MU-NLPC/Calc-aqua_rat huggingface dataset:
If x > y and y > z, which of the following represents the greatest number R?  Pick
A) x − z	B) x − y	C) y − x	D) z − y	E) z − x

Solution: Because x>y>z   thus R=x- z wil lbe greatest   x − zns: x − z
Answer: A
Twenty times a positive integer is less than its square by 96. What is the integer?
Choose the correct answer
A) 24  B) 20  C) 30  D) Cannot be determined  E) None of these

Solution: Let the positive integer be x.   Now, x2 – 20x = 96   or, x2 – 20x – 96 = 0   or, x2 – 24x + 4x – 96 = 0   or, x(x – 24) + 4(x – 24) = 0   or, (x – 24)(x + 4) = 0   or, x = 24, – 4   x ≠ –4 because x is a positive integer   24nswer 24
Answer: A
A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant made after offering the discount?
Select the correct option: A) 30% B) 125% C) 25% D) 20% E) 16.66%

Solution: Explanatory Answer   The easiest way to solve these kinds of problems is to assume a value for the merchant's cost price.   To make calculations easy, it is best to assume the cost price to be $100.   The merchant marks his goods up by 50%.   Therefore, his marked price (quoted price) = cost price + mark up.   Marked price = $100 + 50% of $100 = 100 + 50= 
100 + 50 = 150
$150.   The merchant offers a discount of 20% on his marked price.   Discount offered= 20% of 150 = $30.   Therefore, he finally sold his goods for $150 - $30 = $ 120.   We assumed his cost to be $100 and he sold it finally for $120.   Therefore, his profit   150 -  30= 
  150 -  30 = 120
$ 120.   We assumed his cost to be $100 and he sold it finally for $120.   Therefore, his profit= $20 on his cost of $ 100.   Hence, his % profit = profit/cost price * 100 = 20/100 * 100= 
20/100 * 100 = 20
20%.   Choice 20%
Answer: D
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
Choose the most appropriate option
A) 2:5  B) 2:3  C) 2:4  D) 2:1  E) 2:9

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.4 = (k + 1) * 15.8   = (16.4 - 15.8)k = (15.8 - 15.4)   = k = 0.4/0.6 = 2/3   Required ratio = 2/3 : 1 = 2:3.   Answer:2:3
Answer: B
If s, t and r are positive integers greater than 1, and s and t are factors of r, which of the following must be the factor of r^(st)?
I. s+t
II. t^s
III. s^2 * t^2 Select.
A) I only
B) II only
C) III only
D) I and II
E) II and III

Solution: given that s and t are factors of r.   so we can picture it this way r=s*t*n (n-some another factor of r)   so, r^st= (s*t*n)^st   I. s+t .since the question is MUST BE TRUE, we eleminate this option   II. (s*t*n)^st / t^s= integer YII and IIIS!   III.(s*t*n)^st/ s^2 * t^2 YII and IIIs, since we are said that integer s>1 and integer t>1
Answer: E
Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have?  Choose the correct choice
A) 4  B) 6  C) 9  D) 10  E) 12

Solution: The top and the bottom are each single faces formed by three equilateral triangles joining, as in the diagram on the left, to make an isosceles trapezoid. Top = 1 face, and bottom = 1 face. This is a four-sided figure, so there are four rectangles extending from the bottom of this prism to the congruent figure at the top. Notice, in particular, the larger vertical face in the “back” of the diagram to the right is formed by two faces of the original triangular prisms lying next to each other and smoothly joining. Total = 1 top + 1 bottom + 4 sides = 6 faces. Answer = 6.
Answer: B
1, 9, 25, 49, 81, ?  Choose the correct option.
A) 100 B) 121 C) 144 D) 169 E) 171

Solution: The series consists of squares of consecutive prime numbers.   Answer : 121.
Answer: B
The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?  Choices.
A) 19002	B) 19028	C) 27788	D) 19000	E) 27711

Solution: Money paid in cash = Rs. 1000   Balance payment = (20000 - 1000) = Rs. 19000   Answer: 19000
Answer: D
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Choose the correct choice from the following choices: A) 1/455 B) 1/417 C) 1/418 D) 1/420 E) 1/428

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue   = ³C₃/¹⁵C₃   = (1 * 3 * 2 * 1)/(15 * 14 * 13)   = 1/455   1/455nswer: 1/455
Answer: A
A rectangular lawn of dimensions 80 m * 50 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?	Choose one.
A) A)3820 B) B)930 C) C)9309 D) D)3600 E) E)8302

Solution: Explanation:   Area = (l + b – d) d   (80 + 50 – 10)10 => 1200 m2   1200 * 3 = Rs.3600   Answer: Option 3600
Answer: D
Concentrated lime juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated lime juice, at the most, can fit into 3 wooden boxes?
Choose the most appropriate option
A) 24.	B) 28.	C) 36.	D) 42.	E) 48.

Solution: Concentrated lime juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way .   now, diameter of each tube = 5 inches   therefore, 4*2 can be put in each wooden box   in 3 boxes  3*4*2= 
 3*4*2 = 24
24=24.
Answer: A
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs? Select the correct option:
A) 246  B) 248  C) 492  D) 15,128  E) 30,256

Solution: OK let's take a crack at this one.   So basically we have 144^2 - 142^2   So then (144+142)(144-142)   (246)(2) = 492   ANSWER:492
Answer: C
A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values O are within three standard deviations of the mean?	Pick:  A) 0  B) 1  C) 3  D) 6  E) 7

Solution: Got the question correctly -- the second item -- [highlight] bthe list of elements in the set is required.[/highlight] is not required.   With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.1
Answer: B
In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 50 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?	Select:  A) 0.06N+3200  B) 0.3N+8000  C) 0.4N+7200  D) 0.1N+8000  E) 0.06N+8000

Solution: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 50% votes so, 0.5*0.6*N plus 8,000 votes from independents: total=0.5*0.6*N+8,000=0.3*N+8,000.   Answer: 0.3N+8000.
Answer: B
There are 25 stations between Delhi and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station? Choose one
A) 802  B) 850  C) 852  D) 702  E) 722

Solution: The total number of stations = 27   From 27 stations we have to choose any two stations and the direction of travel (i.e., Delhi to Chennai is different from Chennai to Delhi) in 27P2 ways.   27P2= 27 * 26= 
27 * 26 = 702
702   ANSWER: 702
Answer: D
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? Choose the correct choice from the following answers:
A) 7 B) 9 C) 8 D) 65 E) 2

Solution: S = 4   M = x   DS = x + 4   US = x - 4   6/(x + 4) + 6/(x - 4) = 2   x = 8   Answer: 8
Answer: C
If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?	Answers:
A) Rs. (xd/y) B) Rs. xd C) Rs. (yd/x) D) Rs. yd E) none

Solution: Explanation:   cost of x metres of wire = Rs.d   cost of 1 metre of wire = Rs.(d/x)   cost of y metre of wire = Rs.(y × d/x) = Rs. (yd/x)   Answer: Option Rs. (yd/x)
Answer: C
The area of a square garden is A square feet and the perimeter is p feet. If a=2p+15, what is the perimeter of the garden, in feet?  Choose the correct choice from the following choices:	A) 28	B) 36	C) 40	D) 56	E) 64

Solution: Perimeter of square = P   Side of square = P/4   Area of Square = (P^2)/16 =A   Given that A = 2P + 15   (P^2)/16 = 2P + 15   P^2 = 32P +240   P^2 -32P -240 = 0   P^2 -40P + 6P -240 = 0   P(P-40)+6(P+40) = 0   (P-40)(P+6) = 0   P = 40 or- 6   Discarding negative value , P = 40   Answer is 40
Answer: C
When the positive integer A is divided by 9 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B? Choose the correct choice from the following answers
A) 35	B) 48	C) 54	D) 63	E) 72

Solution: A = 9k+3 = 7j+4   B = 9m+3 = 7n+4   A-B = 9(k-m) = 7(j-n)   Thus A-B is a multiple of 9 and 7, so it is multiple of 63.   The answer is 63.
Answer: D
Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 40 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work? Select:
A) 20	B) 34	C) 38	D) 40	E) 46

Solution: Nice question +1   We have that X/24 - (60-X)/2R = 40   Also X/R - (60-X)/2R = 120   So we get that 2x - 60 = 80R   3x - 60 = 240R   Get rid of R   120 = 3x   x = 38   Hence answer is 38
Answer: C
By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?  Select.
A) Rs.600 B) Rs.480 C) Rs.500 D) Rs.450 E) Rs.550

Solution: SP = 800   Profit = 25%   CP = (SP)*[100/(100+P)]   = 800 * [100/125]   = 640   Loss 800 *  100/125= 
800 *  100/125 = 640
640   Loss= 25% = 25% of 640 = Rs.160   SP = CP - Loss = 640 - 160 = Rs.480   ANSWER:Rs.480
Answer: B
Calculate the cost of u bags of fruits given that the cost of h bags of said fruit is r rupees?	Answers.
A) Rs.(ur/h)
B) Rs.(r*h)
C) Rs.(ur*h)
D) Rs.(u/h)
E) Rs.(r/h)

Solution: Cost of h bags = Rs. r.   Cost of 1 bag = Rs.	r/h   Cost of u bags = Rs.(r/h)* u= Rs.(ur/h)   Rs.(ur/h)nswer is Rs.(ur/h).
Answer: A
In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
Choose the correct answer:	A) 20 m	B) 22 m	C) 24 m	D) 26 m	E) 28 m

Solution: Explanation:   Each row contains 12 plants.   There are 11 gapes between the two corner trees (11 x 2) metres and 1 metre on each side is left.   Therefore Length = (22 + 2)= 
(22 + 2) = 24
24 m.   Answer: 24 m
Answer: C
The ratio of white balls to black balls is 1:2.If 9 grey balls are added then the ratio of white:black:grey is 2:4:3.Find the number of black balls.
Choose the correct answer
A) 11 B) 12 C) 13 D) 15 E) 16

Solution: If 9 grey balls added means, ratio of grey = 3 in all (i.e., 9/3 = 3)   Therefore, black balls = 3 *4= 
3 *4 = 12
12   and the White balls= 3 *2= 
3 *2 = 6
6   i.e., White= 6 ; 12lack = 12 ; Grey = 9   ANSWER:12
Answer: B
How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276  Choose the correct choice from the following
A) 9 B) 7 C) 4 D) 8 E) 6

Solution: 6   6   6xplanation: Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s   2133 9 (X)   2343 12 (/)   3474 18 (X)   4131 9 (X)   5286 21 (/)   5340 12 (/)   6336 18 (X)   7347 21 (/)   8115 15 (/)   9276 24 (/)   Required number of numbers = 6
Answer: E
A store is having a store-wide sale of 10% off all merchandise. If a discontinued item is an additional 25% off, what is the sale price of an item whose original non-sale price was $50?
Choose the correct choice:
A) $33.50 B) $33.75 C) $34.00 D) $34.25 E) $34.50

Solution: sale price = (original price - 10% decrease) - 25% decrease   price = [50 * (90/100)] * (75/100) = 50 * (.90) * (.750) = 45 * .75= 
45 * .75 = 33.75
33.75   The answer is $33.75.
Answer: B
An amount of money is to be divided between Priya, Mani and Rani in the ratio of 2:4:8. If the difference between the shares of Priya and Mani is Rs.200, what will be the difference between Mani and Rani's share?
Answers: A) 1266 B) 3000 C) 2866 D) 2999 E) 400

Solution: 4 -2= 
4 -2 = 2
2 --- 200   8-4= 
8-4 = 4
4 --- > 200/2*4= 
200/2*4 = 400
400   Answer: 400
Answer: E
A person crosses a 600 metre long street in 5 minutes. What is his speed in km per hour?
Select:  A) 8.2  B) 4.2  C) 6.1  D) 7.2  E) 6.5

Solution: 7.2istance = 600 m = 0.6 km   time = 5 min = 1/12 hr   speed = dist/time = 06./(1/12) = 7.2 km/hr   ANSWER 7.2
Answer: D
Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $36400, how many months will it take Joan to pay back her mortgage?  Choose the correct choice
A) 6 B) 8 C) 10 D) 11 E) 13

Solution: Joan starts off with 100 $ .. which is to be tripled every month   Her monthly payments look like this :   100 , 300 , 900 , 2700 ......... Upto 36400   This can be re written as :   100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 364   So we have 1 , 3 , 9 , 27 ..... 36400 in GP   We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)   Therefore to find the Sum of n terms of a GP we use this formula :   Sn = a (1-r^n) / 1 -r   Using this and plugging in the information we get ...   364 = 1 - 3^n / 1-3 ; 1-3^n / -2   Cross multiplying we get   364 x -2 = 1- 3^n   - 728 = 1 - 3^n   - 729 = - 3 ^n   729 = 3 ^n (negatives cancel out)   729 can also be re written as 3 ^ 6   Therefore ; 3 ^6 = 3 ^n   Thus n = 6 (6)
Answer: A
How many ways could three boxes can be arranged in a shelf with five boxes space in which two places in the shelf will remain empty? Choose the correct choice from the following choices
A) 118 B) 60 C) 8 D) 12 E) 120

Solution: ways in which 3 places out 5 can be selected = 5C3   ways in which 3 boxes can be arranged in 3 places = 3!   Total ways of arrangement = 5C3*3!   =5*4/2*6   =10*6= 
10*6 = 60
60   Ans= 60
Answer: B
Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?
Pick one:
A) 2%  B) 2.15%  C) 2.25%  D) 2.50%  E) 3%

Solution: Generally in such cases, there is always loss.   So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.   Loss% = 2.25%ommon loss and gain% 2 = x 2   10 10   Therefore, here common loss and gain % = 15%   Hence,   Loss% = 15 2 = 2.25%   2.25%
Answer: C
What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 2?
Select the correct option.
A) 0.4	B) 1	C) π/4	D) 4	E) π

Solution: Maximum distance straight line is diameter   d = 2r = 4..   ANS option 4.
Answer: D
An object thrown directly upward is at a height of h feet after t seconds, where h = -12 (t-3)^2 + 120. At what height, in feet, is the object 2 seconds after it reaches its maximum height? Choose the correct choice from the following choices:
A) 48  B) 54  C) 60  D) 66  E) 72

Solution: We see that h will be a maximum h=120 when t-3=0, that is when t=3.   At t=5, h = -12*(5-3)^2 + 120 = -12(4) + 120 = 72   The answer is 72.
Answer: E
Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?	Choose the correct choice:
A) 7.19
B) 7.18
C) 7.16
D) 7.15
E) 7.12

Solution: T = (121 + 165)/ (80 + 65) * 18/5   T = 7.15   Answer: 7.15
Answer: D
A train passes a man standing on the platform. If the train is 125 meters long and its speed is 90 kmph, how much time it took in doing so? Pick:
A) 6 sec B) 2 sec C) 9 sec D) 5 sec E) 1 sec

Solution: 5 sec = 125   S = 90 * 5/18= 
90 * 5/18 = 25
25 mps   T= 125/25= 
125/25 = 5
5 sec   Answer:5 sec
Answer: D
Addison High School’s senior class has 300 boys and 240 girls. If 60% of the boys attended the college then 60% of the total class attended college, what percentage of the girls class attended college? Pick:  A) 60  B) 50  C) 46  D) 55.56  E) 65

Solution: Number of boys attending the party : 0.60*300= 
0.60*300 = 180
180   Total students= 300+240= 
300+240 = 540
540   number of students attending the party:  0.60*540= 
 0.60*540 = 324
324   number of girls attending= 324-180= 
324-180 = 144
144   % of girls attending= 144/240 = 60%. 60 is the correct answer
Answer: A
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? Choose the most appropriate option.
A) 2.5 sec
B) 2.9 sec
C) 2.7 sec
D) 8.7 sec
E) 8.5 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5 secnswer: 2.5 sec
Answer: A
In a certain country, 60 percent of the population likes basketball, and 32 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf? Choose the correct choice:
A) 20% B) 33% C) 40% D) 53% E) 67%

Solution: Correct Answer: (D).   Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 32 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 32/60 = 53%, or choice 53%.
Answer: D
The C.P of 15 books is equal to the S.P of 19 books. Find his gain% or loss%?  Choose one.
A) 16 2/3%	B) 16 2/8%	C) 16 2/5%	D) 21 1/19%	E) 16 1/3%

Solution: 15 CP = 19 SP   19 --- 4 CP loss   100 --- ? => 21 1/19% loss.Answer: 21 1/19%
Answer: D
In the rectangular coordinate system, if the line x = 5y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
Pick one.
A) 1/2  B) 2/3  C) 1/4  D) 2/5  E) 3/7

Solution: x = 5y+5, and thus y = x/5 - 1   The slope is 1/5.   The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2   p/2 = 1/5 and thus p = 2/5   The answer is 2/5.
Answer: D
A coin is tossed live times. What is the probability that there is at the least one tail?
Answers: A) 31/32 B) 31/37 C) 31/29 D) 31/28 E) 31/08

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed five times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/32 ; P(T)   = 1 - 1/32   = 31/32   31/32nswer: 31/32
Answer: A
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?	Choose the correct choice from the following: A) 9:37 B) 9:31 C) 9:27 D) 9:19 E) 9:17

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   Answer: 9:31
Answer: B
A man persuaded Weary Willie, with some difficulty, to try to work on a job for thirty days at eight dollars a day, on the condition that he would forfeit ten dollars a day for every day that he idled. At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labor. Can you tell just how many days' work he put in and on how many days he idled?
Choose the most appropriate option: A) 1673 &13 1/3 days B) 1633 &13 1/2 days C) 1433 &13 1/6 days D) 2173 &13 1/5 days E) 2273 &13 1/7 days

Solution: A   1673 &13 1/3 days   Weary Willie must have worked 1673 days and idled 13 1/3 days. Thus the former time, at $8.00 a day, amounts to exactly the same as the latter at $10.00 a day
Answer: A
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
Choose the correct choice from the following answers.
A) 11
B) 18
C) 99
D) 77
E) 51

Solution: A:18 = 2:3   18:C = 2:5   A:18:C = 4:6:15   6/25 * 75= 
6/25 * 75 = 18
18   Answer: 18
Answer: B
If f(b)=b^2, what is the value of (f(a+b)−f(a))/b ?  Select
A) a	B) b	C) 2a + b	D) 2a +-b	E) 2b - a

Solution: start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2   a^2+2ab+b^2 - a^2/b = (simplify a^2)   2ab+b^2/b = (cancel b's)   = 2a+b   Ans : 2a + b
Answer: C
Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
Choose the correct choice from the following:
A) 1	B) 4	C) 3	D) 8	E) 6

Solution: 6 * 22= 
6 * 22 = 132
132   7 * 19= 
7 * 19 = 133
133   --------------   1   1nswer: 1
Answer: A
A man can row upstream 10 kmph and downstream 30 kmph. Find the rate of the stream and man rate in still water. Choose the correct choice from the following choices: A) 15,20 B) 30,20 C) 1,20 D) 20,20 E) 10,20

Solution: 10,20xplanation:   Please remember,   If a is rate downstream and b is rate upstream   Rate of current = 1/2(a-b)   Rate in still water = 1/2(a+b)   => Rate of current = 1/2(30-10) = 10 kmph   => Rate in still water = 1/2(30+10) = 20 kmph   Option 10,20
Answer: E
There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 6 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?	Answers:
A) 64
B) 32
C) 36
D) 48
E) 61

Solution: Make a venn diagram to get a clear picture. Look at the diagram:   Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.   d + f = 20 (People who take 64rt and one other class)   b = 3e (people who take only 64rt is 3 times the people who take Bio and Calculus)   17 + 6 + 5 + b + d + e + f = 100 (Total people)   b + b/3 = 52   b = 39   Number of freshmen who take 64rt = 39 + 20 + 5= 
39 + 20 + 5 = 64
64   64nswer 64
Answer: A
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?  Choose the correct choice from the following answers: A) 287 m B) 287 m C) 288 m D) 150 m E) 287 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150 m
Answer: D