MU-NLPC/Calc-aqua_rat huggingface dataset:
On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?  Choose the correct choice from the following answers:
A) (1.5,1)
B) (2,-5)
C) (0,0)
D) (1,1.5)
E) (2,2)

Solution: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.   One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).   Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PB is the diameter of the circle.   There can be a case when PB is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.   If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y COR(1,1.5)INATE and mark the ans=(1,1.5)
Answer: D
A does a work in 10 days and B does the same work in 5 days. In how many days they together will do the same work ?  Choose the correct option:
A) 1/5
B) 2/7
C) 3/10
D) 3/11
E) 3/17

Solution: Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,   So,   A's 1 day work = 1/10   B's 1 day work = 1/15   (A+B)'s 1 day work =   (1/10+1/5)=(1+2/10)= 3/10   3/10
Answer: C
There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure e in inches of the width of the foil covered prism?	Pick:
A) 4	B) 6	C) 8	D) 9	E) 10

Solution: If the width is w, then length and height would be w/2.   So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)   => w = 2*4= 
2*4 = 8
8 in.   Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes= 8 +2=e =10   Ans 10.
Answer: E
The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the length of the rectangle?
Choose the correct choice:
A) 12 cm B) 15 cm C) 18 cm D) 21 cm E) 24 cm

Solution: 2L+2W = 5W   L = 3W/2   W*L = 150   3W^2/2 = 150   W^2 = 100   W = 10   L = 3(10)/2 = 15   The answer is 15 cm.
Answer: B
A $500 investment and a $1,500 investment have a combined yearly return of 10 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?	Choose the correct choice from the following:
A) 9%  B) 10%  C) 105/8%  D) 11%  E) 12%

Solution: The equation we can form the question :   Return on Total Investment = Sum of individual Investments   (500+1500)(10)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.   Solving the equation, we get x = 11% ( Option 11% )	ANSWER:11%
Answer: D
What is the diffference between the place value and face value of 4 in the numeral 2694? Choose the correct option:
A) 10 B) 0 C) 5 D) 3 E) 1

Solution: place value of 4 = 4 * 1= 
4 * 1 = 4
4   face value of 4= 4   4 - 4= 
4 - 4 = 0
0   0
Answer: B
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?	Choose the correct choice:
A) 5/5	B) 5/8	C) 5/3	D) 5/1	E) 5/6

Solution: Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done 5C1 . 4C1 ways.   The required probability   = (5 * 4)/⁹C₂ = 20/36   = 5/9   Answer:5/8
Answer: B
Find the average of all prime numbers between 1 and 5.  Pick:
A) 30
B) 3.6
C) 5.6
D) 6.6
E) None

Solution: Sol.   There are five prime numbers between 1 and 5.   They are 2, 3, 5, 7, 11   âˆ´ Required average = [2 + 3+ 5+ 7+ 11 / 5] = 28/ 5= 
28/ 5 = 28/5 = around 5.6
5.6   Answer 5.6
Answer: C
Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? Select the correct option:  A) 3:30 pm  B) 3:45 pm  C) 4:00 pm  D) 4:15 pm  E) 4:30 pm

Solution: Total distance, which should be covered by both cars is   190+35= 
  190+35 = 225
225 miles.   Let t be the time so the equation will be 46t+54t=225 thus,   t=2.25 hours   Answer: 4:15 pm
Answer: D
Peeta asks Katniss, 'It is 6 am as per my watch right now.Do you know what will be the time 23, 999, 998 hours later?'
Katniss knows the answer. Do you ?  Choices: A) 5pm B) 6pm C) 4am D) 3am E) 8pm

Solution: D   3am   The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
Answer: D
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?	Pick one:
A) 26	B) 34	C) 64	D) 60	E) 72

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ?  Pick one.
A) 6  B) 8  C) 7  D) 25  E) data insufficient

Solution: given:   x/2y = 3/2   => (x-2y)/2y = 1/2   => x = 3y   Putting x = 3y in (7x+4y)/(x-3y) gives value 25.   ANSWER:25
Answer: D
What is the next number in this series?
4,12,84,3612....	Choose the correct choice from the following options
A) 6526884  B) 6526888  C) 6626884  D) 6527884  E) 6526984

Solution: ((4^2)/2)+4=12   ((12^2)/2)+12=84   ((84^2)/2)+84=3612   ((3612^2)/2)+3612=6526884   6526884NSWER:6526884
Answer: A
In how many ways, a committee of 5 members can be selected from 4 men and 5 ladies, consisting of 3 men and 2 ladies?
Choose the correct option:
A) 40 B) 152 C) 175 D) 200 E) 212

Solution: (3 men out 4) and (2 ladies out of 5) are to be chosen   Required number of ways = (4C3 * 5C2) = 40   40nswer is 40
Answer: A
Rs.360 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?  Choose one.
A) 388  B) 266  C) 120  D) 299  E) 270

Solution: 4x 5x 6x   100 50 25   400x + 250x + 150x = 36000   x = 45   6x = 270   Answer: 270
Answer: E
In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/5 . If the probability that a number 12 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn?  Choose the correct choice from the following options.
A) 8/15	B) 1/6	C) 1/3	D) 1/2	E) 5/6

Solution: You can simply use sets concept in this question. The formula   Total = n(A) + n(B) - n(A and B) is applicable here too.   Set 1: Number 12 or larger   Set 2: Number 20 or smaller   1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)   2/3 + P(Set 2) - 1/5 = 1   P(Set 2) = 8/15   8/15nswer (8/15)
Answer: A
A car is purchased on hire-purchase. The cash price is $24 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
Options.
A) $503
B) $504
C) $555
D) $576
E) $587

Solution: Explanation:   Cash price = $24 000   $576eposit = 10% Ã— $24 000 = $2400   Loan amount = $24000 âˆ’ $2400   Number of payments = 60   = $21600   I=p*r*t/100   I=12960   Total amount = 21600 + 12960= 
21600 + 12960 = 34_560
$34560   Regular payment= total amount /number of payments=576   Answer: $576
Answer: D
A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?	Choose the correct option
A) 600  B) 400  C) 500  D) 670  E) 800

Solution: 800   25 = 800/(1000 - 800) * 100   1000 - 800 = 4800   1000 = 5800 => 800 = 200   1000 - 200= 
1000 - 200 = 800
800
Answer: E
cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?	Choose the correct choice from the following choices:
A) 1002  B) 2899  C) 1000  D) 2807  E) 2800

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer: 1000
Answer: C
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 80 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Pick one:	A) 20%	B) 40%	C) 60%	D) 80%	E) 100%

Solution: Let T be the total number of passengers.   Let x be the number of people with round trip tickets.   0.2T had round trip tickets and took their cars.   0.2x had round trip tickets and took their cars.   0.2x = 0.2T   x = T   The answer is 100%.
Answer: E
There are 15 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl and 2 boys are selected ?  Choose the most appropriate option.
A) 950
B) 1050
C) 2150
D) 2050
E) 1000

Solution: n(s) = sample space = 25C3 = 2300   E = event that 1 girl and 2 boys are selected   n(E) = we have to select 2 boys from 15 and 1 girl from 10   = 15C2 * 10C1   = 1050   Ans - 1050
Answer: B
consider the sequence 1,-2,3,-4,5,6.....what is the average of the first 200 terms of the sequence?  Choose the correct option:	A) -1/2	B) -3/2	C) 0	D) 1/2	E) 3/2

Solution: suppose n=2 => avg is (1+-2)/2= -1/2, when n=4 => avg is -1/2 , similarly for n=200 avg will be -1/2.   -1/2NSWER:-1/2
Answer: A
3 balls are drawn randomly from a bag contains 3 black, 5 red and 4 blue balls. What is the probability that the balls drawn contain balls of different colors?
Choose the correct choice from the following options.
A) 1/3	B) 1/2	C) 2/11	D) 3/11	E) 11/13

Solution: Total number of balls = 3 + 5 + 4= 
3 + 5 + 4 = 12
12   Let S be the sample space.   n(S)= Total number of ways of drawing 3 balls out of 12 = 12C3   Let E = Event of drawing 3 different coloured balls   To get 3 different coloured balls,we need to select one black ball from 3 black balls,   one red ball from 5 red balls, one blue ball from 4 blue balls   Number of ways in which this can be done = 3C1 × 5C1 × 4C1   i.e., n(E) = 3C1 × 5C1 × 4C1   P(E) = n(E)/n(S)=3C1×5C1×4C1/12C3   =3×5×4/(12×11×10/3×2×1)=3×5×4/2×11×10=3×4/2×11×2=3/11   ANSWER:3/11
Answer: D
Of the four numbers, whose average is 40, the first is one-fourth of the sum of the last three. The first number is ?  Pick one:	A) 28	B) 29	C) 11	D) 32	E) 10

Solution: Explanation:   Let the first number be x,   Then, sum of the four numbers = x + 4x = 5x.   so, 5x/4 = 40 or x = (40 * 4) / 5= 
(40 * 4) / 5 = 32
32   Answer: 32
Answer: D
In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?  Choose the correct answer.
A) 6
B) 10
C) 8
D) 12
E) 14

Solution: Explanation:   Let the number of buffaoes be x and number of ducks be y.   Then 4x + 2y = 2(x + y) + 24   => 2x = 24   => x = 12.   Answer: 12
Answer: D
A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:  Choose the correct choice from the following
A) 6 %
B) 6.1 %
C) 6.2 %
D) 6.3 %
E) 6.4 %

Solution: Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.   = $ 4000 × 5/100.   = $ 4000 × 0.05.   = $ 200.   Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.   = $ 3500 × 4/100.   = $ 3500 × 0.04.   = $ 140.   Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.   Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.   = $ 160.   Total invested amount = $ 4000 + $ 3500 = $7500.   Remaining invest amount = $ 10000 - $ 7500 = $ 2500.   We know that, Interest = Principal × Rate × Time   Interest = $ 160,   Principal = $ 2500,   Rate = r [we need to find the value of r],   Time = 1 year.   160 = 2500 × r × 1.   160 = 2500r   160/2500 = 2500r/2500 [divide both sides by 2500]   0.064 = r   r = 0.064   Change it to a percent by moving the decimal to the right two places r = 6.4 %   Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.   Correct Answer: 6.4 %)6.4 %
Answer: E
he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg. What might be the weight of the new person ?
Choose the correct answer.
A) 75 kg
B) 55 kg
C) 45 kg
D) 85 kg
E) 90 kg

Solution: Explanation:   Total weight increased = (8 x 3.5) kg = 28 kg.   Weight of new person = (62 + 28)= 
(62 + 28) = 90
90 kg.   Answer: 90 kg
Answer: E
7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.5 ounces and a standard deviation of 0.2 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?  Choose the correct choice.
A) Four B) Five C) Nine D) Ten E) Eleven

Solution: Mean = 8.5   Standard Deviation = 0.2   within 1.5 standard deviation of the mean   i.e. 1.5 standard deviation AFiveOVE the mean = 8.5+1.5*0.2= 
8.5+1.5*0.2 = 8.8
8.8   and 1.5 standard deviation FiveELOW the mean= 8.5-1.5*0.2= 
8.5-1.5*0.2 = 8.2
8.2   hence, 5 values fall within 1.5 SD from Mean   Answer: Option Five
Answer: B
Vinoth can complete a painting work in 20 days. Prakash can do the same work in 25 days. They start the work together but Vinoth quit after 3 days of work. How many days are required to complete the remaining painting work by Prakash.
Choose the correct choice from the following answers:	A) 15.25 days	B) 16.25 days	C) 17.25 days	D) 18.25 days	E) 19.25 days

Solution: Vinoth can complete the painting work in one day is 1/20   Prakash can complete the same work in one day is 1/25   Both of them can complete the work in 1/20+ days=9/100( 1/20+1/25)   they must have completed in three days=9/100*3=27/100   Remaining work to be done is by Prakash =1-27/100=73/100   For one work, Prakash can do in 25 days   For 73/100 work, he can do in 73/100*25=73/4days or 18.25 days   ANSWER:18.25 days
Answer: D
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good
Choose the correct choice from the following choices.
A) 125/126
B) 125/129
C) 125/128
D) 125/124
E) 125/121

Solution: Required probability = 1 - 1/126 = 125/126.125/126nswer:125/126
Answer: A
If 180/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.  Choose the correct choice:  A) I, II, and III  B) III only  C) I and II only  D) II and III only  E) I only

Solution: The largest possible value of x is 36 (the greatest common factor of 180 and 108), and if x=36 then   III only
Answer: B
A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Choose the correct choice from the following answers
A) 120 m
B) 225 m
C) 300 m
D) 360 m
E) 280 m

Solution: Speed = 54 x	5/18	m/sec = 15 m/sec.   Length of the train = (15 x 20)m = 300 m.   Let the length of the platform be x metres.   Then,	(x + 300)/35	= 15   x + 300 = 525   x = 225 m.Answer: Option 225 m
Answer: B
Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:	Choose the correct choice from the following options:  A) 4  B) 5  C) 6  D) 8  E) 9

Solution: Explanation:   N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)   = H.C.F. of 3360, 2240 and 5600 = 1120.   Sum of digits in N = ( 1 + 1 + 2 + 0 )= 
( 1 + 1 + 2 + 0 ) = 4
4   4NSWER IS 4
Answer: A
In a simultaneous throw of two coins, the probability of getting at least one head is	Choose one:
A) 1/2 B) 1/3 C) 2/3 D) 3/4 E) 3/5

Solution: Here S={HH, HT, TH, TT}   Let E = event of getting at least one head = {HT, TH, HH}   Therefore P(E) = n(E)/n(S) = 3/4   Answer 3/4.
Answer: D
Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 20000 at the end of the year, what should be the share of Narendra? Pick one:  A) A)Rs.7000  B) B)Rs.8000  C) C)Rs.8500  D) D)Rs.8600  E) E)Rs.16000

Solution: The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1.   :. Narendra’s share on profit of Rs.20000 = 20000 × 4/5 = Rs.16000.   Rs.16000)
Answer: E
A train 120 m long crosses a platform 120 m long in 6 sec; find the speed of the train?
Select
A) 144 kmph B) 58 kmph C) 54 kmph D) 94 kmph E) 59 kmph

Solution: D = 120 + 120= 
120 + 120 = 240
240   T= 6   S = 240/6 * 18/5= 
240/6 * 18/5 = 144
144 kmph   144 kmphnswer: 144 kmph
Answer: A
Find the largest number of four digits which is exactly divisible by 27,18,12,15	Pick.
A) 9700	B) 9710	C) 9720	D) 9730	E) None of these

Solution: Explanation:   LCM of 27-18-12-15 is 540.   After dividing 9999 by 540 we get 279 remainder.   So answer will be 9999-279= 
9999-279 = 9_720
9720   Answer: Option 9720
Answer: C
Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:	Choices:	A) three times as much	B) twice as much	C) a third as much	D) half as much	E) the same

Solution: et speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.   We know that   Speed = Distance/Time.   Or, Time = Distance/Speed.   So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.   And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.   = 100/x hr.   So we can clearly see that his new time compared with the old time was: twice as much.
Answer: B
The contents of a certain box consist of 24 oranges and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be oranges? Choose the correct choice from the following answers
A) 24
B) 26
C) 30
D) 46
E) 50

Solution: oranges = (oranges + kiwi + x)*0.3   24 = (30 + 24 + x)*0.3   x = 26.   Answer: 26.
Answer: B
A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?	Options:
A) 32 B) 28 C) 29 D) 44 E) 21

Solution: S = (250 + 300)/45 = 550/45 * 18/5= 
550/45 * 18/5 = 44
44   Answer: 44
Answer: D
A side of an equilateral triangle is tripled. If the previous parameter is 3x, what is the length of one of the sides before it was tripled? Pick.
A) 4x	B) 3x	C) 1x	D) 2x	E) 6x

Solution: If the parameter before it was tripled 3x, one of the sides must have been 3x/3. This reduces to 1x. Answer option 1x.
Answer: C
If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type? Choose the correct choice.
A) 22 B) 24 C) 26 D) 28 E) None of them

Solution: Let 3 engines of former type consume 1 unit in 1 hour.   Then, 4 engines of latter type consume 1 unit in 1 hour.   Therefore 1 engine of former type consumes(1/3) unit in 1 hour.   1 engine of latter type consumes(1/4) unit in 1 hour.   Let the required consumption of coal be x units.   Less engines, Less coal consumed (direct proportion)   More working hours, More coal consumed (direct proportion)   Less rate of consumption, Less coal consumed(direct prportion)   Number of engines 9: 8   Working hours	8 : 13 } :: 24 : x   Rate of consumption (1/3):(1/4)   [ 9 x 8 x (1/3) x x) = (8 x 13 x (1/4) x 24 ) = 24x = 624 = x = 26.   Hence, the required consumption of coal = 26 metric tonnes.   Answer is 26.
Answer: C
An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing? Choose the correct choice from the following answers:
A) Rs.500000	B) Rs.50000	C) Rs.5000	D) Rs.15000	E) Rs.6000

Solution: let x amount he has then 20% of 25% of 30% of x=750   so x=50000   ANSWER:Rs.50000
Answer: B
At what angle the hands of a clock are inclined at 15 minutes past 5?  Select
A) 117/2Â°
B) 64Â°
C) 135/2Â°
D) 145/2Â°
E) 155/2Â°

Solution: Apply the formula:   30h-11/2m=Angle   30*5-11/2*15   150-165/2=135/2   ANSWER:135/2Â°
Answer: C
A man walks a certain distance and rides back in 6 1⁄4h. He can walk both ways in 7 3⁄4h. How long it would take to ride both ways ?	Choose the correct choice from the following
A) 5 hours	B) 4 1⁄2 hours	C) 4 3⁄4 hours	D) 6 hours	E) None of these

Solution: We know that, the relation in time taken with two different modes of transport is   twalk both + tride both = 2 (twalk + tride)   31⁄4 + tride both = 2 × 25⁄4   ⇒ tride both = 25⁄2 - 31⁄4 = 19⁄4 = 43⁄4 hours   Answer 4 3⁄4 hours
Answer: C
It is only in the second option we find the sentence A in continuation with the opening sentence D. Sentence A alone explains, why the fear has such enormous effect on the human beings.  Choose one:
A) 28 B) 99 C) 728 D) 27 E) 271

Solution: Answer:99
Answer: B
What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?	Select:  A) 266  B) 500  C) 287  D) 26  E) 281

Solution: 70 = (P*4*7/2)/100   P = 500   Answer: 500
Answer: B
If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 1/(2x^2 − x)
III. 1/(x + 1) Options:
A) I only	B) II only	C) III only	D) I and II only	E) II and III only

Solution: let x= 4 and 3 b old and new values   ST1: x= 4 -> 4+16 = 20   x=3-> 3+9 = 12 ...decreased   ST2:x= 4-> 2*16-4 = 1/28   x=3->2*9-3 = 1/15   increased   St3: x=4-> 1/4 = .25   x=3->1/3 = .33   I onlyns: I only
Answer: A
the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?	Choose the correct choice from the following options:  A) 10  B) 15  C) 20  D) 25  E) 30

Solution: For the 5 minutes the cyclist continues to overtake the hiker, she is going at 21 miles per hour faster than the hiker.   Once the cyclist stops, the hiker is going at 7 miles per hour while the cyclist is at rest   So the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds. 21/7 * 5 or 15 minutes   Answer is (15)
Answer: B
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 12 meters, and the interior of tank B has a height of 12 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Choose the correct choice from the following answers:
A) 80%
B) 90%
C) 100%
D) 110%
E) 120%

Solution: The radius of tank A is 12/(2*pi).   The capacity of tank A is 10*pi*144 / (4*pi^2) = 360 / (pi)   The radius of tank B is 10 / (2*pi).   The capacity of tank B is 12*pi*100 / (4*pi^2) = 300 / (pi)   Tank A / Tank B = 360/300 = 12/10 = 120%   The answer is 120%.
Answer: E