MU-NLPC/Calc-aqua_rat huggingface dataset:
Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
Choose the correct choice from the following answers.
A) 2  B) 1/2  C) 2/2  D) 3  E) None

Solution: Solution:   1/2   one of two is the possibility   1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.   2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.   Answer 1/2
Answer: B
A person with some money spends1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel.He is left with Rs 100/- How much did he have with him in the beginning ?	Choose the correct choice from the following choices:  A) 150  B) 200  C) 250  D) 270  E) 280

Solution: x/3+ 2x/15 + 8x/60 + 100 = x   x/3 + 4x/15 = x-100   3x= 5x - 500   x = 250   ANSWER:250
Answer: C
How many positive integers less than 5,000 are evenly divisible by neither 14 nor 21?	Choose one:
A) 4,514
B) 4,475
C) 4,521
D) 4,428
E) 4,349

Solution: integers less than 5000 divisible by 14 5000/14 =333.something , so 333   integers less than 5000 divisible by 21 5000/21 = 238.## , so 238   we have double counted some, so take LCM of 14 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 14 and 21 = 333 +238 -47= 
333 +238 -47 = 524
524   now subtract that from 4999. 4999- 524= 4349 answer 4,349.
Answer: E
Ajay can walk 6km in 1 hour. In how many hours he can walk 45km?
Choose the correct option
A) 5hrs  B) 10hrs  C) 7.5hrs  D) 20hrs  E) 30hrs

Solution: 1 hour he walk 6km   he walk 45km in = 45/6 * 1= 
45/6 * 1 = 15/2 = around 7.5
7.5hours   Answer is 7.5hrs
Answer: C
The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
Choose the correct choice from the following answers
A) 15	B) 16	C) 18	D) 21	E) 22

Solution: 3:4   Total parts = 7   = 7 parts --> 28 (7 × 4 = 28)   = 1 part ---->4 (1 × 4 = 4)   = The greater of the two number is = 4   = 4 parts ----> 16 (4 × 4 = 16)   16
Answer: B
Anup was asked to find the value of 7/12 of a sum of money Q. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:	Choose the correct choice from the following answers:  A) 48  B) 89  C) 84  D) 69  E) 49

Solution: Q=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.   So if bythe correct answerquestion means 7/12 of the amount then the answer should be 49.
Answer: E
In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs. 1,57,300 was their profit, how much amount did B receive ?	Choose one
A) 48400  B) 23777  C) 12387  D) 48213  E) 37882

Solution: A : B = 3 : 2 => B : A = 2 : 3 = 4 : 6 and A : C = 2 : 1 = 6 : 3.   So, B : A : C = 4 : 6 : 3 or A : B : C = 6 : 4 : 3.   B's share = Rs. (157300 x 4/13 ) = Rs. 48400   48400nswer: 48400
Answer: A
The sides of a square region, measured to the nearest centimeter, are 10 centimeters long. The least possible value of the actual area of the square region is	Pick:	A) 96.25 sq cm	B) 98.25 sq cm	C) 92.25 sq cm	D) 100.25 sq cm	E) 90.25 sq cm

Solution: Though there might be some technicalities concerning the termnearest(as 9.5 is equidistant from both 9 and 10) the answer still should be : 9.5^2=90.25.   Answer: 90.25 sq cm
Answer: E
A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?	Choose the correct answer:	A) 2/5	B) 2/7	C) 2/9	D) 2/11	E) 2/13

Solution: Total number of ways to select 2 members = 102/92 = 45   Total number of ways to select 2 females = 52/92 = 10   P(two females) = 10/45 = 2/9   The answer is 2/9.
Answer: C
Let a be a positive integer. If w is divisible by 2^a and w is also divisible by 3^(2a), then it is possible that w is NOT divisible by Select.
A) 6
B) 3 × 2^a
C) 2 × 3^(2a)
D) 6^a
E) 6^(2a)

Solution: Since, w is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1   Only for 6^(2a), 6^(2a) doesn't satisfy, if a = 1 and w=18, it is not divisible by 6^2 (i.e 36)   Hence answer is 6^(2a)
Answer: E
The probability of pulling a black ball out of a glass jar is 1/R. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar? Choose the correct choice:
A) 1/(XY) B) R/Y C) Y/X D) 1/(X+Y) E) 1/(X-Y)

Solution: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y   P of pulling a black ball out of a glass jar is 1/R   Lets say P of breaking the jar = n   That means 1/R*n=1/Y   n= R/Y   R/Y is the answer
Answer: B
The average age of the mother and her six children is 13 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?  Choose the correct choice from the following answers
A) 40  B) 41  C) 42  D) 43  E) 44

Solution: Total age of mother and 6 children = avg x n = 13 x (6+1)= 91   If mother is excluded new average is  (13 - 5)= 
 (13 - 5) = 8
8   so for 6 children= 6 x 8=48   so mother's age is  91 - 48= 
 91 - 48 = 43
43   Answer: Option 43
Answer: D
A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answers.
A) 50  B) 27  C) 26  D) 28  E) 24

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer: 26
Answer: C
An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
Pick one: A) 90 B) Required numbers = 80 C) 40 D) 50 E) 89

Solution: Total digits that can be formed = 10C1 * 10C1 = 100.   The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.   So codes that can create confusion are:   01, 06, 08, 09   10, 16, 18, 19   60, 61, 66, 68 (69 would still be 69 when inverted)   80, 81, 86, 89   90, 91, 98, 99 (96 would still be 96 when inverted)   There are 20 such numbers.   Required numbers = 100 - 20= 
100 - 20 = 80
80   ANSWER:Required numbers= 80
Answer: B
A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of X square inches. Which of the following equations must be true?  Choose the correct choice from the following answers.
A) 2W^2 − PW + 2X = 0  B) 2W^2 + PW + 2X = 0  C) 2W^2 − PW − 2X = 0  D) W^2 + PW + X = 0  E) W^2 − PW + 2X = 0

Solution: P = 2(L+W)-----------------1)   X= LW------------------------2)   option A is not possible why ?? because all the terms are positive.   lets try option B , put value of P and A from 1 and 2 we have,   2W^2-2(L+W)W + 2(LW)   2W^2 - 2LW - 2W^2 + 2LW=0.   hence answer is 2W^2 − PW + 2X = 0.
Answer: A
If x+y=4, x-y=36, for integers of x and y, x=?	Answers:  A) 20  B) 15  C) 25  D) 13  E) 42

Solution: x+y = 4   x-y = 36   2x = 40   x = 20   20nswer is 20
Answer: A
Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 50 and the turban. Find the price of the turban.  Choose the most appropriate option:  A) 27  B) 36  C) 29  D) 10  E) 70

Solution: Let the price of turban be x.   Thus, for one year the salary = (90 + x)   For 9 months he should earn 3434 (90 + x).   Now he gets one turban and Rs. 50.   Thus, 3434 (90 + x) = 50 + x or 270 + 3x = 200 + 4x or x = 70   Answer:70
Answer: E
The length of a side of a hexagon is 4 inches. What is the perimeter?
Choose the correct option: A) 22 B) 23 C) 24 D) 25 E) 26

Solution: Hexagon. It means 6 equal sides.   p = 6(4) = 24 inches   Answer 24
Answer: C
For a positive integer n, let PnPn denote the product of the digits of nn and SnSn denote the sum of the digits of nn. The number of integers between 10 and 100 for which Pn+Sn=n Choose the correct choice from the following answers:  A) 9  B) 8  C) 7  D) 6  E) 5

Solution: Let the two digit number be 'ab'   Given, a × b + a + b = 10a + b   a × b = 9a   b = 9   Therefore, for b = 9, the above condition satisfies. So all the two digit numbers for which units digit is 9 are our solutions. They range from 19 to 99. Total 9 numbers.   9nswer:	9
Answer: A
A small pool filled only with water will require an additional 800 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 800 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons? Answers:
A) 1000
B) 1250
C) 1300
D) 2000
E) 2250

Solution: Since pumping in additional 800 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.   So, we have that 1,000 + 800 = 0.8*{total} --> {total} = 2,250.   Answer: 2250.
Answer: E
In a new Engineering Hostels containing 100 rooms. Ankit Garg was hired to paint the numbers 1 to 100 on the doors.
How many times will Ankit have to paint the number eight ? Pick.
A) 10 times	B) 15 times	C) 30 times	D) 20 times	E) 35 times

Solution: 20 times   20 times   8,18,28,38,48,58,68,78,98,80,81,82,83,84,85,86,87,88,88(2),89
Answer: D
The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?  Select the correct option:
A) 15%
B) 32%
C) 44%
D) 62%
E) 80%

Solution: Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 .   So overall increase is from 100 to 144 is 44%   Answer 44%
Answer: C
A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 16%. What is the value of x?
Choose the most appropriate option:
A) 33.33 litres
B) 36.67 litres
C) 37.67 litres
D) 36.5 litres
E) 36 litres

Solution: Working formula ...   Initial Concentration*Initial Volume=Final Concentration*Final Volume.   Let X is the part removed from 100 lts.   36%(1-X/100)^2 = 16% * 100%   (1-x/100)^2=16/36------>(1-x/100)^2=(4/6)^2   100-X=400/6   x=33.33...   33.33 litresns 33.33 litres
Answer: A
In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a13?
Choices.
A) 100  B) 55  C) 25  D) 19  E) 1

Solution: As stated above, (a1+a2+a3......+a13)/13=13   therefore a1+a2+a3.......a13=169 (1)   using the same logic, we got a1+a2+a3..........+a12=144 (2)   (2)-(1) we got a13=25   25
Answer: C
In a set of 5 black balls and 3 red balls, how many selections of 5 balls can bemade such that at least 3 of them are black balls?
Choose the correct choice from the following answers
A) 24 B) 26 C) 46 D) 49 E) 50

Solution: Selecting at least 3 black balls from a set of 5 black balls in a total selection of 5 balls can be   3 B and 2 R   4 B and 1 R and   5 B and 0 R balls.   Therefore, our solution expression looks like this.   5C3 * 3C2 + 5C4 * 3C1 + 5C5 * 3C0 = 46 ways.   46
Answer: C
a sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42.the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is?
Choose the correct choice:
A) 50 sq units B) 60 sq units C) 70 sq units D) 80 sq units E) 90 sq units

Solution: sum of length and breadth will be 21 units . 42/2=21   area will be max when lxb = 11x10=110 sq units   area will be min when lxb = 20x1=20 sq units.   .the difference between the largest and smallest possible ares of the rectangles that the students could have come up with= 110-20= 
110-20 = 90
90 sq units   ANSW90 sq unitsR:90 sq units
Answer: E
Working at constant rate, pump X pumped out half of the water in a flooded basement in 2 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?
Choices
A) a. 10  B) b. 12  C) c. 14  D) d. 18  E) e. 24

Solution: rate of x=1/8   rate of x+y=1/6   rate of y=1/6-1/8=1/24   18 hours   d. 18
Answer: D
Donald duck can can swim his pool downstream(with the pool current helping time) in exact 40 seconds and upstream(against the pool current) in a pool in exact 60 seconds. The length of pool is 2 kilometers.
How long Donald duck can cover distance of one side at a still pool (with no current).  Choose the correct answer:
A) 48 minutes.
B) 58 minutes.
C) 68 minutes.
D) 88 minutes.
E) 78 minutes.

Solution: Solution:   48 minutes.   Donald duck's speed = X km/seconds   pool current speed = Y km/seconds   2/(X+Y) = 40   2/(X-Y) = 60   Solving the simultaneous equations gives X = 1/24   Therefore, to cover 2km will take 2/X = 48 seconds   48 minutes.nswer 48 minutes.
Answer: A
If the given two numbers are respectively 6% and 18% of a third number, then what percentage is the first of the second ? Answers:  A) 20%  B) 25%  C) 18%  D) 33 1/3%  E) none of these

Solution: Here, l = 6 and m = 18   Therefore, first number = l/m x 100% of second number = 6/18 x 100% of second number = 33 1/3% of second number   ANSWER:33 1/3%
Answer: D
A invested Rs. 76,000 in a business. After few months, B joined him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio 2 : 1. After bow many months did B join?  Pick.
A) 4
B) 3
C) 2
D) 1
E) None of them

Solution: Suppose B joined after x months. Then, B's money was invested for (12 - x)   =(76000 x 12)/(57000 x (12-x) =2/1 =912000=114000(12-x)   =114 (12 - x) = 912=12-x=8=x=4   Hence, B joined after 4 months   4nswer is 4.
Answer: A
If n is a positive integer, which of the following expressions must be even?  Pick:  A) (n − 1)( n + 3)  B) (n − 6)( n + 1)  C) (n − 2)( n + 6)  D) (n − 3)( n + 3)  E) (n − 3)( n + 7)

Solution: Whether n is even or odd, (n-6)(n+1) will have one odd factor and one even factor.   The product will be even.   The answer is (n − 6)( n + 1).
Answer: B
A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?  Answers.
A) 1777 meters B) 1822 meters C) 400 meters D) 1111 mete E) None of these

Solution: Answer   Concept : Distance covered by train when it crosses a moving object   When a train overtakes another object such as a motorbike, whose length is insignificant compared to the length of the train, the distance traveled by the train is equal to the length of the train.   Because the motorbike is also moving, we have to take the relative speed between the train and the motorbike and not just the speed of the train.   The length of the train = distance traveled by the train while overtaking the motorbike = relative speed between the train and the motorbike * time taken   In this case, as both the objects i.e., the train and the motorbike are moving in the same direction, the relative speed between them = difference between their respective speeds = 100 - 64= 
100 - 64 = 36
36 kmph.   Distance traveled by the train while overtaking the motorbike= 36 kmph * 40 seconds.   The final answer is in meters and the speed is given in kmph and the time in seconds.   So let us convert the given speed from kmph to m/sec.   1 kmph = 5/18 m/sec   Therefore, 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Relative speed= 10 m/sec. Time taken = 40 seconds.   Therefore, distance traveled = 10 * 40= 
10 * 40 = 400
400 meters.   400 metershoice 400 meters
Answer: C
If x2−1/x+1, then, x = ?	Choose the correct choice from the following choices.
A) 1	B) 0	C) 2	D) Can’t be determined	E) None of these

Solution: (x – 1) = 2 ⇒ x = 3   Answer None of these
Answer: E
Simplfy
b - [b -(a+b) - {b - (b - a+b)} + 2a]	Select:
A) a
B) 2a
C) 4a
D) 0
E) 1

Solution: Explanation:   b-[b-(a+b)-{b-(b-a+b)}+2a]   =b-[b-a-b-{b-(2b-a)}+2a]   =b-[-a-{b-2b+a}+2a]   =b-[-a-{-b+a}+2a]   =b-[-a+b-a+2a]   =b-[-2a+b+2a]   =b-b   =0   Option 0
Answer: D
If a die has 3,4 and 1,6 and 2,5 opposite each other, then how many such dies can be made. Choose the correct choice from the following.
A) 13	B) 3	C) 5	D) 12	E) 11

Solution: there are 3 pairs . consider it A,B,C   A-(1,6)   B-(3,4)   C-(2,5)   Now the possible combinations to place A B C is 6.   because for A - 3 possible place   B- 2 POSSIBLE PLACE   C-1 POSSIBLE PLACE   3*2*1= 
3*2*1 = 6
6   NOW A HAS TWO PAIR SO POSSIBLE COMBO FOR 1 AN12 6 IS 2 ..SAME FOR B AN12 C     2+2+2= 
  2+2+2 = 6
6   SO 6+6= 
6+6 = 12
12   ANSWER:12
Answer: D
The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?	Choose the correct choice from the following choices: A) 11000 B) 11008 C) 11006 D) 110054 E) 11001

Solution: 2 * 22/7 * 1.75 * x = 11000   x = 1000   11000nswer: 11000
Answer: A
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 10 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?  Choose one:
A) 2.9 hrs	B) 8.9 hrs	C) 2.9 hrs	D) 6.7 hrs	E) 8.6 hrs

Solution: Net part filled in 1 hour = (1/4 - 1/10)   = 3/20   The cistern will be filled in 20/3 hrs i.e., 6.7 hrs.   Answer:6.7 hrs
Answer: D
Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Choices.
A) 18  B) 10  C) 12  D) 11  E) 17

Solution: 4/12 + x/15   = 1   x = 10   Answer: 10
Answer: B
1/3rd of work is completed by kiran in 6days. In how many days he can finish the remaining work?	Select:
A) 6days  B) 10days  C) 12days  D) 15days  E) 20days

Solution: 1/3rd work finished in 6days   2/3rd work = 2/3*3*6= 
2/3*3*6 = 12
12days   Answer is 12days
Answer: C
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is Options:  A) 6  B) 12  C) 24  D) 36  E) 48

Solution: possible values of n = 12, 24, 36 and 48.   But it is 12 that can divide all the possible values of n. If we consider 48, it will not divide 12, 24 and 36.   Hence, 12 is the value that MUST divide n.   ANSWER:12
Answer: B
A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr?
Choose the correct choice:	A) 10 km/hr.	B) 20 km/hr.	C) 30 km/hr.	D) 40 km/hr.	E) None

Solution: Sol.   Speed = [150 + 300 / 40.5] m/sec = [450 / 40.5 * 18/5] km/hr = 40 km/hr.   Answer 40 km/hr.
Answer: D
The average age of a class of 32 students is 15 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Answers:
A) 45 Years	B) 46 Years	C) 49 Years	D) 52 Years	E) 48 Years

Solution: Total age of students is 32X15 = 480 Years Total age inclusive of teacher = 33X (15+1) = 528 So, Teacher's age is 528-480= 
528-480 = 48
48 Yrs There is a shortcut for these type of problems Teacher's age is 15+(33X1)= 48 YearsAnswer : 48 Years
Answer: E
A car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?	Answers.
A) 60  B) 72  C) 72.5  D) 73  E) 73.5

Solution: Many approaches are possible, one of them:   Let the distance be 1 kilometer.   Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;   Time to cover this distance at regular speed is 48+12= 
48+12 = 60
60 seconds= 60/3,600 hours = 1/60 hours;   So, we get that to cover 1 kilometer 1/60 hours is needed --> regular speed 60 kilometers per hour (rate is a reciprocal of time or rate=distance/time).   60nswer: 60
Answer: A
A certain sum of money at simple interest amounted Rs.1448 in 9 years at 4% per annum, find the sum?	Choose the correct answer
A) 1064  B) 1080  C) 1980  D) 646  E) 168

Solution: 840 = P [1 + (9*4)/100]   P = 1064   1064nswer:1064
Answer: A
In what time a debt of Rs.7920 due may be cleared by immediate cash down
payment of Rs.3600 at 1/2% per month Choose the correct choice from the following options:  A) 10years  B) 20years  C) 30years  D) 40years  E) NONE OF THESE

Solution: Explanation:   PW=100*Amount / 100+(R+T)   ANSWER IS 20years
Answer: B
A person crosses a 500 m long street in 4 minutes. What is his speed in km per hour?	Pick.
A) 7.5	B) 2.6	C) 3.9	D) 8.2	E) 2.7

Solution: distance = 500 meter   time = 4 minutes = 4 x 60 seconds = 240 seconds   Speed = distance/time=500/240=2.08 m/s=2.08Ã—18/5 km/hr=7.5 km/hr   7.5nswer :7.5
Answer: A
In how many ways can eight different rings be worn on four fingers of one hand?
Pick.
A) 10	B) 12	C) 70	D) 60	E) 18

Solution: Required number of ways = ways of selecting 4 objects out of 8 given objects   = 8704 = 8x 7x 6x 5 /24= 70   Answer 70
Answer: C
The car A has an average speed of 40 miles/hour and car B has an average speed of 60. How much time(in minutes) does the car A take more than car B to cover a distance of 60 miles?	Pick one:
A) 10 B) 20 C) 25 D) 30 E) 40

Solution: Time taken by Car A=60 miles/40 mph   =1.5 hours=90min   Time taken by Car B=60miles/ 60mph   =1 hour = 60 min   Car A takes 30 min more than car B   Answer: 30
Answer: D
For which of the following functions is f(z+b)=f(z)+f(b) for all positive numbers z and b? Choose the correct choice from the following choices.
A) a) f(x)=x^2
B) b) f(x)=x+1
C) c) f(x)=root x
D) d) f(x)=2/x
E) e) f(x)= -3x

Solution: f(z+b)=f(z)+f(b) Its e) f(x)= -3x
Answer: E
In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?
Answers: A) 80 rooms B) 90 rooms C) 70 rooms D) 60 rooms E) 10 rooms

Solution: There are total 450 rooms.   Out of which 299 room number starts with either 1, 2 or 3. (as room number 100 is not there) Now out of those 299 rooms only 90 room numbers end with 4, 5 or 6.   Ans : The probability is 90/450 so 90 rooms   Answer 90 rooms
Answer: B
Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 18% and its breadth is decreased by 16%?  Choose the correct choice from the following options:	A) 5.88% decrease	B) 0.88% decrease	C) 0.88% increase	D) 1.88% decrease	E) 2.88% decrease

Solution: let L and 0.88% decrease be 100 each     100 * 100= 
  100 * 100 = 10_000
10000   L increase by 18%= 118   0.88% decrease decrease by 16% = 84   118 * 84= 
118 * 84 = 9_912
9912   0.88% decrease   ANSWER:0.88% decrease
Answer: B
How many numbers from 10 to 50 are exactly divisible by 3  Choose the correct choice: A) 11 B) 13 C) 15 D) 18 E) 19

Solution: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.   13 Numbers.   10/3 = 3 and 50/3 = 16 ==> 16 - 3= 
16 - 3 = 13
13. Therefore 13 digits   13)
Answer: B
In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 180 votes. Find the total number of valid votes?	Pick one:
A) 430
B) 450
C) 436
D) 434
E) 422

Solution: Let the total number of valid votes be x.   70% of x = 70/100 * x = 7x/10   Number of votes secured by the other candidate = x - 7x/100 = 3x/10   Given, 7x/10 - 3x/10 = 180 => 4x/10 = 180   => 4x = 1800 => x = 450.   Answer:450
Answer: B