MU-NLPC/Calc-aqua_rat huggingface dataset:
Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 100 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York? Choose the correct choice from the following answers
A) 1 hour
B) 1 hour 10 minutes
C) 2 hours 30 minutes
D) 1 hour 40 minutes
E) 2 hours 40 minutes

Solution: Both cars leave at the same time   Both cars travel at constant speed   Stealing a useful piece of information from Paragkan:   If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds   ratio of speed: (a/b) = sq. rt(b/a)   sq. rt(b/a)   sq. rt(90/100)   sq. rt(3/2)   So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.   90*(2/3)where 2/3 represents the lesser amount of time it took A to travel the distance B did in 90 minutes.   = 60 minutes.   Therefore, A took 100 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (100+60)= 
(100+60) = 160
160 minutes on the road.   E. 2 hours 40 minutes
Answer: E
In a kilometer race, A beats B by 48 meters or 12 seconds. What time does A take to complete the race?
Choose the correct choice
A) 238 sec  B) 190 sec  C) 667 sec  D) 167 sec  E) 176 sec

Solution: Time taken by B run 1000 meters = (1000 * 12)/48= 
(1000 * 12)/48 = 250
250 sec.   Time taken by 238 sec= 250 - 12= 
250 - 12 = 238
238 sec.238 secnswer: 238 sec
Answer: A
In how many ways Principal and a vice Principle can be elected from a team of 20 members? Choose the most appropriate option:
A) 480	B) 380 ways	C) 830	D) 840	E) 540

Solution: To do this, if captain is elected first, then we have 20 ways of doing this.   For election of vice-captain, we have only 19 ways left, Bcoz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 20*19= 
20*19 = 380
380ways.   Ans : 380 ways
Answer: B
Set A of 8 positive integers may have the same element and have 36. And set B of 8 positive integers must have different elements and have 36. When m and n are the greatest possible differences between 36 and other elements’ sums in set A and set B, respectively, m-n=?	Choose the correct choice from the following answers:
A) 20
B) 21
C) 23
D) 25
E) 26

Solution: This is maximum-minimum. Hence, 36-(1+1+1+1+1+1+1)=29 and   36-(1+2+3+4+5+6+7)= 
  36-(1+2+3+4+5+6+7) = 8
8. So, 29-8=21. The correct answer is 21.
Answer: B
John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Z of dollars he could have spent for the $12 tickets?  Choose one:
A) $48
B) $60
C) $84
D) $96
E) $120

Solution: 60 ..... 12 *5 Z= 60. (min). Thus answer .$60
Answer: B
Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?	Answers.
A) 234	B) 254	C) 265	D) 340	E) 512

Solution: Let suppose total number of students in class are X.   Then from the question we can conclude it that,   X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512   512
Answer: E
Find the largest 4 digit number which isexactly divisible by 88?	Choose the correct choice from the following answers:
A) 8560  B) 8950  C) 9944  D) 10000  E) 10200

Solution: Largest 4 digit number is 9999   After doing 9999 ÷ 88 we get remainder 55   Hence largest 4 digit number exactly divisible by 88 = 9999 - 55= 
9999 - 55 = 9_944
9944   9944
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?	Choose one:
A) 23/35 B) 23/37 C) 23/39 D) 23/32 E) 23/31

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green   = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7   = 46/70 = 23/35   23/35nswer: 23/35
Answer: A
By selling a watch for Rs. 720/- a man loses 20% at what price should he sell it to gain 10%?	Choose the most appropriate option: A) Rs.810/- B) Rs.880/- C) Rs.900/- D) Rs.990/- E) None of these

Solution: Explanation:   80 % ------> 720 (80 * 9 = 720)   110 % ------> 880 (110 * 9 = 990)   = Rs.990/-   Answer: Option Rs.990/-
Answer: D
7, 10, 8, 11, 9, 12, ?  Choose the correct option.
A) 13  B) 12  C) 10  D) 9  E) 8

Solution: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.   Answer : 10.
Answer: C
An unbiased die is tossed.Find the probability of getting a multiple of 3.
Choose the correct choice:
A) 1
B) 4/3
C) 1/3
D) 2/3
E) 1/2

Solution: S = {1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   Then, E = {3,6}   P(E) = n(E)/n(S) = 2/6 = 1/3   ANSWER:1/3
Answer: C
To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables w are there in the warehouse?  Choose the correct answer.
A) 6
B) 8
C) 10
D) 15
E) 30

Solution: Total number of ways to choose 2 chairs from 5 w= 5C2=10   Total number of combination=150   That means we need get 15 combinations from the selection of tables....   Screening through the answers.... 6C2=15..... 15*10=150   Answer is 6... 6
Answer: A
Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?  Choose the correct choice from the following options.
A) 5 minutes	B) 10 minutes	C) 9 minutes	D) 7 minutes	E) 8 minutes

Solution: Part filled by pipe A in 1 minute =1/12   Part filled by pipe B in 1 minute =1/24   Part filled by pipe A and pipe B in 1 minute=1/12+1/24=1/8   both the pipe together can fill the tank in 8 minutes   Answer is 8 minutes
Answer: E
The present worth of Rs.845 due in 2 years at 4% per annum compound interest is  Choose the correct choice from the following choices:
A) Rs.150.50	B) Rs.154.75	C) Rs.781.25	D) Rs.158	E) None

Solution: Solution   Present Worth	= Rs.[845/(1+4/100)²]   = Rs.(845x25/26x25/26)   = Rs.781.25   Answer Rs.781.25
Answer: C
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?  Choose the correct choice from the following answers.
A) 0
B) 1
C) 10
D) 19
E) 8

Solution: Average of 20 numbers = 0.   Sum of 20 numbers (0 x 20) = 0.   It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).   Answer : 19
Answer: D
Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at thrice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments? Answers
A) 1 hr 20 min
B) 1 hr 7 min
C) 2 hr
D) 2 hr 20 min
E) 3 hr

Solution: Sol:   Lets Perry Rate be P and Rate of Maria be M   (rate)*(time)= Work or rate = work/time   first equation=> P+M = 1/45   converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3   second equation => M+3M =>1/20   converting it to hrs 4M=1/(20/60) =>1/(1/3)= 
1/(1/3) = 3
>3   therefore M= 3/4 and P=7/12   Rate of Perry = 7/12   time= work/rate (work = 1 job)   Time= 1 hrs 7 mins   Answer : 1 hr 7 min
Answer: B
A fair gold coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?  Choose the correct choice from the following options:
A) A)37/256  B) B)56/256  C) C)65/256  D) D)70/256  E) E)81/256

Solution: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.   8!/6!2! = 7*4= 
7*4 = 28
28   8!/7!1!= 8   8!/8! = 1   28 + 8 + 1 8 /8= 
8 /8 = 1
1   28 + 8 + 1= 
28 + 8 + 1 = 37
37/256   ans:37/256
Answer: A
Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?  Choose the correct answer:
A) 90  B) 180  C) 360  D) 540  E) 720

Solution: # ways to distribute Blue marbles(3) is :   1 in each cup= 1   2 in one cup and 1 in other=6   all 3 in one cup = 3   total 1+6+3= 
1+6+3 = 10
10 possibilities   # ways to distribute Red marbles(2) is :   1 in each cup= 3 ways   all in one cup = 3ways   total 6ways.   # ways to distribute Green marbles(1) is :   3 ways   total number of ways = 10*6 *3= 
10*6 *3 = 180
180 ANS:180
Answer: B
A train running at the speed of 52 km/hr crosses a pole in 18 seconds. What is the length of the train?	Pick one:
A) 120 metres B) 180 metres C) 260 metres D) 150 metres E) 100 meters

Solution: Speed=52 x5/18m/sec=130/9	m/sec.   Length of the train = (Speed x Time).   Length of the train =	130/9 x 18m = 260 m.   ANSWER:260 metres
Answer: C
When a train travels at a speed of 60kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
Choices:  A) 75km  B) 50km  C) 60km  D) 85km  E) 95km

Solution: Let x be the time reached with the speed 60km/h   50km/h ----> x+15   Distance is equal so   60(km/h)× xhr = 50(km/h) × (x+15) hr   So   60 x = 50x + 750   So the would be in km   75kmnd x = 75   So   75km   75kmNSWER:75km
Answer: A
A jogger running at 9 kmph along side a railway track is 250 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?  Pick one
A) 3.6 sec
B) 37 sec
C) 36 sec
D) 72 sec
E) None of these

Solution: Speed of train relative to jogger   = (45 – 9) km/h = 36 km/h   = (36 × 5⁄18) m/sec = 10 m/sec   Distance to be covered = (250 + 120)= 
(250 + 120) = 370
370 m.   ∴ Time taken= (370⁄10) sec = 37 sec.   Answer 37 sec
Answer: B
What is the next number of the following sequence
7776,625,64,9,2	Answers:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 7776,625,64,9,2, x   7796 --> 6^5   625 --> 5^4   64 --> 4^3   9 --> 3^2   2 --> 2^1   x --> 1^0 ==> 1   1NSWER:1
Answer: A
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 35 minutes, then the slower pipe alone will be able to fill the tank in
Choices:
A) 144 mins
B) 140 mins
C) 136 mins
D) 132 minw
E) None of these

Solution: Explanation:   Let the slower pipe alone fill the tank in x minutes   then faster will fill in x/3 minutes.   Part filled by slower pipe in 1 minute = 1/x   Part filled by faster pipe in 1 minute = 3/x   Part filled by both in 1 minute =   1/x+3/x=1/35   =>4/x=1/35   x=35∗4=140 mins   Option 140 mins
Answer: B
In a division sum,the divisor is 10 times the quotient and 5 times the remainder.If the remainder is 46,what is the dividend ?	Choose the correct choice from the following choices
A) 5336 B) 5242 C) 6524 D) 3526 E) 4526

Solution: Divisor=(5*46)= 
(5*46) = 230
230   10*quotient=230   quotient =230/10= 
230/10 = 23
23.   dividend=(divisor*quotient)+remainder   =(230*23)+46=(5290+46)= 
(5290+46) = 5_336
5336.   5336nswer is 5336
Answer: A
If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 30 overs in an ideal case scenario? Choose the most appropriate option.
A) 1020  B) 993  C) 985  D) 996  E) None

Solution: Solution:   993   Explanation:   For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:    6 * 5 + 3= 
 6 * 5 + 3 = 33
33   But this will have to go like it only till the 29th over. In the 30th over, he can hit a six in the last ball as well as that will be the last ball of his destination.   Thus runs for the 30th over will be  6 * 6= 
 6 * 6 = 36
36.   Hence the maximum runs= 33 * 29 + 36= 
33 * 29 + 36 = 993
993   Answer 993
Answer: B
3.5 can be expressed in terms of percentage as?
Choose the correct option
A) 0.35%  B) 3.5%  C) 35%  D) 350%  E) 0.0035%

Solution: Answer: Option 350%   3.5 = 35/10 = (35/10 * 100)= 
(35/10 * 100) = 350
350%
Answer: D
If X = Z*Y/Y, -10 < Z < 0 and 5 < Y, which of the following is correct?	Answers.
A) X > 9.
B) 0 < X <9.
C) -9 < X < 0
D) X < -10.
E) X>-10

Solution: Y is +ve & Z is -ve   Eliminate A & B   For min. value max. numerator and minimize denominator   take Y=5.1 & Z=-9.9   X=(-9.9*5.1)/5.1   X=-50.49/5.1   X>-10   Ans X>-10
Answer: E
Dacid obtained 70, 63, 80, 63 and 65 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?	Choose the most appropriate option.
A) 67
B) 26
C) 87
D) 26
E) 68

Solution: Average   = (70+ 63+ 80+ 63+ 65)/5   = 341/5 = 68.2.   Answer: 68
Answer: E
What is the median from the below series
101, 105, 103, 109, 107, 110, 115, 113, and 114 Answers:	A) 105	B) 107	C) 101	D) 113	E) 109

Solution: Ordering the data from least to greatest, we get:   101, 103, 105, 107, 109, 110, 113, 114, 115   The median number was 109. (Four numbers were higher than 109 and four were lower.)   109
Answer: E
In what time a debt of Rs.7920 due may be cleared by immediate cash down
payment of Rs.3600 at 1/2% per month Answers
A) 10years B) 20years C) 30years D) 40years E) 50years

Solution: Explanation:   PW=100x Amount/100+(RxT)   Answer: 20years
Answer: B
Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 5 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 7 percent grade, what is x in terms of y and z?
Choose the correct choice from the following options
A) -1y - 2z B) (y +z) / 4 C) 2y + 3z D) 3y + z E) 3y + 4.5z

Solution: Based on the given information, the following equation could be dervied: 1% * x + 5% * y + 3% * z = 7% * (x+y+z)   Then use algebra to figure out 6%*x = -2%*y - 4%*z. Thus, 3x = -1y - 2z.   -1y - 2z
Answer: A
A tank is filled by 3 pipes A,B,C in 6 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?	Choose the correct choice from the following.
A) 25hr  B) 42hr  C) 40hr  D) 20hr  E) 50hr

Solution: Suppose pipe A alone take x hours to fill the tank   Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.   1/x + 2/x + 4/x = 1/6   7/x = 1/6   x = 42 hours   Answer is 42hr
Answer: B
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train?	Pick one
A) 270  B) 277  C) 200  D) 257  E) 271

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 20 * 10= 
20 * 10 = 200
200 m.   The length of the faster train= 200 m.   Answer: 200
Answer: C
If you roll one fair six-sided die, what is the probability that the number is even or less than 5? Choose the correct choice from the following answers.
A) 3/4
B) 5/6
C) 1/2
D) 2/3
E) 1/6

Solution: The numbers which satisfy the conditions are 1, 2, 3, 4, and 6.   The probability is 5/6   The answer is 5/6.
Answer: B
A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?	Choose the correct option.
A) 160  B) 170  C) 180  D) 200  E) 220

Solution: 25 + 25= 
25 + 25 = 50
50   25% ------ 50   100% ----- ?=> 200   ANSWER:200
Answer: D
The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?  Pick one:
A) 26	B) 28	C) 23	D) 28	E) 21

Solution: Let the initial number of members in the group be n.   Initial total weight of all the members in the group = n(48)   From the data,   48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23   Therefore there were 23 members in the group initially.Answer: 23
Answer: C
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?  Choose the correct choice from the following answers
A) 24 years B) 28 years C) 27 years D) 16 years E) 09 years

Solution: Let the present ages of Sameer and Anand be 5x and 4x years respectively.   Then, (5x + 3)/(4x + 3) = 11/9   9(5x + 3) = 11(4x + 3) => x = 6   Anand's present age = 4x = 24 years.   24 yearsnswer:24 years
Answer: A
The ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?  Choose the correct choice from the following choices:
A) 3/6	B) 3/2	C) 3/9	D) 3/1	E) 3/5

Solution: Let the earnings of P and Q be Rs. 9x and Rs. 10x respectively.   New ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]   => [9x(1 + 1/4)]/[10x(1 - 1/4)] = 9/10 * (5/4)/(3/4)   => 3/2.   Answer: 3/2
Answer: B
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 210 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?	Select the correct option:
A) 88 B) 45 C) 36 D) 80 E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 210= 
240 + 210 = 450
450 m.   Time taken= 450/10= 
450/10 = 45
45 sec.   Answer: 45
Answer: B
Given that 100.48 = x, 100.70 = y and xz = y², then the value of z is close to  Choose the correct option:
A) 1.2
B) 1.45
C) 2.2
D) 2.9
E) NOne

Solution: Sol.   xz = y² ⇔ (10 0.48 )z(100.70)2 (10 0.48z) = 10(2×0.70) = 101.40   ⇔ 0.48z = 1.40 ⇔ z= 140/48 = 35/12 = 2.9 (approx).   Answer 2.9
Answer: D
The probability that A speaks truth is 1/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?  Options.
A) 13/35
B) 18/38
C) 18/36
D) 18/16
E) 18/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability   = 1/5 * 4/7 + 4/5 * 3/7   = 1/35 + 12/35   = 13/35   13/35nswer: 13/35
Answer: A
A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 50 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?  Select.
A) 7 B) 5 C) 12 D) 13 E) 15

Solution: Rate of H = 5 acres/hr   Remaining land to be harvested = 100 - 50= 
100 - 50 = 50
50   Rate of H and K= 50/5= 
50/5 = 10
10 acres/hr   Rate of K= 10 - 5= 
10 - 5 = 5
5   Answer: 5
Answer: B
The average of ten numbers is 8. If each number is multiplied by 8, then what is the average of the new set of numbers?  Pick one:
A) 8
B) 16
C) 64
D) 80
E) 88

Solution: The sum of the ten numbers is 8*10= 
8*10 = 80
80   If each number is multiplied by 8, the new sum is 8*(80).   The average is then   8*8= 
  8*8 = 64
64   The answer is 64.
Answer: C
If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even?  Pick one:
A) 2/3	B) 1/3	C) 1/2	D) 1/6	E) 5/6

Solution: The product to be even either one or both must be even, so:   P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;   Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.   2/3nswer: 2/3.
Answer: A
Find the solution set of the equation x2+x+2=0 in roster form	Choose the correct answer:
A) {1,-2}	B) { }	C) {1,1}	D) {1}	E) none

Solution: (x+2)(x-1)=0   x=-2 or 1   {1,-2}NSWER:{1,-2}
Answer: A
If an integer n is to be selected at random from 1 to 99, inclusive, what is probability n(n+1) will be divisible by 3?  Choose the correct choice from the following:
A) 1/4  B) 1/3  C) 1/2  D) 2/3  E) 3/4

Solution: For n(n+1) to be a multiple of 3, either n or n+1 has to be a multiple of 3.   Thus n must be of the form 3k or 3k-1, but not 3k+1.   The probability is 2/3.   The answer is 2/3.
Answer: D
Find the compound interest on $ 56,000 at 20% per annum for 9 months, compounded quarterly  Choices:
A) 2532  B) 2552  C) 6524  D) 8827  E) 9512

Solution: Principal = $ 56000; Time = 9 months =3 quarters;   Rate = 20% per annum = 5% per quarter.   Amount = $ [56000 x (1+(5/100))^3] = $ 64827.   CI. = $ (64827 - 56000)= 
(64827 - 56000) = 8_827
$ 8827.   Answer 8827.
Answer: D
A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/h and 6km/h and passes them completely in 36 seconds and 30 seconds respectively. The length of the train is:	Choose the correct choice from the following answers:
A) 120m  B) 150m  C) 125m  D) None of these  E) Cannot be determined

Solution: Explanation:   Let the length of the train e x meter, and let the speed of train be y km/h, then   x = (y + 3)5/18 × 36 .........(1)   and x = (y + 6)5/18 × 30 .....(2)   From eq (1) and (2), we get   (y + 3) × 36 = (y + 6) × 30   y = 12 km/h   x = (y + 3) × 5/18 × 36   x = 150 m   Answer: 150m
Answer: B
A set of data consists of the following 8 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
Choose the correct answer:  A) -1 and 9  B) 4 and 4  C) 3 and 5  D) 2 and 6  E) 0 and 8

Solution: If you are in for some calculations , this is how I got to it   mean = 4   sd = \sqrt{8} = 2.8   Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8)= 
(4 - 2.8) = 1.2
1.2 , and one value above SD is (4 + 2.8)= 
(4 + 2.8) = 6.8
6.8   This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.   Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.   1. -1 , 9   distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2   2. 4 , 4   distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8   3. 3 , 5   Distance is - 1.8 and 1.8   4. 2 , 6   Distance is - 0.8 and 0.8   5. 0 , 8   Distnace is - 1.2 and 1.2   Hence from above , we see that adding 4 and 4 , results in a value that would change the SD to the least. Hence 4 and 4
Answer: B