MU-NLPC/Calc-aqua_rat huggingface dataset:
The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 11 and 41 inclusive.  Options:
A) 351 B) 364 C) 416 D) 424 E) 450

Solution: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 11 to 41, inclusive. We're asked for the SUM of this group.   1) Start with the sum of the smallest and the biggest:   11 + 41= 
  11 + 41 = 52
52   2) Now look at the 'next smallest' and the 'next biggest': 13 + 39= 
13 + 39 = 52
52   Now we have proof that there is no middle term. We have 8 bunches of 52.   8(52)= 416   416
Answer: C
Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 12 km each. Then they turned left and ran for another 9 km.
What is the distance (in kilometers) between the the two twins when they stop? Options:
A) 26 B) 28 C) 30 D) 32 E) 34

Solution: The distance between them is the hypotenuse of a right angle triangle with sides 18 km and 24 km. The hypotenuse = sqrt(18^2 + 24^2) = 30   The answer is 30.
Answer: C
If 4a = 16b and 9b = 13c, Find a:b:c?	Choose the correct choice from the following:	A) 52:13:7	B) 13:7:52	C) 7:13:52	D) 7:13:54	E) None of these

Solution: Explanation:   (4a = 16b ==> a/b = 16/4)   and (9b = 13c ==> b/c = 13/7)   ==> a:b = 16:4 and b:c = 13:7   a:b:c = 208:52:28 = 52:13:7   52:13:7nswer: Option 52:13:7
Answer: A
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets Q can be created from this process?  Choose the correct choice from the following options
A) 35	B) 105	C) 210	D) 420	E) 630

Solution: Q=7C4 * 3C2 = 105 Answer B.   7C4 ways to choose 4 numbers for 105ox 1   3C2 ways to choose 2 numbers for 105ox2   1 way for 105ox 3 .105
Answer: B
If a given number ,n, is an odd positive integer, which of the following must then be an even negative integer? Select:
A) -2n - 1
B) n^-2
C) n^2
D) -2n^2
E) 2n - 4n

Solution: Answer: 2n - 4n   A: -2n - 1 = negative odd   B: n^-2 = positive   C: n^2 = positive   D: -2n ^ 2 = positive even   2n - 4n: 2n - 4n = -2n = even and negative
Answer: E
Given two fair dice, what is the probability that the sum of their numbers is 4 if exactly one die shows a 3? Choose one.
A) 2/11 B) 1/18 C) 3/11 D) 2/39 E) 1/5

Solution: P(2/11|B) = Probability of event 2/11 occurring such that event B has already occurred   = P(2/11 & B) / P(B)   Here, event 2/11 is getting a sum of 4   we'll have 3 possibilities : (1,3), (2,2), (3,1)   Event B => one of the 2 dices already shows a 3 [NOTE : there is NO restriction on the other dice => both dices C2/11N throw a 3]   we'll have 11 possibilities : (1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)   So, P(B) = 11/36   Event 2/11 & B occurring => 2 possibilities => (1,3) & (3,1)   So, P(2/11 & B) = 2/36   Therefore P(2/11|B) = 2/11   2/11NSWER:2/11
Answer: A
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.	Pick one.
A) 5:78  B) 5:11  C) 5:12  D) 5:19  E) 5:16

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128 = 5:16   Answer: 5:16
Answer: E
The age of Somu is one-third his father's. 6 years back he was one-fifth of his father's age. What is his persent age ?
Pick
A) 11  B) 13  C) 14  D) 12  E) 10

Solution: Explanation :   Let Somu's age be x and that of his father be 3x.   So, x - 6 = 3x - 6/5 = x = 12   Answer : Option 12
Answer: D
How many different subsets of the set {10, 14, 17, 26} are there that contain an odd number of elements?
Choices.
A) 3
B) 6
C) 18
D) 10
E) 8

Solution: Answer = 8 = 8   {10}   {14}   {17}   {26}   {10, 14, 17}   {14, 17, 26}   {10, 17, 26}   {10, 14, 26}
Answer: E
A man can row a boat at 20 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?  Choose one
A) 30/19  B) 30/17  C) 30/18  D) 30/13  E) 30/11

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 60 km downstream= d/s = 60/26 = 30/13 hours.   Answer: 30/13
Answer: D
What is the maximum number of pieces of birthday cake of size 10” by 10” that can be cut from a cake 20” by 20”?  Pick one:
A) 4
B) 10
C) 16
D) 20
E) 25

Solution: The prompt is essentially asking for the maximum number of 10 x 10 squares that can be cut from a larger 20 by 20square. Since each 'row' and each 'column' of the larger square can be sub-divided into 2 'pieces' each, we have (2)(2) = 4 total smaller squares (at maximum).   4
Answer: A
Three numbers are in the ratio 5 : 6 : 9. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
Options:
A) A)30 B) B)75 C) C)48 D) D)46 E) E)63

Solution: Let the numbers be 5x, 6x, 9x.   Largest number = 9x.   Smallest number = 5x.   Third number = 6x.   9x + 5x = 6x + 48   8x = 48 =>x=6   5x=30=> third number is 48.   30nswer:30
Answer: A
The average age 11 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? Choose the most appropriate option
A) 18	B) 22	C) 77	D) 26	E) 12

Solution: 11 * 2= 
11 * 2 = 22
22 years   Answer: 22
Answer: B
Which of the following are/is prime?
I. 143
II. 147
III. 145  Pick one
A) II only
B) III only
C) III
D) IIII
E) I, II,III

Solution: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice   which leaves us with 2 ) and 3) as possible answers   From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution IIII
Answer: D
A certain bakery has 6 employees. It pays annual salaries of $17,000 to each of 2 employees, $19,000 to 1 employee, and $20,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?	Choose one.
A) $18,200 B) $18,500 C) $18,800 D) $19,000 E) $19,400

Solution: average = 2(17000)+(19000)+3(20000) / 6 = $18,833   The answer is $18,800.
Answer: C
The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $150, by what percent is the price to be reduced?
Choose the correct choice:
A) 10%
B) 15%
C) 20%
D) 25%
E) 30%

Solution: price of a coat in a certain store = $500   the price of the coat is to be reduced by $150   % change = (Final Value - Initial Value)*100 / Initial Value   % Reduction= (Reduction in Price)*100 / Initial Value   i.e. % Reduction= (150)*100 / 500= 
(150)*100 / 500 = 30
30%   Answer: Option 30%
Answer: E
The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
Choose the correct choice from the following:
A) 3629
B) 3608
C) 3600
D) 3613
E) 6192

Solution: P = 144(100/5)2 => P   = 3600   Answer:3600
Answer: C
Pipe A can fill a tank in 10 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?  Choose the correct choice:
A) 18 B) 27 C) 98 D) 27 E) 48

Solution: Let the pipe B be closed after x minutes.   30/10 - x/24 = 1 => x/24 = 30/10 - 1= 
30/10 - 1 = 2
2=> x = 2 * 24= 
2 * 24 = 48
48.   Answer:48
Answer: E
The price of pulses has fallen by 18%. How many quintals can be bought for the same amount which was sufficient to buy 16 quintals at the higher price?  Choose the most appropriate option:	A) 20.5	B) 22.5	C) 19.5	D) 18.4	E) 32.5

Solution: 80% of original price can buy = 16 quintals.   Therefore, he can buy ( 16 x 100 )/ 82 = 19.5 quintals at the lower price.   ANSWER:19.5
Answer: C
What is the value of 4^5+4^6? Choose the most appropriate option
A) 5(4^5)	B) 4^35	C) 17(4^5)	D) 8^12	E) 7(4^5)

Solution: 4^5+4^6   =4^5(1+4^1)   =4^5 * 5   5(4^5)nswer 5(4^5)
Answer: A
If A =x% of y and B =y% of x, then which of the following is true?
Select the correct option:
A) None of these	B) A is smaller than B	C) Relationship between A and B cannot be determined	D) If x is smaller than y, then A is greater than B	E) A is greater than B

Solution: Explanation:   None of these =x/100×y=xy/100 ⋯(1)   B = y/100×x=yx/100 ⋯(2)   Therefore None of these = B   None of theseNSWER IS None of these
Answer: A
Tim bought a new machine to help him picking apples from apple trees. If this new machine can pick 20 apples every 30 minutes and Tim wants to pick 500 apples today. How many hours he is going to take?	Select.
A) 10
B) 12.5
C) 15
D) 17.5
E) 20

Solution: The machine picks 20 apples every 30 minutes = 40 apples/hour. 500 apples is going to take 500/40 apples/hour = 12.5 hours. Correct Option: 12.5. Answer: 12.5
Answer: B
If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 23, 30, 22, 26, 19, 33 and 35 ?
Choose the correct choice from the following choices
A) 33	B) 28	C) 22.5	D) 24	E) 23

Solution: It is given that a quartile is the middle number of all numbers less than median..   so lets arrange the number in ascending order- 42, 23, 30, 22, 26, 19, 33 and 35   19, 22, 23, 26, 30 , 33, 35, 42...   numbers less than median are 19, 22, 23, 26 ..   the median of these numbers = center of 22 and 23 = 22.5   22.5
Answer: C
In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 30 percent, but profits were 20 percent of revenues. The profits in 1999 were what percent of the profits in 1998?	Pick one:
A) 80%
B) 105%
C) 140%
D) 124.2%
E) 138%

Solution: 0,14R = x/100*0.1R   Answer 140%
Answer: C
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 5 km/hr. find the time taken by the boat to go 68 km downstream?  Choose the correct choice from the following
A) 2 hours  B) 3 hours  C) 3 hours 48 minutes  D) 5 hours  E) None

Solution: Solution   Speed Downstream	= (13 + 5) km/hr   = 18 km/hr.   Time taken to travel 68 km downstream	=(68 / 18)hrs   = 3 hrs 48 minutes.   Answer 3 hours 48 minutes
Answer: C
a school has 7 maths 6 physics and 5 chemistry teachers each teacher can teach 3 subjects max what is he minimum number of teachers required	Pick:  A) 3  B) 5  C) 6  D) 7  E) 8

Solution: Total subjects = 7+6+5= 
7+6+5 = 18
18   Max subjects by 1 teacher= 3   So, min of teachers required = 18/3= 
18/3 = 6
6   ANSWER:6
Answer: C
Two trains of length 120 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? Choose the correct choice from the following answers
A) 10 sec B) 22 sec C) 82 sec D) 20 sec E) 89 sec

Solution: Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 320= 
120 + 320 = 440
440 m.   The time required= d/s = 440 /20= 
440 /20 = 22
22 sec.   Answer:22 sec
Answer: B
A wholesaler wishes to sell 100 pounds of mixed nuts at $2.00 a pound. She mixes peanuts worth $1.50 a pound with cashews worth $4.00 a pound. How many pounds of cashews must she use?	Options.
A) 40 B) 45 C) 50 D) 55 E) 60

Solution: From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y   From the equation x + y = 100, we can rewrite y as y = 100 - x and substitute this into our equation to get:   $2.5 * (x + 100 - x) = $1.5x + $4(100 - x)   If you solve for x, you will get x = 60, and therefore y = 40. So the wholesaler must use 40 pounds of cashews.   You can substitute into the original equation to see that: $250 = $1.5(60) + $4(40)   Answer is 50.
Answer: C
A train crosses a platform of 170 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?	Choose the correct option
A) 70 B) 88 C) 167 D) 197 E) 161

Solution: Length of the train be ‘X’   X + 170/15 = X + 250/20   20X + 3400 = 15X + 3750   5x=350   X = 70m   70nswer: 70
Answer: A
When 4 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?
Choose the correct choice
A) 1	B) 4	C) 8	D) 31	E) 30

Solution: Total outcome is 2^4 = 16   Favourable cases = H_ _ H   The second and third places can be occupied by either H or T   There are 2^2 =4 ways that can be done.   Hence, the correct option is 4
Answer: B
A $79.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?	Choose the correct choice:
A) 15%
B) 20%
C) 25%
D) 60%
E) 80%

Solution: Listed selling price of chair = 79.95 $   Discounted selling price of chair = 59.95 $   Discount = 79.95 - 59.95= 
79.95 - 59.95 = 20
20 $   % decrease in price of chair= (20/79.95) * 100% = 25 % approx   Answer 25%
Answer: C
What is the diffference between the place value and face value of 3 in the numeral 1375?  Choose the correct choice from the following answers:
A) 259
B) 270
C) 297
D) 298
E) 300

Solution: place value of 3 = 3 * 100= 
3 * 100 = 300
300   face value of 3= 3   300 - 3= 
300 - 3 = 297
297   297
Answer: C
How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 40 percent alcohol? Choose the correct answer.
A) 7/2
B) 5
C) 100/3
D) 8
E) 39/4

Solution: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.   If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.   According to the statement;   20+x = 40% of (100+x)   OR   20+x=(100+x)2/5   100+5x=200+2x   3x=100   x=100/3   Ans:100/3
Answer: C
The average (arithmetic mean) of the integers from 200 to 800, inclusive, is how much greater than the average of the integers from 50 to 300, inclusive?	Choices: A) 450 B) 375 C) 400 D) 425 E) 300

Solution: For an AP the mean or average of series is average of first and last term.   So, average of numbers between 200 to 800, inclusive = (200+800)/2= 
(200+800)/2 = 500
500   average of numbers between 50 to 300, inclusive= (50+300)/2= 
(50+300)/2 = 175
175   difference= 500 - 175 = 425   Answer is 425
Answer: D
0.03 x 0.0172 is equal to: Choose the correct choice.
A) 6.48 x 10(power -4)  B) 6.84 x 10(power -4)  C) 5.16 x 10(power -4)  D) 5.48 x 10(power -4)  E) None of them

Solution: 3 x 172 = 516. Sum of decimal places = 6.   So, 0.03 x 0.0172 = 0.000516 = 5.16 x 10(power -4)   Answer is 5.16 x 10(power -4)
Answer: C
If a number is 80% more than the another, how much % is the smaller number less than the first ?
Choose the correct answer:
A) 12(1/3)%  B) 44(2/3)%  C) 46(1/3)%  D) 16(4/3)%  E) 44(4/9)%

Solution: Take a number 100,   Then the other number is 180   % the smaller number is less than the first = [80/(180)) x 100]% = 44(4/9)%.   ANSW44(4/9)%R:44(4/9)%
Answer: E
In what time a sum of money double itself at 3% per annum simple interest?  Choose the correct choice from the following options.
A) 33 1/8%	B) 33 1/3%	C) 83 1/3%	D) 33 4/3%	E) 73 1/3%

Solution: P = (P*3*R)/100   R = 33 1/3%   Answer:33 1/3%
Answer: B
Line A has the equation 3x + y = 7. Which of the following lines is perpendicular to Line A?  Choose the correct choice from the following answers:
A) y = 3x + 4  B) y = –3x – 6  C) y = (1/3)x – 1  D) y = (–1/3)x + 2  E) y = (–7/3)x – 5

Solution: What’s tricky about this problem: we have to begin by solving the given equation for y, so that we know its slope.   The slope of the original line is m = –3, and the negative reciprocal of that is +1/3, so the perpendicular line must have a slope of +1/3. Among the answer choices, the only line with a slope of +1/3 is (C).   Answer y = (1/3)x – 1
Answer: C
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Choose the correct choice from the following
A) 266 Sec B) 190 Sec C) 776 Sec D) 166 Sec E) 997 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (D)= 1900 m   T = D/S   T = 1900/10= 
1900/10 = 190
190 Sec   Answer: 190 Sec
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?	Answers:
A) 27 7/6 m B) 27 7/4 m C) 27 7/2 m D) 27 7/9 m E) 27 7/7 m

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.Answer:27 7/9 m
Answer: D
Last year a certain bond yielded 6 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $7,500, what is the bonds face value?
Choose the correct answer:
A) $5,000	B) $6,750	C) $7,425	D) $7,500	E) $9,375

Solution: Interest = 0.06*face value = 0.04*7,500 --> face value = 0.04*7,500/0.06 = 5,000.   $5,000nswer: $5,000.
Answer: A
Williams, a painter, has 9 jars of paint: 4 are orange, 2 are yellow, and the rest are brown. Williams will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no orange paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of orange paint 4) J2, if the paint contains exactly 1 jar of orange paint What is the probability that the new colour will be a shade of J (J1 or J2)?	Choose one:
A) 74/42
B) 37/84
C) 21/42
D) 37/42
E) 42/42

Solution: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2   For C1-3C2(Brown)*2C1(Yellow)=3*2= 
3*2 = 6
6   For C2-3C3(all brown)=1   Total=9C3=84   1-7/84=77/84= 37/42   Answer : 37/42
Answer: D
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:	Choices: A) 10 B) 12 C) 30 D) 40 E) 20

Solution: Dist = (100/45*9)= 
(100/45*9) = 20
20 m   ANSW20R 20
Answer: E
An escalator moves towards the top level at the rate of 12 ft.sec and its length is 210 feet. If a person walks on the moving escalator at the rate of 2 feet per second towards the top level, how much time does he take to cover the entire length.  Choose the correct choice from the following:
A) 15 sec B) 10 sec C) 12 sec D) 8 sec E) 9 sec

Solution: Time taken to cover the entire length = tot.dist/resultant speed   = 210/ (12+2)= 
210/ (12+2) = 15
15 sec   15 secNSWER:15 sec
Answer: A
3 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond? Select the correct option:
A) 2	B) 3	C) 4	D) 6	E) 9

Solution: it is like a circular arrangement.   total ways for n people to arrange in a circle is = factorial (n-1)   in this case n= 3   hence ans = 2 factorial = 2   hence 2
Answer: A
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 56?	Select the correct option.
A) s.3944
B) s.3948
C) s.3942
D) s.3808
E) s.3929

Solution: Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 56   = Rs.3808.   Answer: s.3808
Answer: D
For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 80, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.  Select:
A) K+35
B) (80+K)/2
C) 2K+35
D) (70-K)/2
E) 2(70-K)

Solution: Say Sue was hired when she was already 80 years old (k=80), then she could retire right away, at the age of 80. Now, plug k=80 in the answer choices and see which yields 80. Only C fits.   Answer: (80+K)/2.
Answer: B
A large delicatessen purchased p pounds of cheese for c dollars per pound. If W pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost) Choose the correct choice from the following options:  A) (p − d)(s − c)  B) s(p − d) − pc  C) s(p-W) - cp  D) d(s − c) − pc  E) pc − ds

Solution: Total cost price = c*p ............... (1)   Wastage = W pounds   Quantity sold = p-W   Selling price per pound = s   Total selling price = s(p-W) ........... (2)   Profit = (2) - (1)   = s(p-W) - cp   s(p-W) - cp
Answer: C
A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $800 or tripled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $60,000 in property taxes, but did not pay until October 15th?
Answers.
A) $1,400	B) $2,600	C) $3,400	D) $21,400	E) $22,800

Solution: Original amount = 60,000   Fine for July = 60,000 * 1% = 600   Fine for August = lesser of the 2 , 600+800= 1400 or  600*3= 
 600*3 = 1_800
1800 . Pick 1400   Fine for September= 1400+600= 
1400+600 = 2_000
2000 or  1400*3= 
 1400*3 = 4_200
4200. Pick 2000   Fine for October= 2000+600= 
2000+600 = 2_600
2600 or  2000*3= 
 2000*3 = 6_000
6000. Pick 2600.   The wording of the question should be have been clearer as total fines should be= 2600+2000+1400+600= 
2600+2000+1400+600 = 6_600
6600 and NOT 2600.   2600 is the fine ONLY for the month of October!   $2,600
Answer: B
A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together? Choose the correct choice from the following answers: A) 189/13 days B) 188/13 days C) 180/13 days D) 180/17 days E) 280/13 days

Solution: One day work of A and B = 1/12   One day work of B and C = 1/30   One day work of C and A = 1/36   2(A + B + C) = 1/12 + 1/30 + 1/36   2(A + B + C) = 13/90   (A + B + C) = 13/180   Number of days required = 180/13 days.   Answer:180/13 days
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is? Choose the correct answer
A) 11	B) 27	C) 36	D) 99	E) 27

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer: 36
Answer: C
If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 (512)  Choose the correct choice from the following options
A) 3.876
B) 2.967
C) 2.87
D) 3.912
E) 1.9

Solution: log5 (512)   =	log (512)/log 5   =	log 2^9/log (10/2)   =	9 log 2/(log 10 - log 2)   =	(9 x 0.3010)/(1 - 0.3010)   =	2.709/0.699   =	2709/699   = 3.876   3.876nswer is 3.876.
Answer: A