 1. What is the probability of getting at least one six in a single throw of three unbiased dice?
(1) 1 / 6
(2) 125 / 216
(3) 1 / 36
(4) 81 / 216
(5) 91 / 216

2. When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?
(1) 5 / 6
(2) 11 / 12
(3) 1 / 6
(4) 1 / 12

Solution:
Instead of finding the probability of this event directly, we will find the probability of the non-occurrence of this event and subtract it from 1 to get the required probability.
Combination whose sum of 12 is (6,6)
Combinations whose sum of 11 is (5,6), (6,5).
Therefore, there are totally 3 occurrences out of 36 occurrences that satisfy the given condition.
Probability whose sum of two numbers is greater than or equal to 11 = 3 / 36 = 1 / 12.
Hence probability whose sum of two numbers is lesser than 11 = 1 – 1 / 12 = 11 / 12.

3. The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?
Rs 570
Rs 420
Rs 690
Rs 640
Rs 610

The total salary amount = 15 * 600 = 9000
The salary of the exiting manager = 720.
Therefore, the salary of 12 workers and the remaining 2 managers = 9000 – 720 = 8280
When a new manager joins, the new average salary drops to Rs.580 for the total team of 15 of them.
The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager = 580 *15 = 8700
Therefore, the salary of the new manager is 9000 – 8700 = 300 less than that of the old manager who left the company, which is equal to 720 – 300 = 420.

Alternative method :
The average salary dropped by Rs.20 for 15 of them. Therefore, the overall salary has dropped by 15*20 = 300.
Therefore, the new manager’s salary should be Rs.300 less than that of the old manager = 720 – 300 = 420.

4. If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ?
(1) 24
(2) 31
(3) 32
(4) 30

Solution:
The 5 letter word can be rearranged in 5! Ways = 120 without any of the letters repeating.
Then the 25th word will start will CA _ _ _. The remaining 3 letters can be rearranged in 3! Ways = 6. i.e. 6 words exist that start with CA.
The next word starts with CH and then A, i.e., CHA _ _. The first of the words will be CHAMS. The next word will be CHASM.
Therefore, the rank of CHASM will be 24 + 6 + 2 = 32.

5. The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.
(1) 60 degrees
(2) 120 degrees
(3) 45 degrees
(4) 50 degrees

Solution:
Time is 2:20. Position of the hands: Hour hand at 2 (nearly).
Minute hand at 4
Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]
Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands is 60 degrees – 10 degrees = 50 degrees

6. A 12% stock yielding 10% is quoted at:
A.Rs. 83.33
B.Rs. 110
C.Rs. 112
D.Rs. 120

Explanation:
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 12, money invested = Rs.100x 12= Rs. 120.
10 Market value of Rs. 100 stock = Rs. 120

7. A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
A.5.15 kmph
B.4.14 kmph
C.4.25 kmph
D4.4 kmph

8. What was the day of the week on 28th May, 2006?
A.Thursday
B.Friday
C.Saturday
D.Sunday

Explanation:
28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb. March April May
(31 + 28 + 31 + 30 + 28 ) = 148 days
148 days = (21 weeks + 1 day) 1 odd day.Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.Given day is Sunday.

9. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
A.279
B.283
C.308
D.318
Other number =11 x 7700 = 308.275

10. How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
A.5
B.6
C.7
D.None of these

Explanation:
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.

11. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
A.81 min.
B.108 min.
C.144 min.
D.192 min.

12. A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
A 0%
B.5%
C.7.5%
D.10%

Explanation:
C.P. = Rs. 3000.
S.P. = Rs.3600 x 100
= Rs. 3000.
100 + (10 x 2)
Gain = 0%.

13. Find out the wrong number in the series.
6, 12, 48, 100, 384, 768, 3072
A.768
B.384
C.100
D.48
E.12

Explanation:
Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 124th term = (3rd term) x 2 = 48 x 2 = 96.6th term = (5th term) x 2 = 384 x 2 =768. 4th term should be 96 instead of 100

14. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
A.19
B.28
C.30
D.37 