MU-NLPC/Calc-aqua_rat huggingface dataset:
The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ? Choose the most appropriate option.
A) 20  B) 24  C) 28  D) 32  E) 24

Solution: This is an A.P. in which a = 6, d = 6 and Sn = 1800   Then, n [2a + (n - 1)d] = 1800   2   n [2 x 6 + (n - 1) x 6] = 1800   2   3n (n + 1) = 1800   n(n + 1) = 600   n2 + n - 600 = 0   n2 + 25n - 24n - 600 = 0   n(n + 25) - 24(n + 25) = 0   (n + 25)(n - 24) = 0   n = 24   Number of terms = 24.   24)
Answer: B
what is the 49 th word if the letters of the word ABUSER is arranged in alphabetical order	Choose the correct choice: A) ARBESV B) ARBESW C) ARBESU D) ARBESS E) ARBESE

Solution: Firstly arrange it in alphabatical order i.e   ABERSU   Take first two letter as a constant i.e ABersu   (remaining ersu can be arranged in 4! ways)   the next letter according to dictionary is AEbrsu take first two letter as a constant i.e AEbrsu(remaining brsu can be arranged in 4! ways)   when AB constant no of words will formed = 24   when AE constant no of words will formed = 24   so far we had completed 48 words the   49 word is ARBESU   ANSWER:ARBESU
Answer: C
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:  Pick:	A) 228gallons	B) 267gallons	C) 120gallons	D) 767gallons	E) 167gallons

Solution: Explanation:   Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying]   Volume of {\color{Black} \frac{1}{40}} part = 3 gallons   Volume of whole = (3 x 40) gallons = 120 gallons.   Answer: 120gallons
Answer: C
A salt manufacturing company produced a total of 1000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?  Choose the correct choice from the following answers:
A) 51
B) 53
C) 55
D) 56
E) 57

Solution: Total production of salt by the company in that year = 1000 + 1100 + 1200 + .... + 2100 = 18600.   51verage monthly production of salt for that year = 18600/365 â‰ˆ 51   51NSWER:51
Answer: A
By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error R that the carpenter can make in calculating the volume of the rectangular box?
Options
A) 1%	B) 3%	C) 10%	D) 18%	E) 22%

Solution: the dimensions are between 2-2.1, 1-1.1 and 2-2.1..   so MAX error in Volume=?..   IMPORTANT POINTS TO NOTE   1) Max ERROR would be when actuals and estimate are at the extreme ends..   2) BUT what about MAX % ERROR--   It will be when the base is the lowest...   so the ACTUALS should be lowest or at lower end and the ESTIMATE at the higher end..   SOLUTION   Actuals= 2*2*1=4..   Estimate=2.1*2.1*1.1=4.841..   Max % error R=(4.841-4)/4 *100= 84.1/4 = 21.25%..   21.25% is closest to 22% in the choices..   ans 22%
Answer: E
A theater box office sold an average (arithmetic mean) of 64 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 76, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?	Choose the correct choice.
A) 2:5	B) 1:4	C) 1:3	D) 15:19	E) 64:76

Solution: Deviation from the mean for the daytime staff = 76 - 64= 
76 - 64 = 12
12.   Deviation from the mean for the evening staff= 64 - 60= 
64 - 60 = 4
4.   Thus, the ratio of the number of daytime staff members to the number of evening staff members is 4:12= 1:3.   The answer is 1:3.
Answer: C
The speed of a car is 80 km in the first hour and 40 km in the second hour. What is the average speed of the car?	Choose the correct choice from the following choices: A) 72 kmph B) 60 kmph C) 30 kmph D) 80 kmph E) 82 kmph

Solution: S = (80 + 40)/2= 
(80 + 40)/2 = 60
60 kmph   ANSWER:60 kmph
Answer: B
According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 25, by how much does the temperature in degrees Celsius (C) increase?  Pick:
A) 9 B) 13.88 C) 47 D) 48 3/5 E) 59

Solution: You can plug in values.   C = 5/9*(F-32)   F=32 --> C=0;   F=32+25= 
32+25 = 57
57 --> C=5/9*25=13.88.   Increase = 13.88 degrees.   Answer: 13.88.
Answer: B
Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many Q women are currently in the room?	Choose the correct choice from the following choices:	A) 12	B) 14	C) 15	D) 24	E) 36

Solution: the number of women doubled means that they have become 24 from 12..   and we have to tell the current strength so 24 is the answer..   let the number be 4x and 5x..   given 4x+2=14.. so x=3..   women number Q =5*3-3= 
5*3-3 = 12
12, then doubled=24..   ans 24
Answer: D
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.19200. A's share is?	Choose the correct answer:
A) 8876  B) 2765  C) 6400  D) 1298  E) 1261

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 19200= 
1/3 * 19200 = 6_400
6400   Answer:6400
Answer: C
Nine persons went to a hotel for taking their meals. Eight of them spent 12 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?	Choose the correct option
A) 115 B) 117 C) 119 D) 122 E) None of the above

Solution: Let the average expenditure of all the nine be x.   Then, 12 × 8 + (x + 8) = 9x or 8x = 104 or x = 13.   ∴ Total money spent = 9x = (9 × 13) = 117.   Answer 117
Answer: B
If John takes 11 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?  Choose the correct choice from the following choices: A) 660x/z B) 11x/z C) 660xz D) 660z/x E) 11z/x

Solution: It will take (z/x)(11) minutes which is (z/x)(11)(60) seconds = 660z/x seconds.   The answer is 660z/x.
Answer: D
In a hostel there were 100 students. To accommodate 25 more students the average is decreased by rupees 10. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now?
Select
A) 7500  B) 5000  C) 5400  D) 7000  E) 8500

Solution: Let average is x   100x + 500 = 125(x – 10)   x = 70   100 * 70 + 500= 
100 * 70 + 500 = 7_500
7500   7500nswer:7500
Answer: A
Jim needs $1,000 to buy a new flat-screen TV. Since he has only $7, he borrows the remaining balance from his sister Mary. The loan will be repaid in 3 annual installments at an interest rate of 10%, compounded annually. The formula for calculating the monthly payment P is P = (L x C x r) / (C – 1) where L = amount of the loan, r = annual interest rate, and C = compounding factor = (1 + r)^N where N = number of annual payments. How much does Jim have to pay Mary at the end of each of the next 3 years (rounded to the nearest penny)?	Pick: A) $357.67 B) $375.85 C) $387.40 D) $399.30 E) $433.33

Solution: L = 993   r = 0.1   C = 1.1^3 = 1.331   Insert all of these in the formula and we get   P = 993*1.331*0.1/0.331   In order to resolve above without a calc, we need to find the approx value of 0.1331/0.331 ~ 0.4~   ~ 993*0.4   ~ 397   Answer $399.30
Answer: D
The difference between the place value and the face value of 7 in the numeral 856973 is  Choose the correct choice from the following: A) 63 B) 6973 C) 5994 D) 6084 E) None of these

Solution: (Place value of 7) - (Face value of 7) = (70 - 7)= 
(70 - 7) = 63
63   63nswer: Option 63
Answer: A
Sara is an avid lottery player. In the certain game she plays, she must pick one number between 30 and 39, inclusive, one number between 40 and 49, inclusive, and one number between 50 and 59, inclusive. She believes that she will have the best chance of winning if her three numbers, as a set, have the greatest number of distinct prime factors possible. According to Sara’s theory, which of the following sets of three numbers should she use?	Choose the correct option.
A) 32−48−52 B) 33−42−56 C) 39−40−54 D) 38−49−51 E) 36−42−56

Solution: A: 32 (2 as the only PF), 48 (2 and 3 as PF), 52 ( 2 and 13 and PF) - Distinct Prime Factors as a set = 3 (2, 3, and 13).   B: 33 (11 and 3 as PF), 42 (2,3, and 7 as PF), 56 (2 and 7 as PF) - Distinct Prime Factors as a set = 4 (11, 3, 2, and 7).   C: 39 (3 and 13 as PF), 40 (2 and 5 as PF) and 54 (3 and 2 as PF) - Distinct Prime Factors as a set = 4 (3, 13, 2, and 5)   D: 38 (2 and 19 as PF), 49 (7 only) and 51 (17 and 3 as PF) - Distinct Prime Factors as a set = 5 (2, 19, 7, 3, and 17).   E: 36 (2 and 3 as PF), 42 (2, 3, and 7) and 56 ( 2 and 7 as PF) - 38−49−51istinct Prime Factors as a set = 3 (2, 3, 7)   Answer 38−49−51.
Answer: D
Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?  Choose the correct choice from the following answers
A) 50 m  B) 60 m  C) 80 m  D) 82 m  E) 84 m

Solution: Let breadth = x metres.   Then, length = (x + 20) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 20) + x] = 200   2x + 20 = 100   2x = 80   x = 40.   Hence, length = x + 20 = 60 m   60 m
Answer: B
The measures of the 2 acute angles of a triangle are in the ratio of 3 : 7. What arethe measures of the 2 angles? Choose the correct choice from the following choices:  A) 20°  B) 70°  C) 110°  D) 63°  E) 140°

Solution: If the ratio of the two angles is 3:7, then the measures of two angles can be written as 3x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence   3x + 7x = 90   10x = 90   x = 9   Measures of the two acute angles are   3x = 3 × 9 = 27°   7x = 7 × 9 = 63°   63°
Answer: D
In how many years will a sum of money doubles itself at 10% per annum on simple interest?
Choose the correct choice from the following.
A) 70%
B) 20%
C) 10%
D) 28%
E) 20%

Solution: P = (P*10*R)/100   R = 10%   Answer:10%
Answer: C
If positive integer n is divisible by both 5 and 16, then n must be divisible by which of the following?
Choose the correct choice from the following answers.
A) 8 B) 12 C) 18 D) 24 E) 48

Solution: A number divisible by both 5,16 is 80 which s divisible by 8.   IMO : 8nswer 8 8
Answer: A
What is the difference between the place value and face value of 3 in the numeral 1375?  Choose the correct choice from the following options:
A) 297  B) 300  C) 310  D) 320  E) 322

Solution: place value of 3 = 3 * 100= 
3 * 100 = 300
300   face value of 3= 3   300 - 3= 
300 - 3 = 297
297   297
Answer: A
A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?  Choices.
A) 65 km/hr B) 17 km/hr C) 76 km/hr D) 49 km/hr E) 15 km/hr

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 4) km/hr.   x - 4 = 45 => x = 49 km/hr.   Answer: 49 km/hr
Answer: D
A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 40 miles on the highway?	Pick one
A) 28  B) 30  C) 33  D) 35  E) 38

Solution: 10*1/25 gpm+40*1/40 gpm=1.4 total gallons   50 total miles/1.4 total gallons=35.7 average mpg   D. 35
Answer: D
A number increased by 30% gives 780. The number is	Choose the correct choice from the following:  A) 250  B) 400  C) 450  D) 600  E) 520

Solution: Formula = TOTAL=100% ,INCRESE = "+" 600ECREASE= "-"   A number means = 100 %   That same number increased by 30 % = 130 %   130 % -------> 780 (130 × 6= 780)   100 % -------> 600 (100 × 6 =600)   600)
Answer: D
In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen? Choose the correct option:
A) 100 B) 40 C) 66 D) 80 E) 75

Solution: Two ways...   1) total ways = 10C3 = 10!/7!3! = 120..   ways without python developer = 6C3= 6!/3!3!=20..   ways of at least ONE python developer = 120-20 =100..   2) ways of selecting ONLY one = 4*6C2 = 4*15 = 60..   ways of selecting ONLY two = 4C2*6C1 = 6*6 = 36..   ways of selecting all three = 4C3 = 4 = 4..   Total = 60+36+4=100...   100NSWER:100
Answer: A
Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +1?	Choose the correct answer
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 --> only   In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. i.e 0,1,5 or 6   Intersection of values is 6, thus the units digit of p + 1 is 6 + 1 = 9.   7nswer: 7.
Answer: A
P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
Select.
A) 8/15 B) 9/15 C) 11/15 D) 13/17 E) 15

Solution: 8/15mount of work P can do in 1 day = 1/15   8/15mount of work Q can do in 1 day = 1/20   8/15mount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   8/15mount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15   8/15)   Fraction of work left = 1 – 7/15= 8/15
Answer: A
In a group of ducks and cows, the total number of legs are 40 more than twice the number of heads. Find the total number of cows.
Options
A) 12 B) 14 C) 16 D) 18 E) 20

Solution: Let the number of ducks be d   and number of cows be c   Then, total number of legs = 2d + 4c = 2(d + 2c)   total number of heads = c + d   Given that total number of legs are 40 more than twice the number of heads   => 2(d + 2c) = 40 + 2(c + d)   => d + 2c = 20 + c + d   => 2c = 20 + c   => c = 20   i.e., total number of cows = 20   Answer is 20.
Answer: E
A driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 20 km/hr. What was the average speed for the whole journey?	Choices
A) 24 km/h B) 26 km/h C) 28 km/h D) 30 km/h E) 32 km/h

Solution: time 1 = d / 60   time 2 = d / 20   total time = d/60 + d/20 = 4d/60 = d/15   average speed = total distance / total time = 2d / (d/15) = 30 km/h   The answer is 30 km/h.
Answer: D
x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) + (10x + z) could NOT equal  Choices
A) 55 B) 60 C) 95 D) 63 E) 110

Solution: 1) firstly we are not given that all are different integers..   2) since each is a positive single digit integer and x=a/4... a can take only 4 and 8 as value, and x can take 1 and 2..   3) same as 2) for b and z.   so in (10a + b) + (10x + z) ..   10a+b can be   44,48,84,88..   10x+z can be   11,12,21,22..   ans 63
Answer: D
If d is the standard deviation x, y, and z, what is the standard deviation of x +7, y + 7, z + 7 ?	Choose the correct option.
A) 7d B) 7d+7 C) 7d+14 D) d E) 7d+21

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}   When 7 is added in each term of set {x, y, z} then the new set {x+7, y+7, z+7} will remain same as the previous standard deviation i.e. d   Answer: d
Answer: D
Ram and Ramesh can do a work piece of work in 6 days. Ram alone can do it in 10 days. In how many days can Ramesh alone can do it?
Choose the correct choice from the following answers:
A) 11 days  B) 12 days  C) 15 days  D) 13 days  E) 10 days

Solution: Explanation:   Ram and Ramesh can do a work in 6 days.   part done by Ram and Ramesh in 1 day =1/6   Ram alone can do it in 10 days. Therefore,   Part done by Ram alone in 1 day =1/10. Therefore,   part can do by Rames alone in 1 day =1/6 - 1/10 = 2/30   Net work can do by Ramesh only = 30/2= 
30/2 = 15
15   Answer : 15 days
Answer: C
The ratio of alcohol and water in three mixtures of alcohol and water is 3:2, 4:1, and 7:3. If equal quantities of the mixture are drawn and mixed, the concentration of alcohol in the resulting mixture will be? Choose the correct choice from the following choices
A) 65%  B) 70%  C) 75%  D) 80%  E) 90%

Solution: The ratios are given such that the sum of alcohol and water can be brought up to 10 for each mixture. (Since equal quantities are to be added)   For 3:2 lets take 6 parts alcohol and 4 parts water   For 4:1 lets take 8 parts alcohol and 2 parts water   For last since the sum is already 10, 7 parts alcohol and 3 parts water.   Mixing these three will give   6+8+7= 
  6+8+7 = 21
21 units alcohol and  4+2+3= 
 4+2+3 = 9
9 units water   or, 21 units alcohol in 30 units of mixture     21/30 *100= 
  21/30 *100 = 70
70%   Answer : 70%
Answer: B
A and B started a business with initial investments in the ratio 8 : 3, after some months B withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long B was in the business ?
Choose the correct option.
A) 6 months B) 28 months C) 9 months D) 5 months E) 7 months

Solution: Let Sumit in the business for ‘a’ months.   Investment Ratio Amit to Sumith = 8 : 3.   Profit sharing ratio = 8 : 7.   Amit is in the business for 12 months.   Then Sumit in the business for   (8 × 12) / (3 × a) = 8 / 7 => 24a = 672 or   a = 672 / 24= 
672 / 24 = 28
28 or 28 months   Option 28 months
Answer: B
A deer is standing 50 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 80 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?	Choose the correct choice from the following options
A) 90
B) 100
C) 110
D) 120
E) 130

Solution: Let x be the length of the tunnel.   When the deer runs 50 meters west, the train goes 500 meters to a point 80 meters from west entrance of the tunnel.   When the deer runs east, the deer runs x-50 meters while the train goes x + 500 + 80 meters.   x + 500 + 80 = 10(x-50)   9x = 1080   x = 120 meters   The answer is 120.
Answer: D
If k and t are integers and k^2 – t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2	Choose the correct answer:  A) None  B) I only  C) II only  D) III only  E) I, II, and III

Solution: k^2–t^2 is an odd integer means that either k is even and t is odd or k is odd and t is even.   Check all options:   I. k + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;   II. k^2 + 2kt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;   III. k^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.   Nonenswer: None.
Answer: A
Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: D12, H16, __, P24, T28, ... What number should fill the blank?	Choose one:
A) H16 B) I17 C) J18 D) K19 E) L20

Solution: L20   L20   In this series, the letters progress by 4, and the numbers increase by 4.
Answer: E
Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 18 kmph and Prasanna moves southward at a speed of 27 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
Select:  A) 11  B) 50  C) 28  D) 45  E) 18

Solution: Explanation:   We know 60 min = 1 hr   Total northward Laxmi's distance = 18kmph x 1hr = 18 km   Total southward Prasanna's distance = 27kmph x 1hr = 27 km   Total distance between Prasanna and Laxmi is = 18 + 27= 
18 + 27 = 45
45 km.   Answer: 45
Answer: D
A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 94 km downstream  Choose the correct choice from the following choices:
A) 1 hour 40 min
B) 2 hour 40 min
C) 1 hour 20 min
D) 1 hour 30 min
E) 1 hour 50 min

Solution: Speed of the boat in still water = 42 km/hr   speed of the stream = 10 km/hr   Speed downstream = (42+10)= 
(42+10) = 52
52 km/hr   Distance travelled downstream= 94 km   Time taken =distance/speed   =94/52   = 1.81 hours   = 1 hour 50 min.   ANSW1 hour 50 minR:1 hour 50 min
Answer: E
The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8400 for a computer table, then what was the cost price of the computer table? Choose the most appropriate option
A) 7000 B) 2699 C) 2670 D) 6725 E) 2601

Solution: CP = SP * (100/(100 + profit%))   = 8400(100/120) = Rs. 7000.   7000nswer:7000
Answer: A
A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used? Choose one
A) 5  B) 1  C) 8  D) 7  E) 4

Solution: 7 * 8 : 9 * x = 8:9 => x= 7   Answer:7
Answer: D
Some consecutive natural numbers, starting with 1, are written on the board. Now, one of the numbers was erased and the average of the remaining numbers is 800/39. Find the number which was erased.
Choose the correct choice from the following choices.
A) 24  B) 20  C) 18  D) 16  E) 15

Solution: Explanation:   We know that average of n consecutive numbes average = n×(n+1)/2 /n =(n+1)/2   If the given n is sufficiently large, the average does not change much even though we exclude one or two numbers from it. So the approximate number of observations is almost double to the average (Remember: the average of consecutive numbers almost lies in the middle)   The approximate average is 800/39 = Approx 20. So the initial numbers may be nearer to 40.   In this question it is actually 40 as from the denominator of the new average 800/39. The initial numbers are 40.   Sum of 40 consecutive numbers = 40×(40+1)/2=820   Sum of 39 numbers = average x number of observations = 800/39×39 = 800   So the number excluded = 820 - 800= 
820 - 800 = 20
20   Correct Option: 20
Answer: B
What is the least common multiple of 152 and 190? Answers:
A) 304 B) 14440 C) 760 D) 28880 E) 1520

Solution: Yes there is a shorter way   152 = 2*2*2*19   190 = 2*5*19   I think everyone knows how to do this.   Then   choose 2*2*2 and choose 5 and choose 19   2*2*2*5*19= 
2*2*2*5*19 = 760
760 answer is 760
Answer: C
The speed of a boat in still water in 42 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 44 minutes is:	Choose the correct choice from the following options
A) 86.6 km B) 46.6 km C) 35.2 km D) 35.6 km E) 26.6 km

Solution: Speed downstream = (42 + 6)= 
(42 + 6) = 48
48 kmph   Time= 44 minutes =44/60 hour = 11/15 hour   Distance travelled = Time × speed =11/15×48 = 35.2 km   ANSWER:35.2 km
Answer: C