MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 7 cups placed on a table; 4 are juice cups and the other 3 are tea cups. If 2 cups are to be selected at random from the 7 cups, what is the probability that at least one of the juice cup will be selected?  Pick one
A) 6/7
B) 2/7
C) 3/7
D) 4/7
E) 5/7

Solution: Total probability=7C2=21   4C2 +4C1*3C1=6+12= 
6+12 = 18
18   therefore the probability that at least one of the fashion magazines will be selected= 18/21=6/7   answer is 6/7
Answer: A
The positive integers a and b leave remainders of 4 and 7, respectively, when divided by 9. What is the remainder when a − 2b is divided by 9? Select.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: a=9x+4   so a could be 4, 13,22, 31,40,49,58,67,76,85   b=9y + 7   so b could be 7,16,25,34,43   Selecting any random number for a and b such that a-2b is positive number,   say a=22, b=7 => 2b=14   Hence a-2b = 8 Hence remainder when divided by 9 =8   say a=67, b=25 => 2b=50   Hence a-2b = 17 Hence remainder when divided by 9 is again 8   say a=49, b=7 => 2b=14   Hence a-2b = 35 Hence remainder when divided by 9 is again 8   Answer is 8.   ANSWER:8
Answer: D
In a group of 800 people, 2/5 play at least one instrument, 96 play two or more. What is the probability that one student play exactly one instrument? Select.
A) 2/125	B) 3/125	C) C)2/25	D) 3/25	E) 7/25

Solution: P(playing 2 or more instruments) = 96/800 = 3/25.   Then, the probability of playing exactly one instrument is given by:   P(playing 1 or more instruments) - P(playing 2 or more instruments) = 2/5 - 3/25 = 7/25.   Answer 7/25.
Answer: E
A certain sum becomes four times itself at simple interest in nine years. In how many years does it become ten times itself?
Choose the correct choice.
A) 27 years.	B) 25 years.	C) 29 years.	D) 17 years.	E) 37 years.

Solution: Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.   R = (100 * 3x)/(x * 9) = 100/3 %   If the sum becomes ten times itself, then interest is 9x.   The required time period = (100 * 9x)/(x * 100/3) = (100 * 9x * 3)/(x * 300) = 27 years.   27 years.NSWER:27 years.
Answer: A
Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7400 less if they could find two more equal investors. How much is the total investment in the new business.
Choose the correct choice from the following options:  A) a)	$ 64,000  B) b)	$ 54,000  C) c)	$ 55,500  D) d)	$ 5,400  E) e)	$3,600

Solution: Initially each invest in x. Hence total investment is 3x.   Total investment is also 5(x-7400).   3x = 5(x-7400)   x= 5*7400/2= 
5*7400/2 = 18_500
18500   3x= 55500 and the answer is c)	$ 55,500.
Answer: C
A box contain the number of balls which is as much greater than 20 is less than 30. The number of balls is?
Pick:
A) 40 B) 25 C) 30 D) 50 E) 35

Solution: Answer   Let the number be x.   Then, x - 20 = 30- x   â‡’ 2x = 30+ 20= 
30+ 20 = 50
50   â‡’ 2x= 50   âˆ´ x = 25   Correct Option: 25
Answer: B
If x is even and y is odd, then x-y	Select the correct option:
A) Even whenever xy is odd
B) Odd
C) Odd whenever xy is even
D) Even
E) It cannot be determined

Solution: x is even and y is odd, then x + y is   Let's take x=4 and y=7.   x+y=4+7= 
4+7 = 11
11.   x+y=11=odd.   Option: Odd
Answer: B
The price of 2 saris and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Choose the correct choice from the following answers:	A) Rs. 2200	B) Rs. 2300	C) Rs. 2400	D) Rs. 2480	E) Rs. 2490

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Rs. 2400
Answer: C
The average of weight of three men A,B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg.more than that of D, replaces A, then the average weight of B,C,D and E becomes 79 kg. The weight of A is :	Choose the correct option
A) 70 kg	B) 72 kg	C) 75 kg	D) 80 kg	E) none

Solution: Explanation:   A+B+75 kg = 3×84=252   A+B+75 kg+D= (4×80)=320   D = (320-252)= 
(320-252) = 68
68 and E= (68+3)= 
(68+3) = 71
71   Now, B+75 kg+D+E= (4×79)=316   B+75 kg+D=(316-71)= 
(316-71) = 245
245 kg   So, A= (320-245)= 
(320-245) = 75
75 kg   75 kgorrect Option: 75 kg
Answer: C
The floor of a rectangular room is 15 m long and 12 m wide. The room is surrounded by a verandah of width 2 m on all its sides. The area of the verandah is : Choose the correct answer.
A) 124 m2
B) 120 m2
C) 108 m2
D) 58 m2
E) None of these

Solution: 124 m2rea of the outer rectangle = 19 × 16 = 304 m2   124 m2rea of the inner rectangle = 15 × 12 = 180 m2   Required area = (304 – 180) = 124 m2   124 m2nswer 124 m2
Answer: A
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?
Choose the correct option:
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Let 1 men's 1 day work = x and 1 boy's 1 day work = y.   Then, 6x + 8y = 1/10 and 26x + 48y = 1/2   Solving these two equations, we get:   x = 1/100 and y = 1/200   (15 men + 20 boys)'s 1 day work = (15/100 + 20/200) = 1/4   15 men and 20 boys can do the work in 4 days.   4nswer:4
Answer: A
How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits S equal to 28?  Choose the correct choice from the following answers:
A) 14
B) 24
C) 28
D) 48
E) 96

Solution: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.   Start from the largest number possible 9874.   Then the next largest number possible is 9865.   After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.   So you have two solutions. Each can be rearranged in 4!=24 ways. So S=24+24=48.48
Answer: D
Exactly three sides of a certain 10-sided die are red. What is the probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll?  Choose the correct choice from the following:
A) 0.184 B) 0.16 C) 0.18 D) 0.147 E) 0.148

Solution: Total no. of sides = 10   Sides that are red =3   Probability that the die lands with red side up = 3/10   Therefore, Probability that the die does not land with red side up = 1 - 3/10 = 7/10   Probability that Kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll   = (1st roll - non red face) X (2nd roll - non red face) X (3rd roll - red face)   = (7/10) X (7/10) X (3/10)   = 128/1000   = 0.147   0.147
Answer: D
The value of Underrot 32pi/4 + Underrot 25 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)	Choose the correct choice from the following answers: A) 6 B) 35 C) 41 D) 30 E) 23

Solution: Under root (32pi/4) ~ 25   Under root (25) = 5   Hence, 25+5 = 30 is the approx answer. 30 is the correct answer.
Answer: D
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? Choose the correct answer:  A) 3.6  B) 7.2  C) 8.4  D) 10  E) 11

Solution: Speed =(600/5*60)m/sec.   = 2 m/sec.   Converting m/sec to km/hr   =(2*18)/5	km/hr   =7.2 km/hr.   Answer:7.2
Answer: B
At what rate percent on simple interest will a sum of money double itself in 30 years?
Choose one.
A) 3 1/3%  B) 8 1/3%  C) 3 5/3%  D) 5 1/3%  E) 3 1/7%

Solution: P = (P*30*R)/100   R = 3 1/3%   3 1/3%nswer: 3 1/3%
Answer: A
A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?	Choose the correct choice from the following:
A) 1/14
B) 1/7
C) 2/7
D) 5/7
E) 1/2

Solution: Total ways to choose 4 employees from 8 employees = 8C3   Two women = 5C2   Two Men = 3C1   P = (5C2 * 3C1)/8C2 = 5/7 hence 5/7.
Answer: D
A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?
Select.
A) 238 B) 180 C) 988 D) 177 E) 171

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 120)/25 = x/15 => x = 180 m.   Answer: 180
Answer: B
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d|	Select
A) 10 B) 12 C) 15 D) 18 E) 20

Solution: This is the hard one, definitely a 700+ level question. We need numbers a, b, c, and d such that   6x^2 + x - 12 = (ax + b)(cx + d)   This means that ac = 6, bd = –12, and ad + bc = 1. The a & c pair could be (1, 6) or (2, 3), in some order. The absolute values of the b & d pair could be (1, 12) or (2, 6) or (3, 4), and of course, in each case, one of the two would have to be negative. After some trial and error, we find:   6x^2 + x - 12 = (2x + 3)(3x - 4)   Thus, we see:   |a| + |b| + |c| + |d| = 2 + 3 + 3 + 4= 
2 + 3 + 3 + 4 = 12
12   Answer= 12
Answer: B
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction? Choose the correct choice from the following options
A) 3/15	B) 3/10	C) 3/11	D) 3/12	E) 3/16

Solution: The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.Answer: 3/11
Answer: C
The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 3 times the probability that both events A and B occur. What is the probability that event A occurs?
Pick one
A) 44/7 B) 9/8 C) 25/8 D) 3/4 E) 7/8

Solution: Let us say probability of A occuring is a.   Let us say probability of B occuring is b.   a = 2b   Probability (either A or B or both) = 3 times Probability (A and B)   a*(1-b) + b*(1-a) + ab = 3*ab   Substituting a=2b in the second equation:   2b*(1-b) + b*(1-2b) + 2b*b = 3*2b*b   3b-2b^2 = 6b^2   3b = 8b^2   b = 3/8 = 3/8   So, a = 2b = 3/4   THE CORRECT ANSWER IS 3/4.
Answer: D
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.19
II.18.16
III. 17.17 Choices: A) I only B) II only C) III only D) I and II only E) I and III only

Solution: Problem statement was difficult to parse. but some how I managed to understand what we can do.   1) x/y = 15 + 0.19   2) x/y = 18 + 0.16   3) x/y = 17 + 0.17   w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)   therefore :   1) y*0.19=60 -- we can't get y an integer.   2) y*0.16=60 -- we can get y an integer.   3) y*0.17=60 -- we can't get y an integer.   Therefore 2 are possible answers.   Ans II only.
Answer: B
Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 40 km and the other at the rate of 50 kmph. In what time will they be completely clear of each other from the moment they meet?
Answers: A) 11.04 B) 10.0 C) 6.85 D) 5.85 E) 6.15

Solution: T = (111 + 165)/ (40 + 50) * 18/5= 
(111 + 165)/ (40 + 50) * 18/5 = 276/25 = around 11.04
11.04   11.04NSWER:11.04
Answer: A
An automobile manufacturer offers a station wagon with either a 14-cylinder engine or a 12-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 14-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?	Pick one.
A) 93	B) 94	C) 95	D) 96	E) 98

Solution: 14-cylinder engine wagons = 2*2*2*2*2*2= 
2*2*2*2*2*2 = 64
64 (manual or automatic, with or without trailer);   12-cylinder engine wagons= 2*2*2*2*2= 
2*2*2*2*2 = 32
32 (manual or automatic).   Total= 64 + 32= 
64 + 32 = 96
96.   Answer: 96.
Answer: D
On increasing the price of T.V. sets by 50%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? Pick
A) 4  B) 5  C) 56  D) 20  E) 7

Solution: Explanation:   Let the price be = Rs.100, and number of units sold = 100   Then, sale value = Rs.(100 × 100) = Rs.10000   New sale value = Rs.(150 × 80) = Rs.12000   Increase% = 2000/10000 × 100 = 20%   Answer: 20
Answer: D
A trader has 200 kg of sugar, out of which he sells some with 10% profit and the rest with 25% profit. He gains 15% on the whole. Find the quantity of sugar sold at 25% profit?	Choices:  A) 120 kg  B) 96.5 kg  C) 84 kg  D) 67 kg  E) None of these

Solution: Explanation:   Let CP of each kg. of sugar = Rs.1.   Cost Price of 200 kg of sugar = Rs.200.   Let quantity of sugar sold with 25% profit be X.   Therefore, (200 – X) kg of sugar sold at a profit of 10%   Then,   (125/100 * X) + 110/100 (200 – X) = 115/100 * 200   125X + 110(200 – X) = 115 * 200   125X + 22000 – 110X = 23000   125X – 110X = 23000 – 22000   15X = 1000   X = 1000/15   X = 66.66 kg   Quantity of sugar that was sold at 25% gain is 66.66 kg   Therefore, option nearby for 66.66 is 67 (d)   ANSWER: 67 kg
Answer: D
By selling 15 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%?
Choose the correct choice from the following answers
A) 8  B) 9  C) 11  D) 89  E) 81

Solution: 85% --- 15   115% --- ?   15/115 * 15 = 11   Answer: 11
Answer: C
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
Choose the correct choice from the following answers:	A) 44, 36	B) 42, 33	C) 43, 36	D) 42, 36	E) None

Solution: Let the marks secured by them be x and (x + 9)   Then sum of their marks = x + (x + 9) = 2x + 9   Given that (x + 9) was 56% of the sum of their marks   =>(x+9) = 56/100(2x+9)   =>(x+9) = 14/25(2x+9)   => 25x + 225 = 28x + 126   => 3x = 99   => x = 33   Then (x + 9) = 33 + 9= 
33 + 9 = 42
42   Hence their marks are 33 and 42   42, 33
Answer: B
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:  Answers.
A) Rs. 2000 B) Rs. 10,000 C) Rs. 15,000 D) Rs. 20,000 E) Rs. 26,000

Solution: Principal = Rs.(100 x 5400)/(12x3)	= Rs. 15000.   Answer: Option Rs. 15,000
Answer: C
Pipes A and B can fill a tank in 4 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
Choose one:  A) 3 hrs  B) 3 9/77 hrs  C) 3 9/17 hrs  D) 3 9/27 hrs  E) 3 9/19 hrs

Solution: Net part filled in 1 hour = 1/4 + 1/6 - 1/12   = 4/12 = 1/3   The tank will be full in 3 hrs   3 hrsnswer:3 hrs
Answer: A
P is three times as fast as Q and working together, they can complete a work in 20 days. In how many days can Q alone complete the work? Choose one:
A) 26 1/2 days
B) 27 1/2days
C) 29 3/4days
D) 14 1/4 days
E) 10 1/2days

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 20 days, which means Q can do the work in 80 days.   Hence, P can do the work in 26 1/2 days.   26 1/2 daysnswer:26 1/2 days
Answer: A
How many 3's are there in the following sequence which are neither preceded by 6 nor immediately followed by 9 ?
9 3 6 6 3 9 5 9 3 7 8 9 1 6 3 9 6 3 9 Choices:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: 4   9 3 6 6 3 95 9 3 78 9 16 3 9 6 3 9
Answer: D
Which of the following is closest to (-9/10)^199？ Choose the correct choice from the following options
A) -1
B) -1/2
C) 0
D) 1
E) 2

Solution: (-9/10)^4 = 6561/10,000 which is already less than 2/3.   For larger exponents, the expression will get closer and closer to zero.   The answer is 0.
Answer: C
"How old are you, Alchemerion?" asked one of the wizards appearances the wizards answer with a riddle, "I am still Very young as wizards go.I am only three times my son's age. My father is 40 year more than twice of my age. Together the three of us are a 1240 year old". How old is Alchemerion Choose the correct choice from the following answers: A) 300 B) 320 C) 340 D) 360 E) 380

Solution: let Alchemerion be A   let son be S   let father be F   A= 3* S   F= 40 +(2*A)   therefore 1240=(S+F+A)   1240=(A/3)+ (40+(2*A) )+ A   A=360   ANSWER:360
Answer: D
A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is
Pick one.
A) 35  B) 36 2/3  C) 37 1/2  D) 40  E) 42

Solution: Let distance = x km and usual rate = y kmph.   Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)   Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)   On dividing (i) by (ii), we get: x = 40.   Answer : 40.
Answer: D
Jill has 14 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars? Choose the correct choice from the following options.
A) 3
B) 6
C) 9
D) 12
E) 24

Solution: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 14 1 3/4w = 14w=8The total number of jars = 3w =24Answer: 24
Answer: E
What is the height of the tower ? A man standing at a distance of 1km from the bottom of the tower makes an angle 300 degrees with the top of the tower .An insect starts from the bottom of the tower and reaches the top in 25sec. Choose the correct choice from the following choices
A) 0.577km  B) 0.477km  C) 0.677km  D) 0.577k7  E) 0.977km

Solution: tan = opp side/adj side   tan 30= height/1   ht=0.577km   0.577kmNSWER:0.577km
Answer: A
Find the sum of first 35 natural numbers Choose the correct answer:
A) 470  B) 468  C) 630  D) 463  E) 520

Solution: Explanation:   Sum of n natural numbers   =n(n+1)/2   =35(35+1)/2=35(36)/2=630   Answer: Option 630
Answer: C
To create paint with a certain shade of gray, one must combine 2.75 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?	Choose one.
A) 127.2	B) 129.4	C) 347.1	D) 694.4	E) 705.6

Solution: Since the ratio of Black to White is 2.75 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.   Now between A and B:   Black:White = 2.75:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: A
A pupil's marks were wrongly entered as 83 instead of 70. Due to the average marks for the class got increased by half. The number of pupils in the class is?
Choose one:
A) 18	B) 82	C) 26	D) 27	E) 29

Solution: Let there be x pupils in the class.   Total increase in marks   = (x * 1/2) = x/2   x/2 = (83 - 70) => x/2   = 13 => x = 26.   Answer: 26
Answer: C
If a car at 60 km/hr instead of 50 km/hr,the car would have gone 20 km more. The actual distance traveled by the car is?
Pick one:  A) 100 km  B) 58 km  C) 60 km  D) 90 km  E) 65 km

Solution: Let the actual distance traveled be x km. Then,   x/50 = (x + 20)/60   6x - 5x = 100 =>x = 100 km.   100 kmnswer :100 km
Answer: A
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 500 bolts?	Options:
A) 36
B) 72
C) 120
D) 144
E) 180

Solution: Old Machine   100 bolts in 60 mins   so,   5/3 bolts in 1 min   New Machine   150 bolts in 60 mins   so,   5/2 bolts in 1 min   together,   5/3 + 5/2 =   25/6 bolts in 1 min   so, for 500 bolts   500 * 6 / 25= 
500 * 6 / 25 = 120
120 mins   Ans 120
Answer: C
Which of the following is equal to 1(1/3)%?  Options
A) 0.012/100	B) 0.12/100	C) 1.3/100	D) 12/100	E) 12/10

Solution: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/3   How about adding a space:Which of the following is equal to (1 1/3)%   (1 1/3)% = 1.3% = 1.3/100   Answer:   1.3/100
Answer: C
A van takes 6 hours to cover a distance of 252 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Select the correct option
A) 28 Kmph	B) 60 Kmph	C) 70 Kmph	D) 80 Kmph	E) 90 Kmph

Solution: Time = 6   Distence = 252   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 252/9= 
252/9 = 28
28 Kmph   28 Kmph
Answer: A
Two pipes A and B can separately empty a cistern in 45 min and 30 min respectively. There is a third pipe in the top of the cistern to fill it. If all the three pipes are simultaneously opened, then the cistern is full in 90 min. In how much time, the third pipe alone can fill the cistern?	Choose the correct answer.
A) 22.5 min  B) 15 min  C) 30 min  D) 20 min  E) 25 min

Solution: Work done by the third pipe in 1 min = (1/45 + 1/30) - 1/60 = 4/90.   [+ve sign means filling]   The third pipe alone can fill the cistern in  90/4= 
 90/4 = 45/2 = around 22.5
22.5 min.   22.5 minNSWER:22.5 min
Answer: A
A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 11 salespeople on staff, how many different arrangements of winners are possible?
Choose the correct choice from the following choices:	A) 1,728	B) 1,440	C) 990	D) 220	E) 6

Solution: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 11 salespeople on staff, how many different arrangements of winners are possible?   11*10*9= 
11*10*9 = 990
990   Answer : 990
Answer: C
A train 1000 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?	Choose the correct choice from the following options:
A) 288 m B) 256 m C) 1000 m D) 278 m E) 287 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (1000 + x)/60   = 65/3   x = 300 m.   Answer:1000 m
Answer: C
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Choose the correct answer.
A) 10.9  B) 10.6  C) 10.4  D) 10.8  E) 10.1

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer: 10.8
Answer: D
Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 38 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:18, at what time will they be reading the same page?	Select.
A) 7:48 B) 8:18 C) 8:48 D) 9:18 E) 9:48

Solution: Since Tom reads an average of 1 page every 2 minutes, Tom will read 24 pages in the first 48 minutes. Jan can catch Tom at a rate of 8 pages per hour, so it will take 3 hours to catch Tom.   The answer is 8:18.
Answer: B