1. If each of the three non-zero numbers  a ,  b , and  c  is divisible by 3, then  abc  must be divisible by which one of the following the numbers?
(1) 8
(2) 81
(3) 27
(4) 122
(5) None of these

2. Find the remainder when 289 is divided by 89?
(1) 1
(2) 2
(3) 88
(4) 89
(5) None of these

3. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(1) 44 5/11%
(2) 45 5/11 %
(3) 40 5/11%
(4) 30 %
(5) 40%

4. In the new budget , the price of kerosene oil rose by 15%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase (approx.)?
(1) 13.04
(2) 10
(3) 9
(4) 15
(5) 4

5. The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
(1) 245
(2) 240
(3) 243
(4) 241
(5) 242

6. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done
(1) 356
(2) 556
(3) 856
(4) 756
(5) 456

7. A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the current.
(1) 5
(2) 3
(3) 6
(4) 4
(5) None of these

8. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25% then determine the value of x.
(1) 18
(2) 16
(3) 17
(4) 15
(5) 14

9. After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.5, find the first discount?
(1) 10%
(2) 25%
(3) 20 %
(4) 30 %
(5) 35%

10. A person can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream?
(1) 3/2 hours
(2) 7 hours
(3) 7 (1/4) hours
(4) 7/2 hours
(5) 5/2 hours

1. (3) : Since each one of the three numbers a, b, and c is divisible by 3, the numbers can be represented as 3p,3q, and 3r, respectively, where p, q, and r are integers.
The product of the three numbers is 3p×3q×3r=27(pqr).
Since p, q, and r are integers, pqr is an integer and therefore abc is divisible by 27.

2. (2) 211 leaves a remainder 1.
Thus2^(89)=(211)^8(2) leaves a remainder of 2.

3. (2) : Number of runs made by running =110−(3×4+8×6)
= 110 - (60)
= 50.
Required percentage = (50)/ (110) x 100  = 45 5/11%
4. (1) : Reduction in consumption = [((R/(100+R))*100]%

5. (5) : The order of each letter in the dictionary is ABLORU.
Now, with A in the beginning, the remaining letters can be permuted in 5! ways.
Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways.
With L in the beginning, the first word will be LABORU, the second will be LABOUR.
Hence, the rank of the word LABOUR is 5!+5!+2= 242

6. (4) : From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
So we can have
(5 men) or (4 men and 1 woman) or (3 men and 2 woman)
(7C5)+(7C4 x 6C1 )+(7C3 x 6C2 )
=[(7×6)/(2×1)]+[(7×6×5)/(3×2×1)×6]+[(7×6×5)/(3×2×1)×(6×5)/(2×1)]=21+210+525=756

7. (2) :Let rate upstream = x km / hr and rate downstream = y km / hr.
Then,  40/x+ 55/y   =13   ...(i)
and   30/x+44/y=10       ...(ii)
Multiplying (ii) by 4 and (i) by 3 and subtracting, we get :
11/y=1 or  y=11.
Substituting y = 11 in (j), we get : x = 5.
\threrefore Rate in still water =
1/2(11+5)kmph=8kmph.
Rate of current= 1/2(11−5)kmph=3kmph.

8. (2) : Let the cost price 1 article = Re 1
Cost price of x articles = x
S.P of x articles = 20
Gain = 20 -x
=>25=(20−x)/(x)∗(100)=>2000−100x=25x=>x=16

9. (3) : Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
(87.5)/(100 )  X   (100-x)/100  X  150=105=>100-x=(105   X   100   X  100)/(150   X   87.5)=80
x=(100-80)=20
first discount = 20%

10. (4) :Let the speeds of boat and stream be x and y km/hr respectively.
Then, Rate downstream = (x + y) km/hr and Rate upstream = (x - y) km/hr
Given d / (x+y) + d / ( x-y ) =5 hrs 15 minutes = 21/4 hours
and 2d / (x+y) = 7 => d / (x+y)=7/4 => 2d / (x+y)=7/2

Hence, he takes 7/2 hours to row 2d km distance downstream