MU-NLPC/Calc-aqua_rat huggingface dataset:
If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 23?	Answers
A) 101
B) 187
C) 191
D) 201
E) 264

Solution: ok, not sure if this is the best explanation, but here is my way of solving this :   tn +1 = tn + n,   t 3 = 14   so:   t 4 = t 3 + 3   t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4   ....   so we get   t 23 = t 3 + 3 + 4 + 5 + 6....+ 22   the 3 + 4 + 5 + ... + 22 sequence is equal the sequence 1 + 2 + ... + 22, minus 1 + 2 at the beginning (so, minus 3)   and the 1 + 2 ... + 22 sequence is equal to n*(n+1)/2 with n being 22, so equal to  22 * 23 / 2= 
 22 * 23 / 2 = 253
253   so :   t 23= t 3 + 253 - 3   t 23 = 14 + 253- 3 = 253 + 11= 
253 + 11 = 264
264, hence answer 264
Answer: E
Out of seven models, all of different heights, five models will be chosen to pose for a photograph. If the five models are to stand in a line from shortest to tallest, and the fourth-tallest and sixth-tallest models cannot be adjacent, how many different arrangements of five models are possible?	Choose the correct choice from the following
A) 6	B) 11	C) 17	D) 72	E) 210

Solution: Total no. of ways "5 models can be selected from 7" = 7C5 = 21.   Fourth tallest and Sixth tallest can never stand adjacent to each other. Also, all selected models will be lined up from shortest to tallest.   Hence, we have to pull out the no. of ways 4 & 6 stand adjacent to each other from the above total, i.e = 21.   The following will be the way in which 4 & 6 stand close to each other.   1 2 3 4 6   1 2 4 6 7   1 3 4 6 7   2 3 4 6 7   So, the answer will be   21-4= 
  21-4 = 17
17 ways.   ANS:17
Answer: C
Two pipes A and B can separately fill a tank in 10 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?  Pick
A) 450  B) 540  C) 542  D) 829  E) 279

Solution: 1/10 + 1/15 - 1/x = 1/15   x = 10   10 * 45= 
10 * 45 = 450
450   450nswer: 450
Answer: A
A rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If 6 people choose their seats at random, what is probability that person P directly faces person Q?	Pick:
A) 1/5	B) 1/8	C) 2/7	D) 5/6	E) 3/5

Solution: Person P will be seated somewhere at the table.   Each of the other 5 people has an equal chance of sitting opposite person P.   The probability that person Q sits across is 1/5.   The answer is 1/5.
Answer: A
In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
Select the correct option:  A) 1:4  B) 1:3  C) 2:3  D) 3:4  E) None of these

Solution: Explanation:   33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3. Answer: 1:3
Answer: B
Of 30 applicants for a job, 11 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree? Options.
A) 14  B) 13  C) 8  D) 7  E) 5

Solution: C. 8   30 - 3= 
30 - 3 = 27
27   27 - 11 - 18= -8   Then 8 are in the intersection between 4 years experience and degree.   Answer 8
Answer: C
How many multiples of 2 are there between 10 and 100(both are inclusive)?	Choose the correct choice from the following answers: A) 2 B) 7 C) 6 D) 46 E) 3

Solution: the answer is (100-10)/2+1= 
(100-10)/2+1 = 46
46   Answer is 46
Answer: D
If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is	Select the correct option
A) a) 407	B) b) 518	C) c) 519	D) d) 521	E) e) 525

Solution: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.   There are 8 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 4th and 5th numbers in the set). This means that numbers 4 and 5 in this set are 413 and 415. Because we know that number 4 is 413, we know that the smallest number is 3 odd numbers below this, which means that it is 3*2= 
3*2 = 6
6 below this (every odd number is every other number). Therefore   413-6= 
  413-6 = 407
407, answer choice a) 407
Answer: A
If N = 2^0.15 and N^b = 32, b must equal	Select
A) 3/80	B) 3/5	C) 4	D) 100/3	E) 80/3

Solution: 15/100 = 3/20   N = 2 ^ 3/20   N^b = 2^5   (2^3/20)^b = 2^5   b = 100/3   Answer: 100/3
Answer: D
The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone?
Choose the correct choice from the following:  A) 87  B) 26  C) 48  D) 37  E) 20

Solution: π * 12 * 4   = 48   Answer:48
Answer: C
Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine? Choose the correct choice from the following options
A) 0  B) 1/10  C) 1/7  D) 1/4  E) 1/3

Solution: You know how to solve for Total number of people who can use at least one machine:   Total = n(A) + n(B) - n(A and B)   Total people who can use at least one machine = 17 + 18 - 15= 
17 + 18 - 15 = 20
20   So all 20 people know how to use at least one machine. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to use any machine.   0nswer 0
Answer: A
A CAR HAS RUNS 10000 MILES USING 5 TYRES INTERCHANGABLY TO HAVE A EQUAL WORNOUT BY ALL TYRES HOW MANY MILES EACH TYRE SHOULD HAVE RUN?
Choose the correct choice from the following choices
A) 7000 miles.
B) 8000 miles.
C) 9000 miles.
D) 6000 miles.
E) 5000 miles.

Solution: Total distance traveled by all the tires is 4*10000= 
4*10000 = 40_000
40000 miles.(since only 4 tires can be active at a time.   To make an equal run, Distance traveled by each tire is   40000/5= 
  40000/5 = 8_000
8000 miles.   ANSWER:8000 miles.
Answer: B
A person buys an article at Rs.800. At what price should he sell the article so as to make a profit of 35%? Choices
A) 600
B) 277
C) 269
D) 261
E) 1080

Solution: Cost price = Rs.800   profit = 35% of 800 = Rs.280   Selling price = Cost price + Profit   = 800 + 280= 
800 + 280 = 1_080
1080   Answer: 1080
Answer: E
A train covers a distance at a speed of 240kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of?	Pick one.
A) 516  B) 840  C) 560  D) 720  E) 920

Solution: 720istance = 240*5= 
240*5 = 1_200
1200km   Required speed= 1200*3/5= 
1200*3/5 = 720
720 km/hr   Answer is 720
Answer: D
Calculate how many ways a woman who has 4 bags and 5 books can put the books in her bag?
Choose the correct choice from the following choices
A) 1034 B) 1025 C) 1024 D) 1025 E) 1324

Solution: First book can be put in 4 ways, similarly second, third ,forth and fifth books also can be put in 4 ways.   So total number of ways = 4 x 4 x 4 x 4 x 4 = 1024   1024
Answer: C
Two pipes P and Q can fill a tank in 4 hours and 5 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank? Choose the correct choice from the following choices:	A) 4 hours 20 min	B) 5 hours 49 min	C) 3 hours 50 min	D) 3 hours 22 min	E) 2 hours 13 min

Solution: 2 hours 13 minxplanation:   Part filled by P in 1 hour = 1/4   Part filled by Q in 1 hour = 1/5   Part filled by (P + Q) in 1 hour = ( 1/4 + 1/5) = (9/20)   Time taken to fill the tank is (20/9) = 20/9*60 = 133 mins = 2 hrs 13 mins   ANSW2 hours 13 minR 2 hours 13 min
Answer: E
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Choose one.
A) 5.74 km
B) 5.78 km
C) 5.76 km
D) 5.79 km
E) 5.29 km

Solution: M = 6   S = 1.2   DS = 7.2   US = 4.8   x/7.2 + x/4.8 = 1   x = 2.88   D = 2.88 * 2= 
2.88 * 2 = 5.76
5.76   Answer:5.76 km
Answer: C
What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage?	Options
A) 99.6	B) 95.2	C) 97.5	D) 98.25	E) None of these

Solution: Explanation:   Use the formula,   CP= 100 â€“ discount + brokerage%   CP= 100-5+1/5   95.2   Thus the CP is Rs 95.2.   ANSWER 95.2
Answer: B
The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 900 gm and 750 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?	Choose the correct answer:
A) 3.84
B) 1.75
C) 3.36
D) 2.72
E) None of these

Solution: Here's how I did it. My notes from reading the problem were:   1L A = 900 gm   1L B = 850 gm   We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Eachpartis 4/5 of a liter.   So if we have 3 parts A, we have 900*3*(4/5)= 
900*3*(4/5) = 2_160
2160   If we have 2 parts B, we have 750*2*(4/5)= 
750*2*(4/5) = 1_200
1200   2160 + 1200= 
2160 + 1200 = 3_360
3360   Solving for units gives us 3.36   So the answer is 3.36
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?  Choose the correct option.
A) 16 km/hr
B) 56 km/hr
C) 43 km/hr
D) 50 km/hr
E) 87 km/hr

Solution: Speed of the train relative to man   = (125/10) m/sec   = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45   ==> x   = 50 km/hr.   Answer:50 km/hr
Answer: D
If 5^k + 5^k = (5^9)^(5^9) - 5^k, then k = ? Choose the most appropriate option
A) 5^11 - 1  B) 11/2  C) 242  D) 3^10  E) 3^11 - 1

Solution: 5^k + 5^k = (5^9)^5^9 - 5^k   5*(5^k) = 5 ^ (25 * 5^9 ) = 5^(5^2 * 5^9) = 5^(5^11)   5^k+1 = 5^(5^11)   So k+1 = 5^11   So k = 5^11 -1   5^11 - 1nswer is 5^11 - 1
Answer: A
The cash realised on selling a 14% stock is Rs.107.25, brokerage being 1/4% is?
Choices.
A) 366
B) 107
C) 102
D) 192
E) 122

Solution: Cash realised= Rs. (107.25 - 0.25)   = Rs. 107.   Answer: 107
Answer: B
An employer pays Rs.20 for each day a worker works and for fests Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal? Choose the correct choice from the following answers: A) 40 B) 30 C) 70 D) 20 E) 10

Solution: Suppose a worker remained ideal for x days then he worked for 60-x days   20*(60-x)-3x=280   1200-23x=280   23x=920   x=40   40nswer is 40.
Answer: A
A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
Choose the most appropriate option:
A) 104
B) 140
C) 200
D) 150
E) 250

Solution: 624/6= 
624/6 = 104
104 kmph   104NSWER 104
Answer: A
The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person
Choose the most appropriate option.
A) 15 B) 20 C) 25 D) 30 E) 35

Solution: Explanation:   Let's take the present age of the elder person = x   and the present age of the younger person = x – 16   (x – 6) = 3 (x-16-6)   => x – 6 = 3x – 66   => 2x = 60   => x = 60/2= 
60/2 = 30
30   Answer: Option 30
Answer: D
Working alone at its constant rate, machine K took 3 hours to produce 1/8 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?  Select
A) 9.6
B) 12.4
C) 16.2
D) 18.3
E) 21.5

Solution: Machine K works at a rate of 1/24 of the units per hour.   The rate of K + M together is 7/8 * 1/6 = 7/48 of the units per hour.   The rate of machine M is 7/48 - 2/48 = 5/48.   It would have taken machine M a total time of 9.6 hours.   The answer is 9.6.
Answer: A
The number 219 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers?
Select:	A) 20	B) 21	C) 19	D) 17	E) 15

Solution: sum of the squares of 3 different positive integers = 219   13^2 + 7^2 + 1^2 = 219   now,   sum of these 3 different integers = 13 + 7 + 1= 
13 + 7 + 1 = 21
21   Ans - 21
Answer: B
Griffin has a bag of marbles that contains 7 black marbles and 5 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be black? Select:
A) 4/15 B) 5/22 C) 6/35 D) 7/44 E) 8/55

Solution: P(3 black marbles) = 7/12*6/11*5/10 = 7/44   The answer is 7/44.
Answer: D
A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds  Select the correct option
A) 5 sec	B) 6 sec	C) 7 sec	D) 8 sec	E) 9 sec

Solution: Explanation:   Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.   Distance moved in passing the standing man = 100 m.   Required time taken = 100/(50/3) = (100 ×(3/50)) sec =6 sec   Answer: Option 6 sec
Answer: B
A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 181 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?  Choose the correct choice from the following
A) 6564  B) 7372  C) 8281  D) 9331  E) can not be determined

Solution: Let the side for growing cabbages this year be X ft. Thus the area is X^2.   Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.   The area would have increased by 181 sq ft as each cabbage takes 1 sq ft space.   X^2 - Y^2 = 181   (X + Y)(X - Y) = 181   181 is a prime number and thus it will be (91+90)*(91-90).   Thus X = 91 and Y = 90   X^2 = 91^2 = 8281   The answer is 8281.
Answer: C
Given that 2x + 15 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
Pick.
A) -4 and -1
B) -5 and 4
C) -4 and 1
D) -2 and 5
E) 2 and 5

Solution: 2x + 15 > 5   i.e 2x >5-15   i.e. 2x > -10   i.e. x > -5   Also, 5x - 13 < 7   i.e. 5x <7+13   i.e 5x < 20   i.e x < 4   i.e. -5 < x < 4   Answer: Option -5 and 4
Answer: B
Difference between the length &breadth of a rectangle is 15 m. If its perimeter is 90 m, then its area is?? Pick one:	A) 2000 m^2	B) 2340 m^2	C) 450 m^2	D) 2556 m^2	E) 2534 m^2

Solution: We have: (l - b) = 15 and 2(l + b) = 90 or (l + b) = 45   so 2 l = 60 = > l = 30 & b = 15   Area = 30 * 15= 
30 * 15 = 450
450 m^2   Answer : 450 m^2
Answer: C
During a Thanksgiving weekend, a car rental company rented seven-tenths of the vehicles with it including three fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?	Choose the correct choice from the following:
A) 20%	B) 30%	C) 40%	D) 60%	E) 25%

Solution: 60% of the vehicles are 4WDs:   60 are 4WDs and 40 are not.   Seven-tenths (70%) of the vehicles were rented:   70 rented and 30 not.   Three fifths of the 4WDs were rented:    3/5*60= 
 3/5*60 = 36
36 4WDs were rented and 24 not.   So, out of 30 vehicles that were not rented 24 were 4WDs and 6 not: 6/30= 20%.   20%nswer: 20%.
Answer: A
If the average (arithmetic mean) of x, x + 2, and x + 4 is 93, what is the value of x?	Answers
A) 95	B) 91	C) 102	D) 101	E) 85

Solution: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2   Given that x + 2 = 93   x = 91   Answer : 91
Answer: B
Find the missing number. 1, 4, 9, 16, 25, 36, 49, (....)  Choose the most appropriate option
A) 80 B) 67 C) 64 D) 85 E) 96

Solution: The series is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, ...   Hence, next term = 8^2 = 64   Answer is 64
Answer: C
A rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. What is the largest size of the tile which could be used for the purpose ?	Choose the correct option
A) 14 cms
B) 21 cms
C) 42 cms
D) None of these
E) Cannot be determined

Solution: Solution   Largest size of the tile .   H.C.F of 378 cm and 525 cm = 21 cms.   Answer 21 cms
Answer: B
A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is? Choose the correct choice from the following choices.
A) 22
B) 28
C) 25
D) 82
E) 34

Solution: M = 20   S = 5   DS = 20 + 5 = 20.Answer:25
Answer: C
A University library checks out books for a 5-week period, but allows them to be renewed up to 6 times. What is the Maximum no.of Weeks the library will allow a book to be checked out?
Choose the correct choice from the following options:
A) 35
B) 36
C) 37
D) 39
E) 41

Solution: Library checkout is 5 week period and can be renewed 6 times. So he can keep for a maximum of 8 weeks.   when he is allotted the book   0-5 weeks (1st renew)   5-10 weeks (2nd renew)   10-15 weeks (3rd renew)   15-20 weeks (4th renew)   20-25 weeks (5th renew)   25-30 weeks (6th renew)- maximum renew   after that,   30-35 (submission)   So 35 weeks is maximum.   35NSWER:35
Answer: A
Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many Q hours does it currently take Anne to clean the house on her own? Choose the most appropriate option:
A) 6	B) 7	C) 8	D) 12	E) 14

Solution: Lets suppose Anne and Bruce take A and B hrs working separately   So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)   After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to Q=1/3 (As the work is completed in Q=3 hours)   Solving these 2 equations we can find B as 12   So, 12
Answer: D
An bus covers a certain distance at aspeed of 100 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?  Choose the correct choice from the following answers:
A) 560 km/h
B) 567 km/h
C) 300 km/h
D) 723 km/h
E) 720 km/h

Solution: Distance = (100 x 5) = 500 km.   Speed = Distance/Time   Speed = 500/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 500 x 3/5 km/hr = 300 km/hr.   300 km/h
Answer: C
In a simultaneous throw of two coins, the probability of getting atleast one headis:
Select.
A) 1/2 B) 1/3 C) 2/3 D) 3/4 E) 1/4

Solution: n(S)=4   E = even getting at least one head   N(E)=3   P(E)=3/4   ANSWER 3/4 3/4
Answer: D
A right circular cylinder has a height of 22 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? Choose one
A) 500(π – 3) B) 500(π – 2.5) C) 500(π – 2) D) 550(π – 1.5) E) 500(π – 1)

Solution: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?   The square base has sides of sqrt(50) due to the 45-45-90 triangle   22*25*pi - 15*sqrt(50)^2   =550(π – 1.5)   D. 500(π – 1.5)
Answer: D
A table is bought for Rs.1000/- and sold at Rs.1500/- find gain or loss percentage Choose the correct choice from the following choices
A) 25% gain
B) 35% gain
C) 45% loss
D) 50% gain
E) None

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (1500 - 1000)/1000 = 50% gain   50% gain
Answer: D
7^6n -1^ 6n When n is an integer > 0 is divisible by
Answers:
A) 112  B) 127  C) 145  D) 187  E) 185

Solution: 127   127
Answer: B
The sum of three consecutive integers is 93. What are the integers? Choices.
A) 20,21,22 B) 10,11,12 C) 30,31,32 D) 40,41,42 E) 30,31,32

Solution: First x Make the first number x   Second x+1 To get the next numberwe go up one or+1   Third x+2 Add another 1(2 total) to get the third   F +S +T =93 First (F) plus Second (S) plusThird (T) equals 93   (x)+(x+1)+(x+2)=93 Replace F with x, S with x+1, and T with x+2   x+x+1+x+2=93 Here the parenthesis aren′t needed.   3x+3=93 Combine like terms x+x+x and 2+1   −3 −3 Add 3 to both sides   3x=90 The variable ismultiplied by 3   3 3 Divide both sides by 3   x=30 Our solution for x   First 30 Replace x in our origional listwith 30   Second  (30)+1= 
 (30)+1 = 31
31 The numbers are 30, 31, and 32   Third (30)+2= 
(30)+2 = 32
32   correct answer 30,31,32
Answer: E
A rectangular plot measuring 60 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed? Pick.
A) 44m B) 66m C) 26m D) 56m E) 25m

Solution: Perimeter of the plot = 2(60+50) = 220m   no of poles =220/5= 
220/5 = 44
44m   44mnswer: 44m
Answer: A
A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 10 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)	Select the correct option: A) 32 B) 53 C) 74 D) 86 E) 95

Solution: There is one post for each length of chain, plus one final post at the end.   The length of the fence in feet is 10.5x + 0.5, where each is the number of chain lengths.   The length of the fence is an integer when x = 1,3,5,7,...   The length of the fence could be 11, 32, 53, 74, 95,...   The answer is 86.
Answer: D
A train 1600 m long can cross a pole in 40 sec and then find the speed of the train?
Select:
A) 140	B) 142	C) 144	D) 146	E) 148

Solution: Length = Speed * time   Speed = L/T   S = 1600/40= 
1600/40 = 40
40 M/Sec   Speed= 40*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 144 Kmph   Answer:144
Answer: C
2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations.what is the ratio of their speeds ?	Choose one:
A) 11:9	B) 11:2	C) 91:9	D) 11:1	E) 11:5

Solution: In same time ,they cover 110km & 90 km respectively so ratio of their speed =110:90   = 11:9   11:9nswer:11:9
Answer: A
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
Choose the correct answer: A) 20,000 square meters. B) 40,000 square meters. C) 60,000 square meters. D) 80,000 square meters. E) 100,000 square meters.

Solution: Let us first find the distance d jogged   distance = rate ? time = (12 km / hr) ? 30 minutes   = (12 km/hr) ? 0.5 hr = 6 km   The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to   6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters   Let L and W be the length and width of the field. The length is twice the width. Hence   L = 2 W   The perimeter is 600 meters and is given by   2 (L + W) = 600   Substitute L by 2 W   2 (2 W + W) = 600   Simplify and solve for W   4 W + 2 W = 600   6 W = 600   W = 100   Find L   L = 2 W = 200   Find the area 20,000 square meters. of the rectangle   20,000 square meters. = L * W = 200 * 100 = 20,000 square meters   correct answer 20,000 square meters.
Answer: A
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle? Choose the most appropriate option
A) 35 cm2	B) 37 cm2	C) 87 cm2	D) 16 cm2	E) 35 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 28/2= 
2.5 * 28/2 = 35
35 cm2   Answer: 35 cm2
Answer: E