 10 times in the tens place and 10 times in the units place, (which includes the number 55)

\ it occurs in a total of 10 + 10 – 1 numbers i.e. 19 numbers. Similarly from 0100 to 0199, from 0200 to 0299, 0300 to 0399 from 0400 to 0499, 0600 to 0699,........ 0900 to 0999. It occurs in 8(19) numbers.

From 0500 to 0599, there are 100 numbers. The micromanometer reading could change from 0499 to 0600.

Total number of numbers skipped from 0000 to 0999 = 19 (9) + 100 = 271

Similarly from 1000 to 1999 and from 2000 to 2999, 271 + 271 numbers are skipped.

Finally, 3005 and 3015 are also skipped.

\Total number of skips = 271(3) +2 = 815

\ Actual pressure = 3016 – 815 = 2201 Choice (A)

Question 11.

In an isosceles ΔABC , AB=AC. D is point on AC such that BD=BC=2cm, then ar(ΔABC)=?

a. 4 cm^2 b. 7 cm^2 c. 2 cm^2 d. √7 cm^2 e. None of these

Question 12.

If ax+12y = 17 & 3x+by= 61 is a pair of parallel lines and a & b are positive real numbers then what would be minimum value of sum of a and b.

a. 10 b.11 c. 12 d. 14 e. None of these

Question 13.

If line x=k equally divides a triangle whose vertices are (9,1), (1,1) and origin. Then k=?

a. 2 b. 3 c. 4 d. 5 e. None of these

Question 14.

If 2sinA + 3cosB = 3√2 & 3sinB+ 2cosC = 1, then C (in degree) =? Where A,B & C are angles of a triangle.

a. 30 b. 60 c. 150 d. (a) or (c) e. None of these

Question 15.

If a+b+c+d+e = 8 & a^2+b^2+c^2+d^2+e^2 = 16, where a,b,c,d& e are real numbers then maximum (a,b,c,d,e)=?

a. 4 b. 2 c. 16/5 d. 6/5 e. None of these

Question 16.

A monkey is at origin (0, 0). It always jumps from a point having integer coordinates to a point with integer coordinates and always covers a distance of 5 units in each jump. Then minimum number of jumps monkey required to go from (0, 0) origin to (0, 1) ?

a. 2 b. 3 c. 4 d. 5 e. None of these