MU-NLPC/Calc-aqua_rat huggingface dataset:
Three workers have a productivity ratio of 1 to 2 to 4. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?	Choose the correct choice from the following answers:
A) 12 to 1	B) 6 to 1	C) 5 to 1	D) 20 to 3	E) 1 to 5

Solution: The fastest worker who does 4 units of job worked for all 10 hours, so he did   4*10= 
  4*10 = 40
40 units of job;   The slowest worker who does 1 unit of job worked for only   4+2= 
  4+2 = 6
6 hours (first 4 hours and last 2 hours), so he did   1*6= 
  1*6 = 6
6 units of job;   The ratio thus is 40 to 6, or 20 to 3.   Answer: 20 to 3
Answer: D
In a hostel there were 100 students. To accommodate 10 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?	Choose the correct choice from the following answers:	A) A)Rs.5800	B) B)Rs.9900	C) C)Rs.5400	D) D)Rs.5900	E) E)Rs.5430

Solution: 100x + 400   = 110(x – 5)   x = 95   100 * 95 + 400= 
100 * 95 + 400 = 9_900
9900   Answer:Rs.9900
Answer: B
A person incurs 5% loss by selling a watch for $1140. At what price should the watch be sold to earn 5% profit?
Choose the correct option.
A) $1260  B) $1200  C) $1150  D) $1320  E) $1290

Solution: Let the new S.P. = x   then (100-loss%): (1st S.P.) = (100+gain%): (2nd S.P.)   (100-5)/1140 = (100+5)/x   x=105*1140/95= 
105*1140/95 = 1_260
1260   new price= $1260   correct option is $1260
Answer: A
An escalator moves towards the top level at the rate of 15 ft.sec and its length is 200 feet. If a person walks on the moving escalator at the rate of 5 feet per second towards the top level, how much time does he take to cover the entire length.
Select:  A) 5sec  B) 10sec  C) 20sec  D) 15sec  E) 25sec

Solution: Explanation :   Time taken to cover the entire length = tot.dist/resultant speed = 200/ (15+5)= 
200/ (15+5) = 10
10sec   Answer : 10sec
Answer: B
There are 7 red shoes & 3 green shoes . If two of red shoes are drawn what is the probability of getting red shoes	Choose the correct choice from the following options:
A) 1/13 B) 1/14 C) 1/15 D) 7/15 E) 7/16

Solution: taking 2 red shoe the probablity is 7C2   from 10 shoes probablity of taking 2 red shoe is 7C2/10C2=7/15   ANSWER:7/15
Answer: D
A shipment of 230 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Choose the correct choice:
A) 1/250 B) 1/84 C) 1/11 D) 9/68 E) 1/3

Solution: Probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = (84/230)   Probability of chosing one defective phone from a lot of 229(we already picked one) which ontains 83(we already picked one) defective phones is = (83/229)   Combined probability of series of events = product of the probabilities = (84/230)*(83/229)   84/230 is close to (23/63) and (83/229)= (29/80)   so answer is (23/63)*(29/80) = (9/68)   So, answer will be 9/68
Answer: D
John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.54 more than Jane, what was the original price of the dish?	Select:
A) 24  B) 34.8  C) 36  D) 42  E) 84

Solution: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:   0.15p - 0.15*0.9p = 0.54 --> 15p - 13.5p = 54 --> p = 36.   Answer: 36.
Answer: C
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?  Choose the correct option:
A) 372  B) 375  C) 278  D) 267  E) 288

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   75 ----- ?=> 375   Answer:375
Answer: B
Mixture A is 25 percent milk, and mixture B is 65 percent milk. If the two are poured together to create a 4-gallon mixture that contains 40 percent milk, approximately how many gallons of mixture A are in the mixture? Pick one:
A) 1.5 B) 1.75 C) 2.85 D) 2.5 E) 3.0

Solution: (65-40)/(40-25) = Qa/Qb   25/15 = Qa/Qb   5/3 = Qa/Qb   Qa = (5/7) * 4 = 20/7 = 2.85 approx   Answer : 2.85
Answer: C
In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score K that Lindsey could have received on her midterm exam?	Choices:	A) 52%	B) 64%	C) 72%	D) 76%	E) 80%

Solution: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:   100-------------88----------------------------x   And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: A
There are 11 dozen mangoes in a box. If there are 16
such boxes, how many mangoes are there in all the
boxes together?
Choose the correct choice
A) 2112	B) 3096	C) 6192	D) 628	E) None

Solution: Number of mangoes = 11 dozens   = 11 × 12 = 132   ∴ Number of mangoes in 16 boxes   = 16 × 132 = 2112   2112nswer 2112
Answer: A
The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.  Pick one:  A) 40  B) 26  C) 27  D) 28  E) 22

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 20) / 2 = 40.40nswer:a
Answer: A
A shipment of 250 smartphones contains 67 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Choose one:
A) 1/250  B) 1/14  C) 1/11  D) 1/9  E) 1/3

Solution: Probability of chosing one defective phone from a lot of 250 which ontains 67 defective phones is = (67/250)   Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 66(we already picked one) defective phones is = (66/249)   Combined probability of series of events = product of the probabilities = (67/250)*(66/249)   67/250 is close to (26/97) and (66/249)= (22/83)   so answer is (26/97)*(22/83) = (1/14)   So, answer will be 1/14
Answer: B
If x+y=24, x-y=40, for integers of x and y, x=?
Pick one
A) 20  B) 23  C) 25  D) 32  E) 42

Solution: x+y = 24   x-y = 40   2x = 64   x = 32   Answer is 32
Answer: D
A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $14000 left with him. find salary.. Pick.
A) $10400	B) $14000	C) $144000	D) $1800	E) $140000

Solution: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount   [1-(1/5 + 1/10 + 3/5)} * total salary= $14000, = [1-9/10] * Total salary = $14000, Total salary = $14000*10= 
14000*10 = 140_000
$140000, correct answer ($140000)
Answer: E
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 90 ps per meter is? Choose the correct choice:
A) 287
B) 369
C) 225
D) 279
E) 361

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 0.9   = Rs.225   Answer:225
Answer: C
A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.	Choose the correct choice from the following choices.
A) 360, 160, 200	B) 160, 360, 200	C) 200, 360,160	D) 200,160,300	E) 300,260,100

Solution: let ratio be x.   Hence no. of coins be 5x ,9x , 4x respectively   Now given total amount = Rs.206   => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206   we get x = 40   => No. of 50p coins = 200   => No. of 25p coins = 360   => No. of 10p coins = 160   Answer:200, 360,160
Answer: C
There is a total of 100 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/5. What is the probability that the marble will be either red or blue? Choose the most appropriate option.
A) 2/3	B) 3/5	C) 7/10	D) 9/20	E) 11/20

Solution: P(red or blue) = 1 - P(white) - P(green) = 20/20 -5/20 - 4/20 = 11/20   The answer is 11/20.
Answer: E
A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
Choose the correct choice from the following answers
A) 1,250 meters / minute  B) 1,760 meters / minute  C) 1,443 meters / minute  D) 1,980 meters / minute  E) 1,667 meters / minute

Solution: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify   75 kilometers per hour = 75 km/hr   = (75 × 1000 meters) / (60 minutes) = 1,250 meters / minute   correct answer 1,250 meters / minute
Answer: A
A man swims downstream 36 km and upstream 18 km taking 6 hours each time, what is the speed of the man in still water? Pick one.
A) 4.5  B) 5.5  C) 6.5  D) 4.8  E) 2

Solution: 36 --- 6 DS = 6   ? ---- 1   18 ---- 6 US = 3   ? ---- 1 M = ?   M = (6 + 3)/2= 
(6 + 3)/2 = 9/2 = around 4.5
4.5   4.5nswer: 4.5
Answer: A
The product of 4 consecutive even numbers is always divisible by:	Choose the correct choice from the following options:
A) 600
B) 768
C) 864
D) 384
E) 356

Solution: To solve this question, we need to know two facts.   Fact 1:   The product of 4 consecutive numbers is always divisible by 4!.   Fact 2:   Since, we have 4 even numbers, we have an additional 2 available with each number.   Now, using both the facts, we can say that the product of 4 consecutive even numbers is always divisible by,   =(24)×4!=(24)×4!   =16×24=16×24   =384   Option(384)
Answer: D
If 4d^4 − 41d^2 + 100 = 0, then what is the sum of the two greatest possible values of d ?	Choose the correct choice from the following choices.
A) 4
B) 9/2
C) 7
D) 41/4
E) 25

Solution: just forget about the value of d^4 for the moment and let d^2= X. (its better to work with power of 2 than 4)   now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.   so d^2 = 4 and 25/4   so d= +2 and minus 2 and +5/2 and minus 5/2   The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = 9/2
Answer: B
According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 320 6 ounces servings of orange juice?	Choose the correct choice:
A) a) 25	B) b) 34	C) c) 50	D) d) 40	E) e) 100

Solution: Its D.   Total juice rquired = 320*6= 
320*6 = 1_920
1920 ounce   12 ounce concentate makes= 12 * 4= 
12 * 4 = 48
48 ounce juice   Total cans required= 1920/48= 
1920/48 = 40
40.   Answer d) 40
Answer: D
A circular ground whose diameter is 70 metres, has a 2.8 metre-broad garden around it. What is the area of the garden in square metres?  Choose the correct choice from the following answers.
A) 540.72 B) 740.64 C) 640.64 D) 620.45 E) 725.26

Solution: Req. area = Ï€[(37.8)2 â€“ (35)2]   = 22â„7 Ã— (72.8 Ã— 2.8)[since a2 - b2 = (a + b)(a - b)]   = 22 Ã— 72.8Ã— 0.4 = 640.64 sq m   Answer 640.64
Answer: C
R is the set of positive odd integers less than 10, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ? Choose the correct choice from the following:
A) None B) Two C) Four D) Five E) Seven

Solution: squares < 10 {1,4,9}   S = {1,9}   R = {1,3,.....10}   Hence Two.
Answer: B
The average of first five multiples of 5 is :	Choose the correct choice from the following choices:
A) 3
B) 9
C) 12
D) 15
E) 17

Solution: Solution   Average = 5(1+2+3+4+5)/5 =75/5= 
75/5 = 15
15 Answer 15
Answer: D
Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.35 per ounce, what is the share of Arabica in this blend?	Select:
A) 20%
B) 24%
C) 50%
D) 33%
E) 40%

Solution: a= amount of arabica coffee   1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta   therefore:   .4a + .3(1-a) = .35   .4a + .3 - .3a = .35   a= .5   therefore: .5/1 ounce = 50%. Therefore, the answer should be 50%
Answer: C
Find the area of a cuboid of length 4cm , breadth 6 cm . and height 5cm.	Choices
A) 120 cm cube B) 110 cm cube C) 220 cm cube D) 430 cm cube E) 480 cm cube

Solution: 120 cm cuberea of a cuboid = lxbxh =4cm x 6cm x 5cm = 120 cm cube   answer :120 cm cube
Answer: A
If all the sides of a right triangle increase in length by 10%, then by what percentage does the area of the triangle increase?
Choices
A) 21%  B) 42%  C) 80%  D) 96%  E) 120%

Solution: Let B be the base and H be the height of the original triangle.   The original area is (1/2)BH.   The area of the expanded triangle is (1/2)(1.1B)(1.1H) = (1.1)(1.1)(1/2)BH = 1.21(1/2)BH   The answer is 21%.
Answer: A
A person takes 10 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed? Choices:
A) 50 minutes
B) 20 minutes
C) 40 minutes
D) 60 minutes
E) 80 minutes

Solution: Let the distance and original speed be d km and k kmph respectively.   d/0.8k - d/k = 10/60 => 5d/4k - d/k = 1/6   => (5d - 4d)/4k = 1/6 => d = 4/6 k=2/3k   Time taken to cover the distance at original speed   = d/k = 2/3 hours = 40 minutes.   ANSWER:40 minutes
Answer: C
A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 17 miles per hour." What was their average speed in the whole journey?
Answers
A) 10 miles/hour
B) 12 miles/hour
C) 11 miles/hour
D) 12.6 miles/hour
E) 14 miles/hour

Solution: 2xy/x+y=12.6 miles/hour   ANSWER:12.6 miles/hour
Answer: D
A certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?  Choose the correct choice from the following.
A) a) 12,000 B) b) 10,800 C) c) 10,900 D) d) 11,000 E) e) 11,100

Solution: Let x = number of people in smallest district   x*1.1 = number of people in largest district   x will be minimised when the number of people in largest district is maximised   10*x*1.1 = 11x = total number of people in other districts   So we have 11x + x = 144k   x = 12,000   a) 12,000nswer : a) 12,000
Answer: A
calendar=52097083 november=538=8651
march=2*308 blue=7154 december=?
Pick.
A) 9535&153	B) 9585&153	C) 9525&153	D) 9525&*53	E) 9525&*54

Solution: from above in formation   d=9   e=5   c=2   e=5   m=3   b=1   e=5   r=8   95253158( Order doesnot matter i guess!)   another thing is &=8 for mathcing above ans   ANSWER:9525&153
Answer: C
How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 3%?	Choose the most appropriate option:
A) 0—1.5 gal	B) 1.5—3 gal	C) 3—4.5 gal	D) 4.5—6 gal	E) 16+ gal

Solution: Let amount of water that must be added in gallons to dilute concentration of brine solution = x   Amount of brine already present = 10/100 * 10= 
10/100 * 10 = 1
1 gallon   1/(10+x) *100= 3   =>100 = 30 + 3x   => x= 70/3 = 23   Answer 16+ gal
Answer: E
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?	Select
A) 6 hrs  B) 6 2/3 hrs  C) 7 hrs  D) 7 1/2 hrs  E) 8 hrs

Solution: Explanation:   (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20   (A + C)'s 1 hour work = (1/12 + 1/20) = 2/15   Part filled in 2 hrs = (3/20 + 2/15) = 17/60   Part filled in 6 hrs = 3 * 17/60 = 17/20   Remaining part = 1 - 17/20 = 3/20   Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.   Total time taken to fill the tank = (6 + 1)= 
(6 + 1) = 7
7 hrs.   ANSWER IS 7 hrs
Answer: C
A runs 5/2 time as fast as B, and gives B and a start of 40m. How long should the racecourse be so that A and B might reach in the same time?
Pick:
A) 150 m  B) 100 m  C) 75 m  D) 80 m  E) 90 m

Solution: verification of options..... (2/5)*100 =40   So answer is 100m   ANSWER:100 m
Answer: B
The game of blackjack is played with a deck consisting of 13 cards (one of each of the numbers 2-10, one jack, one queen, one king, and one of ace) in each of four suits: clubs, diamonds, hearts, and spades.
In a game of blackjack, if your first card is a spade, what are the R odds that it is an ace?  Choose the correct choice:  A) 1/52  B) 1/26  C) 1/13  D) 1/4  E) 5/13

Solution: The question should ask about the probability not the odds.   There are 13 spades, the probability R that the spade we already have is an ace is therefore 1/13.   Answer: 1/13.
Answer: C
In a 200 m race,A covers the distance in 45 seconds and B in 60 second.In this race A beats B by : Choose the correct choice from the following options
A) 20 m	B) 50 m	C) 45 m	D) 60 m	E) None of these

Solution: Solution   Distance covered by B in 15 sec. = (200/60x15)m =50m.   ∴ A beats B by 50 metres.   Answer 50 m
Answer: B
Ram professes to sell his goods at the cost price but he made use of 850 grms instead of a kg, what is the gain percent?  Options.
A) 11 1/7% B) 11 7/7% C) 11 1/9% D) 17.64% E) 11 1/2%

Solution: 850 --- 150   100 --- ? => 17.64%   Answer:17.64%
Answer: D
For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is Answers.
A) Rs. 8000 B) Rs. 9000 C) Rs. 9900 D) Rs. 9990 E) Rs. 10000

Solution: Sol. Income in first year = * x 42000 = Rs. 24000   Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)   = 66000 - S6000 = Rs. 10000   Rs. 10000
Answer: E
Find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm? Choose the correct choice: A) 320cm2 B) 280cm2 C) 384cm2 D) 290cm2 E) 350cm2

Solution: Let other diagonal = 2x cm.   Since diagonals of a rhombus bisect each other at right angles, we have:   (20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm.   So, other diagonal = 32 cm.   Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 24 x 32) cm2 = 384 cm2   hence 384cm2
Answer: C
A person starting with Rs.64 and making 6 bets, wins three times and loses 3times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for 1/2 the money remaining at the time of the bet, then the final result is? Select the correct option
A) Rs.23  B) Rs.37  C) Rs.45  D) Rs.67  E) Rs.77

Solution: As the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5, we will multiply initial amount by 1.5 thrice and by 0.5 thrice (in any order).   The overall resultant will remain same.   So final amount with the person will be (in all cases):   =64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)==64(1.5)(1.5)(1.5)(0.5)(0.5)(0.5)= Rs 2727   Hence the final result is:   64−27=3764−27=37:   A loss of Rs.37   Rs.37
Answer: B
If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.7
II. 12.3
III. 9.5
Select:
A) I only B) I and II only C) II only D) III only E) I and III only

Solution: Mean = 12   SD = 1.3   2 SD above mean = 12+2*1.3= 
12+2*1.3 = 14.6
14.6   2 SD below mean= 12-2*1.3= 
12-2*1.3 = 9.4
9.4   12.3 and 9.5 lies in the range of 2SD from mean   I onlynswer: Option I only
Answer: A
Susan has nine hamsters. In order to feed each hamster 4 blocks of food each day, how much food must she buy for 7 days?  Choose the correct option:  A) 210  B) 228  C) 243  D) 252  E) 271

Solution: 4 blocks of food per day multiplied by 9 hamsters = 36 blocks per day. 36 multiplied by 7 days = 252 blocks of food, hence answer : 252.
Answer: D
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?	Choose the correct choice from the following options:
A) 2287	B) 2689	C) 1667	D) 8112	E) 1691

Solution: A = 7500(26/25)2 = 8112   Answer: 8112
Answer: D
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 7% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue? Choose one.
A) 2 B) 5 C) 700/107 D) 110/20 E) 9/4

Solution: Let price be 10/ticket   then 220 tickets for this month's performance at its usual price=2200   which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000   now new revenue this month=200*10.7= 
200*10.7 = 2_140
2140   as per question asked 2000=2140(1-A/100)----->A=700/107%   Ans 700/107
Answer: C
The circumferences of two circles are 264 meters and 704 meters. Find the difference between the areas of the larger and the smaller circles?	Choose the correct choice from the following options.
A) 29960 sq m
B) 33880 sq m
C) 43120 sq m
D) 27680 sq m
E) 12786 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 704   s = 264/2∏ and l = 704/2∏   Difference between the areas = ∏l^2 - ∏s^2   = ∏{132^2/∏^2 - 352^2/∏^2}   = 132^2/∏ - 352^2/∏   = (132 - 352)(132 + 352)/∏   = (220)(484)/(22/7)   = 33880 sq m   Answer:33880 sq m
Answer: B
If |x – 9/2| = 5/2, and if y is the median of a set of t consecutive integers, where t is odd, which of the following must be true?
I. xyt is odd
II. xy(t^2 + t) is even
III. x^2y^2t^2 is even	Choices.
A) II only is true  B) III only is true  C) I and III  D) II and III  E) I, II, and III

Solution: given:   t is Odd   y is the median of odd numbers, hence y is Odd   x = solving the modulus you get 7 and 2. Hence x is Even or Odd   Therefore: t = O, y = O and x = O or E   Statement I = x*y*t = y*t*x = O x O x O/E = O x O/E = Odd or even. So False   Statement II = xy(t^2 + t) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true   Statement III. x^2y^2t^2 is even. E/O x O x O = Odd or even. Hence False.   II only is truenswer = II only is true.
Answer: A
The ratio of ages of two friends is 3:5 and sum of their ages is 80 years. What are their present ages in years?
Select:
A) 10,60
B) 20,60
C) 40,30
D) 30,50
E) 20,50

Solution: 3x + 5x== 80   x==10   (30,50)   ANSWER:30,50
Answer: D
The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 1 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 8
Tennis 7
Baseball 4
Choose the most appropriate option.
A) 6	B) 9	C) 11	D) 13	E) 17

Solution: X = 8 + 7 + 4 - (3 + 2 + 1)= 
8 + 7 + 4 - (3 + 2 + 1) = 13
13   Answer is 13
Answer: D