MU-NLPC/Calc-aqua_rat huggingface dataset:
How much interest can a person get on Rs. 8200 at 17.5% p.a. simple interest for a period of two years and six months?	Select the correct option:
A) 3587.58 B) 3587.52 C) 3587.5 D) 3587.59 E) 3582.52

Solution: I = (8200 * 2.5 * 17.5)/100 = (8200 * 5 * 35)/(100 * 2 * 2) = Rs. 3587.50.Answer: 3587.5
Answer: C
A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $350 and $200 per unit, respectively. What is the fewest number of computer printers that the company can purchase? Options: A) 9 B) 10 C) 11 D) 12 E) 13

Solution: The smallest amount that the company can spend is the LCM of 350 and 200, which is 1400 for each, which is total 2800.   The number of 1st type of computers which costing $350 = 1400/350= 
1400/350 = 4
4.   The number of 2nd type of computers which costing $200= 1400/200= 
1400/200 = 7
7.   Total= 4+7= 
4+7 = 11
11   Answer is 11.
Answer: C
Which of the following equations is NOT equivalent to 4x^2 = a^2 - 9 ?
Choose the correct choice from the following choices:	A) 4x^2 + 9 = a^2	B) 4x^2 - a^2 = -9	C) 4x^2= (a + 3)(a - 3)	D) 2x = a - 3	E) x^2 = (a^2-9)/4

Solution: 4X^2 = a^2 - 9   The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.   Looking at Answer D, we have....   2X = a - 3   While you COULD take the square root of both sides of the original equation, it's important to note that the square root of a^2 - 9 is NOT (a-3).   a^2 - 9 can be factored into (a-3)(a+3), but neither of these parentheses is the square root of a^2 - 9.   You can see the proof when you square either of the two parentheses:   (a-3)^2 = a^2 - 6X + 9   (a+3)^2 = a^2 + 6x + 9   Thus, 2x = a - 3 is NOT equivalent to the prompt.
Answer: D
The table shows the number of calls received by each of five operators during each of 5 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 5 periods the least?
Choose the correct option.
A) Operator A: 3, 7, 7, 3, 4  B) Operator B: 4, 5, 5, 6, 5  C) Operator C: 8, 2, 5, 5, 6  D) Operator D: 6, 4, 4, 6, 6  E) Operator E: 3, 4, 5, 8, 7

Solution: Operator A: 3, 7, 7, 3, 4   it has 2 numbers right at the average, Operator A: 3, 7, 7, 3, 4 has none.
Answer: A
9.6 , 9.8 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.255 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean? Choices
A) 90%	B) 75%	C) 80%	D) 85%	E) 70%

Solution: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.255; 10+0.255} = {9.745; 10.255}.   From the 8 listed numbers, 6 are within this range so 6/8=75%.   Answer: 75%.
Answer: B
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?  Choose one:
A) 10	B) 5	C) 8	D) 6	E) 11

Solution: C's age be x years.   Then, B's age = 2x years.   A's age = (2x + 2) years.   (2x + 2) + 2x + x = 27   5x = 25 => x = 5   Hence, B's age = 2x = 10 years.   10NSWER 10
Answer: A
The population of a town is 1,76,400 . If it increases at the rate of 5% per year, what will be its population 2 years hence ? What was it 2 years ago ?	Choices.
A) 140000	B) 180000	C) 160000	D) 200000	E) None of them

Solution: Population after 2 years = 176400*[1+(5/100)]^2   =[176400*(21/20)*(21/40)]   = 194481.   Population 2 years ago = 176400/[1+(5/100)]^2   =[716400*(20/21)*(20/21)]= 160000.   Answer is 160000.
Answer: C
An aeroplane covers a certain distance at a speed of 150 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:	Choose the correct choice.
A) 1300 kmph  B) 160 kmph  C) 180 kmph  D) 1080 kmph  E) none

Solution: Explanation: Distance = (150 x 2) = 300 km.   Speed = Distance/Time   Speed = 300/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]   Required speed = 300 x 3/5 km/hr = 180 km/hr.   Answer: Option 180 kmph
Answer: C
Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?	Pick one:
A) 7	B) 8	C) 6	D) 5	E) 1

Solution: Explanation:   1/10 + 1/15 = 1/6 * 4 = 2/3   1 - 2/3 = 1/3   1/10 + 1/15 - 1/x = 1/3   x = 8   Answer:8
Answer: B
Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.2 a meter?	Select the correct option
A) 201  B) 132  C) 772  D) 592  E) 261

Solution: 2 * 22/7 * 16 = 100.5   100.5 * 2 = Rs.201   201nswer: 201
Answer: A
A computer wholesaler sells ten different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
Pick.
A) 15/56	B) 3/28	C) 1/28	D) 1/15	E) 1/168

Solution: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 8 avilable. so 8C1 is the numerator.   Total no of ways we can choose 3 from 10 is 10c3, which is the denominator.   So, the probability: 8c1/10c3= 1/15 ans is 1/15.
Answer: D
On a Saturday night, each of the rooms at a certain motel was rented for either $50 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $50, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night ?	Choose the correct choice from the following answers:	A) $400	B) $800	C) $1,000	D) $1,600	E) $2,400

Solution: Let total rent the motel charge for all rooms =x   If 10 rooms that were rented for 60 $ had instead been rented for 50 $,   then total difference in prices = 10 $ * 10 = 100 $   Total rent the motel charged would have been reduced by 25 %   .25x = 100   => x= 400   $400nswer $400
Answer: A
In how many ways a committee consisting of 3 men and 2 women can be formed from 9 men and 3 women?  Choose the correct answer
A) A)252	B) B)15	C) C)20	D) D)18	E) E)21

Solution: Required number of ways = 9C3*3C2 = 84*3= 
84*3 = 252
252   252nswer is 252
Answer: A
In a survey about potential presidential candidates A and B, 32% of the public like A and 50% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither? Choose the correct choice from the following answers
A) 27.5 %  B) 35.5 %  C) 39.5 %  D) 22%  E) 67%

Solution: Let x be the percentage of people who like both.   Then the percentage of people who like only 1 but not both is 2x.   32% + 50% = 2x + 2(x) because the percentage who like both are counted twice.   Then x = 20.5% and 2x = 41%   100% = 20.5% + 41% + Neither   Neither = 39.5%   The answer is 39.5 %.
Answer: C
A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?  Choose the correct option.
A) 109% B) 160% C) 100% D) 600% E) 108%

Solution: MP = 100   100%P = 75   SP = 150   ------   75 ---- 75   100 ---- ? => 100%   Answer:100%
Answer: C
For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.567] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?  Choose the correct choice from the following choices.
A) 0	B) 1	C) 27	D) 0	E) Cannot be determined

Solution: K=[lCM of 80 and 45] * (any integer)   however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer   for value of k(60) * any integer unit value will be always zero .   0
Answer: D
A shopkeeper sells 20% of his stock at 20% profit ans sells the remaining at a loss of 10%. He incurred an overall loss of Rs. 500. Find the total worth of the stock?  Choose the correct choice from the following choices:	A) 13500	B) 12000	C) 12500	D) 15000	E) 15500

Solution: Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 6/5 = 6x/25   The SP of 80% of the stock = 4/5 * x * 0.9 = 24x/25   Total SP = 6x/25 + 18x/25 = 49x/50   Overall loss = x - 24x/50 = x/25   x/25 = 500 => x = 12500   Answer:12500
Answer: C
A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is?  Choose the correct choice:
A) A)$58  B) B)$42  C) C)$65  D) D)$48  E) E)$62

Solution: avg = sum of observations/number of observations   avg income=(45+50+60+65+90)/5= 
(45+50+60+65+90)/5 = 62
62   Answer is $62
Answer: E
What annual payment will discharge a debt of Rs. 1060 due in 2 years at the rate of 5% compound interest?
Options
A) 993.2	B) 551.25	C) 570.07	D) 543.33	E) 646.33

Solution: Explanation:   Let each installment be Rs. x. Then,   x/(1 + 5/100) + x/(1 + 5/100)2 = 1060   820x + 1060 * 441   x = 570.07   So, value of each installment = Rs. 570.07   Answer: Option 570.07
Answer: C
Two trains of length 210 m and 120 m are 160 m apart. They start moving towards each other on parallel tracks, at speeds 74 kmph and 92 kmph. After how much time will the trains meet? Choose the correct choice from the following choices
A) 35/10  B) 31/10  C) 31/10  D) 36/10  E) 37/10

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (74 + 92)*5/18 = 46.1 mps.   The time required = d/s = 160/46.1= 35/10 sec.   35/10nswer:35/10
Answer: A
Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 15 years old. At what age did the father get married ?  Choose the correct choice
A) 20years	B) 21years	C) 22years	D) 23years	E) 25years

Solution: Explanation:   Ayush's present age = 15 years.   His mother's present age = (15 + 20)= 
(15 + 20) = 35
35 years.   Ayush's father's present age= (35 + 5)= 
(35 + 5) = 40
40 years.   Ayush's father's age at the time of Ayush's birth= (40 - 15)= 
(40 - 15) = 25
25 years.   Therefore Ayush's father's age at the time of marriage= (25 - 2)= 
(25 - 2) = 23
23 years.   Answer: 23years) 23 year
Answer: D
On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?	Choose the correct answer:
A) Tuesday  B) Wednesday  C) Thursday  D) Friday  E) Saturday

Solution: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3   Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 2 /1*(2-1)= 
2 /1*(2-1) = 2
2*1/1*1= 
2*1/1*1 = 2
2   Hat combinations= 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4   Total Combinations = Shirt Combos*Sweater Combos*Hat Combos    3*2*4= 
 3*2*4 = 24
24 combinations   24 / 7 (days of the week)= remainder of 3   Purchased on Tuesday, 3rd day is Friday. Next day, which he won't have a new combination for, is Saturday. (Saturday)
Answer: E
The present worth of Rs. 242 due in 2 years at 10% per annum compound interest is:
Options: A) Rs. 180 B) Rs. 240 C) Rs. 220 D) Rs. 200 E) Rs. 300

Solution: Explanation:   Present worth of Rs. x due T years hence is given by   Present Worth (PW) = x/(1+R/100)^T   Present Worth (PW) = 242/(1+10/100)^2=242/(11/10)^2=Rs. 200   Answer : Option Rs. 200
Answer: D
A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?	Pick.
A) 30/83 hours B) 15/13 hours C) 15/4 hours D) 30/19 hours E) 32/13 hours

Solution: Speed downstream = 10 + 6= 
10 + 6 = 16
16 kmph.   Time required to cover 60 km downstream= d/s = 60/16   = 15/4 hours.   Answer:15/4 hours
Answer: C
A man jumps into a river from a overbridge ,at the same time a hat drops in the river which flows with the stream of the water. That man travels 10 minute upstream and returns back where he was asked to catch the hat. He catches hat at a distance of 1000 yard down at a second bridge . Find the speed of the river.
Options
A) 50 B) 60 C) 55 D) 70 E) 75

Solution: Explanation :   Suppose x is the distance travelled by the man in 10 min upstream.   Then   => x/(v-u) = 10 where v is man's speed and u is river speed)   Total time taken to swim by the man upstream and down stream is equal to the time taken by the   hat to travel 1000 yards with the speed of river :   => 1000/u = 10 + (x+1000) / (u+v)   => now substitute x = 10(v-u) and simplify   we will get,   => 100v = 2uv   => 2u = 100   => u = 50 yards per minute   Hence (A) is the correct answer.   50nswer : 50
Answer: A
The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire? Choose the correct answer.
A) 2:5 B) 2:7 C) 2:1 D) 2:3 E) 2:2

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2   => h1/h2 = 2/5   i.e. h1 : h2 = 2:5   2:5nswer:2:5
Answer: A
How many three letter words are formed using the letters of the word TIME?
Pick one.
A) 65 B) 62 C) 35 D) 24 E) 53

Solution: The number of letters in the given word is four.   The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2= 
4 * 3 * 2 = 24
24.   Answer:24
Answer: D
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?  Choose the correct choice from the following answers
A) 1.9
B) 1.5
C) 2.8
D) 3.0
E) 3.9

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer: 1.5
Answer: B
Excluding stoppages, the speed of the bus is 54 kms /hr and with stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?  Choose the correct choice from the following options
A) 9 B) 10 C) 11 D) 12 E) 20

Solution: By including stoppages, bus will cover 9km less..(54km -45km = 9km)   Excluding stoppages, x = 54 kmph   Including stoppages, y = 45 kmph   Difference, z = 9km   Time taken to cover that 9km(bus stops per hour(60minutes))= z/x(60minutes)   = 9/54(60)   = 1/6(60)   = 10minutes.   ANSWER:10
Answer: B
Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 70% of the previous term. What is the value range of the five numbers?	Choose the correct choice from the following options:
A) 7,599  B) 9,750  C) 9,975  D) 9,984  E) 10,736

Solution: 1st number= 10,000   2nd number = 70% of 10,000= 7000   3rd number= 70% of 7000= 4900   4th number = 70% of 4900= 3430   5th number= 70% of 3430= 2401   Range = 10,000-2401=7599   7,599 is the answer
Answer: A
There are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. If it was decided that the positions would be filled at random, then what is the probability W that the both positions will be taken by members of just one party?
Options:
A) 1/25
B) 12/49
C) 1/4
D) 24/49
E) 1/2

Solution: W probability of one party having both spots:   (1/2) * (24/49) = 12/49   (1/2) or (25/50) because it does not matter which party or which person gets the first spot. (24/49) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates.   Since this result can happen for both parties, (12/49) + (12/49) = (24/49)   Answer: 24/49
Answer: D
The average of seven results is 156 and that of the first six is 169. The fifth result is? Choose the most appropriate option:
A) 120	B) 160	C) 89	D) 78	E) 148

Solution: 7 * 156 â€“ 6 * 169 = 78   Answer: 78
Answer: D
A man complete a journey in 1010 hours. He travels first half of the journey at the rate of 2121 km/hr and second half at the rate of 2424 km/hr. Find the total journey in km.  Select
A) 121 km
B) 242 km
C) 224 km
D) 112 km
E) 110 km

Solution: Solution 1   Average Speed =2Ã—21Ã—2421+24=22.4 km/hr=2Ã—21Ã—2421+24=22.4 km/hr   Total distance =22.4Ã—10=224 km   ANSWER IS 224 km
Answer: C
Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 150 miles per hour and the train's average speed when traveling from point B to point C was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?
Select
A) 22.5
B) 21.43
C) 25.5
D) 26.5
E) 27.5

Solution: Average speed = distance/time   Because we are looking for average speed we can pick a distance for the variable d.   Speed A-21.43 = 150   Speed 21.43-C = 100   Average Speed = total distance/total rate   rate = distance/time   A====================21.43==========C   If A-21.43 is twice the length of 21.43-C then let A-21.43 = 2d and let 21.43-C = d   Average speed = 3d/(2d/150) + (d/100)   3d/(4d/300 + (3d/300)   3d/(7d/50)   150d/7d   Average speed = 21.43   ANSWER: 21.43
Answer: B
A father is now three times as old as his son. Six years back, he was four times as old as his son. The age of the son (in years) is
Select the correct option.
A) 12
B) 15
C) 18
D) 20
E) 25

Solution: If father's age is F and son's age is S, then   F=3S   and   F-6 = 4*(S-6)   3S-6 =4S-24   S=18   F=54 years   ANSWER:18
Answer: C
A fruit juice company earns $150 per 100 gallons of apple juice sold, $170 per 100 gallons of guava juice sold, $130 per 100 gallons of grape juice sold, $100 per 100 gallons of orange juice. If the company manages to sell 230 gallons of apple, 210 gallons of guava, 310 gallons of grape, 270 gallons of orange on a particular day. What is the average earning of the company per 100 gallon of the juice sold?
Choose the correct choice from the following answers
A) 134.8
B) 141.2
C) 147.2
D) 152.3
E) 160.1

Solution: Earning of the company from apple=150/100x230=345   Earning of the company from guava=170/100x210=357   Earning of the company from grape=130/100x310=403   Earning of the company from orange=100/100x270=270   Total earning of the company=345+357+403+270= 
345+357+403+270 = 1_375
1375   Total juice sold=1020   134.8verage earning per 100 gallon of juice sold=(1375/1020)x100   =$134.8   134.8nswer: 134.8
Answer: A
A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.
Choose one
A) 140
B) 260
C) 320
D) 480
E) 500

Solution: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 2*30/60⋅x km and 2*20/60⋅(x+2) km. From the equation: 2*30/60⋅x=2*20/60⋅(x+2) we get x=28 km/hr.   The intial speed of the biker is 28 km/h.   Half the distance between the two towns is   2h30min×28=2.5×28=70.   So the distance is 2×70=140 km
Answer: A
A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?  Choose the correct choice from the following.
A) 287	B) 279	C) 200	D) 278	E) 379

Solution: When the second train leaves Mumbai the first train covers 40 * 1= 
40 * 1 = 40
40 km   So, the distance between first train and second train is 40 km at 10.00am   Time taken by the trains to meet= Distance / relative speed = 40 / (50 -40)= 
40 / (50 -40) = 4
4 hours   So, the two trains meet at 2 p.m. The two trains meet 4 * 50= 
4 * 50 = 200
200 km away from Mumbai.   Answer:200
Answer: C
If P = 775 × 778 × 781, what is the remainder when P is divided by 14?  Options:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: P 775/14 leaves a remainder 5   778/14 leaves a remainder 8   781/14 leaves a remainder 11   5*8*11= 
5*8*11 = 440
440   So the remainder will be the remainder of 440/14 which is 6   6ns 6
Answer: A
The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 7 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
Choose the correct choice from the following answers.
A) 45	B) 65	C) 75	D) 79	E) 90

Solution: A + B + C = 3 *84= 
3 *84 = 252
252   A + B + C + D= 4 * 80= 
4 * 80 = 320
320 ---- (i)   So, D= 68& E = 68 + 7= 
68 + 7 = 75
75   B + C + D +E= 79 * 4= 
79 * 4 = 316
316 --- (ii)   From Eq. (i) & (ii)   A-E= 320 – 316 = 4   A = E +4 = 75 + 4= 
75 + 4 = 79
79   79
Answer: D
Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 1 hours, how many minutes did it take Cole to drive to work?	Select the correct option:
A) 35
B) 50
C) 62
D) 75
E) 78

Solution: First round distance travelled (say) = d   Speed = 75 k/h   Time taken, T2 = d/75 hr   Second round distance traveled = d (same distance)   Speed = 105 k/h   Time taken, T2 = d/105 hr   Total time taken = 1 hrs   Therefore , 1 = d/75 + d/105   LCM of 75 and 105 = 525   1= d/75 + d/105   => 1 = 7d/525 + 5d/525   => d = 525 / 12 Km   Therefore, T1= d/75   => T1 = 525 / (12 x 75)   => T1 = (7 x 60) / 12 -- in minutes   => T1 = 35 minutes.   35
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 24 sec, then the speed of each train is?  Select the correct option.
A) 78  B) 89  C) 36  D) 54  E) 23

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (360 + 360)/24 => x =15   Speed of each train = 15 m/sec.   = 15 * 18/5= 
15 * 18/5 = 54
54 km/hr.   Answer: Option 54
Answer: D
If Deepesh had walked 20 km/h faster he woulh have saved 1 hour in the distance of 60km. what is the usual speed of Deepesh? Pick:
A) 100  B) 299  C) 208  D) 273  E) 222

Solution: Explanation:   Let the original speed be x km/h, then   \inline \frac{600}{x}-\frac{600}{(X+20)}=1   \inline \Rightarrow 600\left ( \frac{x+20-x}{x(x+20)} \right )=1   \inline \Rightarrow \: \: x^{2}+120x-12000=0   \inline \Rightarrow \: \: (x-120)(x-100)=0   \inline \Rightarrow \: \: x=100 \: \: and\: \: x=120   \inline \therefore original speed = 100km/h   100nswer: 100
Answer: A
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points T is in the same quadrant as the fourth vertex of the square?  Choices:
A) (-5, -3)  B) (-5, 3)  C) (5, -3)  D) (3, -5)  E) (3, 5)

Solution: The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points T is in the same quadrant as the fourth vertex of the square?   I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means   Vertex #1 = (c, d) is in QII (that is, negative x and positive y)   Vertex #2 = (c, -d) is in QIII (that is, both xy negative)   Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)   That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =(3, 5).
Answer: E
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.740 in 2 years? Choices: A) 221 B) 287 C) 400 D) 288 E) 671

Solution: 671xplanation:   740 = P(21/20)2   P = 671   Answer:671
Answer: E