MU-NLPC/Calc-aqua_rat huggingface dataset:
A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 200 square feet, what is the total length of the fence, in feet?  Options
A) 10 B) 20 C) 30 D) 40 E) 80

Solution: two sides EACH = x the third = 2x and the wall length is thus 2x too   x*2x = 2x^2 = 200 ie x^2 = 100 ie x = 10   L = 20 W=10   TOTAL LENGHT OF FENCE = 2*10 + 20= 
2*10 + 20 = 40
40   MY ANSWER IS 40
Answer: D
The price of rice is reduced by 2%. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier?	Pick one.
A) 48 kg  B) 49 kg  C) 50 kg  D) 51 kg  E) None

Solution: Sol.   Let the original price be Rs. 100 per kg.   Money required to buy 49 kg of rice = Rs. (100 x 49) = Rs. 4900.   New price = Rs. 98 per kg.   ∴ Quantity of rice bought = [4900 / 98= 
4900 / 98 = 50
50 kg.   Answer 50 kg
Answer: C
Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?
Choose the correct choice from the following options.
A) 9 min	B) 8 min	C) 4 min	D) 6 min	E) None of these

Solution: Explanation:   Tank can be filled by pipe A in 12 minutes and pipe B in 24minutes.   => Part filled by A in 1 minute= 1/12   => Part filled by 8 min in 1 minute= 1/24   => Part filled by both in 1 minute= 1/12 + 1/24   = 3/24=1/8   Time taken to fill the entire tank = 8 minutes   ANSWER 8 min
Answer: B
H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is:  Choices.
A) 240 B) 790 C) 840 D) 180 E) 120

Solution: Explanation:   4 * 27 * 3125 = 2^2 * 3^3 * 5^5;   8 * 9 * 25 * 7 = 2^3 * 3^2 * 5^2 * 7;   16 * 81 * 5 * 11 * 49 = 2^4 * 3^4 * 5 * 7^2 * 11   H.C.F = 2^2 * 3^2 * 5 = 180.   Answer: Option 180
Answer: D
A train sets off at 2:00 pm at the speed of 70 km/h. Another train starts at 3:00 pm in the same direction at the rate of 80 km/h. At what time will the second train catch the first train? Choose the correct choice from the following choices
A) 10:00  B) 10:30  C) 11:00  D) 11:30  E) 12:00

Solution: In one hour the first train travels 70 km.   The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.   The second train will catch the first train in   70/10= 
  70/10 = 7
7 hours, so at 10:00 pm.   The answer is 10:00.
Answer: A
The H.C.F. of two numbers is 12 and their difference is 12. The numbers are  Choose the correct choice from the following:	A) 66, 78	B) 70, 82	C) 94, 106	D) 84, 96	E) None

Solution: Solution   Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96   Answer 84, 96
Answer: D
A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
Select:
A) 9/4
B) 3/2
C) 4/3
D) 1/3
E) 1/2

Solution: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:   2x/3   Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us   √(2x/3) = x   2x/3 = x^2   2x = 3x^2   3x^2 – 2x = 0   x(3x – 2) = 0   x = 0 or   3x – 2 = 0   3x = 2   x = 1/3   Because x is positive, x = 1/3. The answer is 1/3.
Answer: D
A(5, w^2) is the (x, y) coordinate of point located on the parabola Y = X^2 + 11. What is the value of w? Options
A) 3.  B) 4.  C) 5.  D) 6.  E) 9.

Solution: y=x^2 +11   w^2=5^2+11   w^2=36   W=6   Answer 6.
Answer: D
If x,2x+2,3x+3 are the first three terms of a GP,then what is its fourth term?
Choose the correct choice from the following choices:	A) -11.5	B) -12.5	C) -13.5	D) -14.5	E) -15.5

Solution: (2x+2)/x= (3x+3)/(2x+2)   4x^2+8x+4 = 3x^2+3x   x^2+5x+4=0   x=-4   so series will be   -4,-6,-9,-13.5   ANSWER:-13.5
Answer: C
In a vessel, there are 10 litres of alcohol. An operation is defined as taking out five litres of what is present in the vessel and adding 10 litres of pure water to it. What is the ratio of alcohol to water after two operations? Choose the most appropriate option.
A) 1 : 0	B) 1 : 5	C) 1 : 1	D) 1 : 2	E) 1 : 9

Solution: Final concentration = Initial concentration (1−replacement quantityfinal volume)(1−replacement quantityfinal volume)   Final concentration = =1×(1−1015)=13=1×(1−1015)=13   Final concentration = 13×(1−1020)=1613×(1−1020)=16   So ratio of alcohol : water = 1 : 5   Answer:1 : 5
Answer: B
an article with cost price of 240 is sold at 20% profit. what is the selling price?	Options.
A) 288	B) 200	C) 204	D) 207	E) 210

Solution: sp=1.20*240= 
1.20*240 = 288
288   288NSWER:288
Answer: A
If a fair coin is tossed seven times, what is the probability of getting exactly five heads in a row?  Pick one
A) 1/8	B) 1/16	C) 3/32	D) 3/64	E) 5/128

Solution: Let X represent either H or T (it doesn't matter which).   P(HHHHHTX) = 1/64   P(THHHHHT) = 1/128   P(XTHHHHH) = 1/64   The sum of these probabilities is 5/128   The answer is 5/128.
Answer: E
A man sold 18 toys for Rs. 16800, gaining thereby the cost price of 3 toy find the cost price of a toy  Choose the correct choice from the following choices.
A) Rs. 600  B) Rs. 800  C) Rs.500  D) Rs.900  E) Rs. 990

Solution: Let the cost of one toy = X.   Then, cost of 18 toys = 18X.   Gain = 3X.   SP of 18 toys = Rs. 16800.   Gain = SP – CP   3X = 16800 – 18X   21X = 16800   X = Rs. 800.   ANSWER : OPTION Rs. 800
Answer: B
If A, B and C together can finish a piece of work in 2 days. A alone in 12 days and B in 18 days, then C alone can do it in?	Pick one.
A) 5 days  B) 4 days  C) 3 days  D) 2 days  E) 7 days

Solution: 3 days = 1/2 - 1/12 – 1/18 = 1/3 => 3 days   ANSWER:3 days
Answer: C
Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?  Choose the correct choice from the following options:
A) A)12
B) B)36
C) C)72
D) D)240
E) E)720

Solution: in order not to have two boys or two girls next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).   Total ways = 2721*3!*3!   =2*6*6= 
2*6*6 = 72
72   Ans - 72
Answer: C
What is the probability for a family with five children to have two boys and three girls (assuming the probability of having a boy or a girl is equal)?  Choose the most appropriate option:
A) 1/2	B) 1/4	C) 3/8	D) 3/16	E) 5/16

Solution: One possible case is: girl - girl - girl - boy - boy   The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32   There are 5C3 = 10 such cases so we should multiply by 10.   P(two boys and three girls) = 10/32 = 5/16   The answer is 5/16.
Answer: E
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Select:
A) 833 1/3 grams	B) 850 1/3 grams	C) 825 1/3 grams	D) 810 1/3 grams	E) 870 1/3 grams

Solution: A   833 1/3 grams   If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: A
Pick the odd man out:
154, 235, 352, 460, 324 Options: A) 324 B) 323 C) 279 D) 266 E) 0002

Solution: Explanation:   Sum of the digit in each number, except 324 is 10.   324NSWER: 324
Answer: A
23, 29, 31, 37, 41, 43, (...)  Choose the correct option:
A) 53  B) 48  C) 47  D) 59  E) 61

Solution: All are prime numbers in their order, starting from 23   Hence, next number is 47   Answer is 47.
Answer: C
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,6), (10,0) and (10,6). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?  Choose one:	A) 1/2	B) 1/3	C) 1/4	D) 1/5	E) 1/6

Solution: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.   The center of the rectangle is the point (5,3).   The slope of line passing through points (1,1) and (5,3) = (3-1)/(5-1) = 1/2   The answer is 1/2.
Answer: A
If x^6 + y^6 = 500, then the greatest possible value of x is between  Choose the correct choice.
A) 0 and 3  B) 3 and 6  C) 6 and 9  D) 9 and 12  E) 12 and 15

Solution: for the greatest possible value of x^6, we must minimize the value of y^6 i.e. lets say y^6 = 0   then we need to find a number x such that x^6 < 500. 2^6 = 64 and 3^6 = 729 so we can say that the maximum possible value of x can be a little less than 3 hence answer = between 0 and 3   hence 0 and 3
Answer: A
A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?	Choose the most appropriate option
A) 90 B) 25 C) 40 D) 23 E) 60

Solution: 1/9 - 1/x = 1/10   => 90 hrs   90NSWER 90
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?	Answers
A) 8 B) 9 C) 4 D) 7 E) 1

Solution: 7 * 8 : 9 * x = 8:9   => x= 7   Answer: 7
Answer: D
Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2-12y+32=0
Select the correct option:	A) If x>y	B) If x>=y	C) If x<y	D) If x<=y	E) x=y or relationship cannot be established

Solution: Solution:-   X=3,4 and Y= 4,8   X<= Y   If x<=y
Answer: D
A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1100, what is the reduced price for kg?  Choose the correct answer:
A) s.40 B) s.46 C) s.55 D) s.41 E) s.42

Solution: 800*(25/100) = 275 ---- 5   ? ---- 1   => Rs.55   Answer: s.55
Answer: C
A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 810 sq. feet, how many feet of fencing will be required?
Choose the correct choice:	A) 34	B) 40	C) 68	D) 84	E) None

Solution: EXPLANATION   We have: l = 30 ft and lb = 810 sq. ft.   So, b = 27 ft.   Length of fencing = (l + 2b) = (30 + 54)= 
(30 + 54) = 84
84 ft.   Answer 84
Answer: D
A train 130 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is Choose the most appropriate option
A) 54 kmph
B) 60 kmph
C) 66 kmph
D) 72 kmph
E) 82 kmph

Solution: speed of train relative to man: 130/6 * 18/5 km/hr   = 78 km/hr   let speed of train= x   therefore x+6 = 78   x= 78-6= 
78-6 = 72
72 km/hr   ANSWER:72 kmph
Answer: D
The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 3 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 8
Tennis 5
Baseball 4 Choose the most appropriate option:	A) 6	B) 9	C) 11	D) 12	E) 17

Solution: X = 8 + 5 + 4 - (3 + 2 + 3)= 
8 + 5 + 4 - (3 + 2 + 3) = 9
9   Answer is 9
Answer: B
The fuel indicator in a car shows 1/5th of the fuel tank as full. When 22 more liters of fuel are poured in to the tank, the indicator rests at the 3/4of the full mark. Find the capacity of the tank.  Choose the most appropriate option.
A) 25 litres
B) 35 litres
C) 30 litres
D) 40 litres
E) None of these

Solution: x/5 + 22 = 3x/4 => x = 40 litres   Answer: 40 litres
Answer: D
If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was?	Choose the correct choice from the following answers:
A) 120000
B) 160000
C) 187899
D) 178968
E) 789698

Solution: X * (105/100) * (105/100) * (105/100) = 185220   X = 185220/1.157625= 
185220/1.157625 = 160_000
160000   Answer:160000
Answer: B
A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.	Choose the most appropriate option
A) 21:23  B) 27:25  C) 23:27  D) 23:24  E) 23:26

Solution: Solution :   Given SI1 = SI 2   P1 : P2 = 1/R1T1 : 1/R2T2   = 1/(10*5) : 1/(9:6)   27:25   27:25
Answer: B
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform?  Pick:	A) 37 min	B) 55 min	C) 48 min	D) 67 min	E) 45 min

Solution: C   48 min   Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +360)/ 36 * 5/18 = 48 min.
Answer: C
How long will it take a sum of money invested at 6 % p.a. S.I. to increase its value by 60%?	Choices
A) 11 years	B) 12 years	C) 10 years	D) 15 years	E) 8 years

Solution: Sol.   Let the sum be x. Then, S.I. = 60% of x = 3x/5; Rate = 6%.   âˆ´ Time = [100 * 3x/5 * 1/x*6] = 10 years   Answer 10 years
Answer: C
If x and y are different integers, both divisible by 11, then which is not necessarily true?	Choose the correct choice from the following choices:
A) x^2 + y^2 is divisible by 11 B) x - y is divisible by 11 C) xy is divisible by 11 D) x + y is divisible by 11 E) x + y is divisible by 22

Solution: Let x = 11k and let y = 11j.   Then x+y = 11(k+j) and k+j could be even or odd.   Thus 11(k+j) is not necessarily divisible by 22.   The answer is x + y is divisible by 22.
Answer: E
In a simultaneous throw of 2 dice what is the probability of getting a total of 2?
Select the correct option:
A) 1/4	B) 1/36	C) 2/11	D) 3/13	E) 1/5

Solution: n(S) = 6*6= 
6*6 = 36
36   E= {(1,1)}   Probability = 1/36   Answer is 1/36
Answer: B
How many Three digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is replaced?  Select.
A) 5
B) 10
C) 15
D) 20
E) 30

Solution: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.   Tens place can be filled by any of the remaining 5 numbers.   So, there are 5 ways of filling the tens place.   The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.   Therefore Required number of numbers = 1 x 5 x 4 = 20.   Answer 20.
Answer: D
If a - b = 3 and a2 + b2 = 29, find the value of ab.	Select:  A) 10  B) 12  C) 15  D) 18  E) 20

Solution: Explanation:   2ab = (a2 + b2) - (a - b)2   = 29 - 9= 
29 - 9 = 20
20   ab= 10.   10nswer: 10
Answer: A
The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?  Choose the correct choice from the following options.
A) 3:4	B) 3:5	C) 4:3	D) data inadequate	E) None of these

Solution: Let P's age and Q's age be 6x and 7x years respectively.   Then, 7x - 6x = 4 => x = 4   Required ratio = (6x + 4) : (7x + 4)   28 : 32 = 7:8   ANSWNone of theseR:None of these
Answer: E
If the complement of a certain angle is seven times the measure of that certain angle, then what is the measure of that certain angle?  Choose the correct choice from the following options:
A) 45°
B) 30°
C) 11.25°
D) 18°
E) 15°

Solution: The complement of angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.   The original angle is x, so the complement is 7x, and together, these add up to 90 degrees.   x + 7x = 90   8x = 90   x = 11.25°   Answer = (11.25°)
Answer: C
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 50 years now, the son's age 10 years back was?  Choose the correct choice from the following:  A) 12yr  B) 15yr  C) 14yr  D) 10yr  E) 20yr

Solution: Let the son's present age be x years   Then, 50-x = x   x = 25   Son's age 10 years back = 25-10= 
25-10 = 15
15years   Answer is 15yr
Answer: B
For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/16	Choose the correct answer
A) a) 12	B) b) 6	C) c) 10	D) d) 16	E) e) 19

Solution: It seems that the accepted answer is wrong, according to WolframAlpha. The answer should be 31, which isn't even listed as a selectable answer.   e) 19
Answer: E
A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?	Choose the correct choice from the following answers:
A) 1/2
B) 10/21
C) 9/11
D) 7/11
E) 6/11

Solution: Total number of balls = 2 + 3 + 2= 
2 + 3 + 2 = 7
7   Let S be the sample space.   n(S)= Total number of ways of drawing 2 balls out of 7 = 7C2   Let E = Event of drawing 2 balls , none of them is blue.   n(E) = Number of ways of drawing 2 balls , none of them is blue   = Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2   (âˆµ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2= 
7 - 2 = 5
5)   P(E)= n(E)/n(S)=5C2/7C2=(5Ã—4/2Ã—1)/(7Ã—6/2Ã—1)=5Ã—4/7Ã—6=10/21   Answer :10/21
Answer: B
The volume of a cube is 1728 cc. Find its surface? Choose the correct choice from the following options:
A) 864 B) 288 C) 299 D) 267 E) 289

Solution: a3 = 1728 => a = 12   6a2 = 6 * 12 * 12= 
6 * 12 * 12 = 864
864   864nswer:864
Answer: A
Deepak can read x pages in 10 minutes. At this rate, how long will it take him to read y pages?
Answers: A) (12/x)*y B) (5/x)*y C) (10/x)*y D) (10x)*y E) (13/x)*y

Solution: x page in 10 mins   i.e. 1 page in 10/x mins   i.e. y pages in (10/x)*y   Answer: option (10/x)*y
Answer: C
The speed of a railway engine is 84 Km per hour when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 Km per hour when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is:
Choose the correct choice from the following choices: A) 19 B) 18 C) 16 D) 17 E) 14

Solution: the reduction in speed is directly proportional to the square root of the number of compartments attached   Doesreductionmean amount subtracted? or percentage decrease? There are at least two interpretations, and the wording does not provide a clear interpretation between them.   Evidently what the question intends is the subtraction interpretation. What is subtracted from the speed is directly proportional to the square root of the number of compartments attached.   In other words, if S = speed, and N = number of compartments, then   S = 84 - k*sqrt(N)   wherekis a constant of the proportionality. In general, if A is directly proportional to B, we can write A = k*B and solve for k.   If N = 9, then S = 24   24 = 84 - k*sqrt(9) =84 - 3k   k = 20   Now, we need to know: what value of N makes S go to zero?   0 = 84 - 20*sqrt(N)   20*sqrt(N) = 84   sqrt(N) = 4.2   n = 4.2^2 >17   With 18 compartments, the train does not budge. Therefore, it would budge if there were one fewer cars. Thus, 17 is the maximum number of cars the engine can pull and still move.   17
Answer: D
Two out of ten employees are capable of doing a certain task. Sixty percent of the five employees, including the two who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?  Choose the correct answer: A) 43.33% B) 66.66% C) 13.33% D) 38.33% E) 23.33%

Solution: Given 60% of 10 employees including 2 who are capable of doing task.   60% of 10 employeees   = 60/100 * 10= 
60/100 * 10 = 6
6 employees===> 2 employees who are capable of doing the task and four employee who is not capable.   percentage of employees assigned who are not capable   = 4/6 * 100   = 66.66%   ANSWER:66.66%
Answer: B
Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully adhered to, in how many different ways can the women pose?  Select the correct option
A) 2 B) 14 C) 15 D) 16 E) 18

Solution: Shortest (1) and highest (8) women are fixed:   XXX8   1XXX   2 and 7 have two options, so total 4 patterns:   1:   2xx8   1xx7   |2468| |2568|   |1357| |1347|   2.   2x78   1xxx   |2478| |2578| |2678|   |1356| |1346| |1345|   3.   xxx8   12x7   |4568| |3468| |3568|   |1237| |1257| |1247|   4.   xx78   12xx   |3478| |3678| |3578| |5678| |4578| |4678|   |1256| |1245| |1246| |1234| |1236| |1235|   14 options.   Answer: 14.
Answer: B
Can you find the smallest non fractional number such that
If the number gets divided by 7 , we get the remainder of 1;
If the number gets divided by 8 , we get the remainder of 2
If the number gets divided by 9 , we get the remainder of 3;
If the number gets divided by 10 , we get the remainder of 4. Options.
A) 1500
B) 3210
C) 2150
D) 2518
E) 2300

Solution: D.2518   As we know LCM of the numbers 7 8 9 & 10 is 2520.   So if i divide 2520 by any of the four number , it gives remainder as 0.   Now to get reminder as desired, is should be 2 short of 2518. (3-1,4-2,5-3,6-4 )   Ans:option 2518
Answer: D
In a race where 10 cars are running, the chance that car X will win is 1/7, that Y will win is 1/3 and that Z will win is 1/5. Assuming that a dead heat is impossible, find the chance that one of them will win. Choose the correct option
A) 1/140	B) 1/180	C) 71/105	D) 21/113	E) 57/120

Solution: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).   = 1/7 + 1/3 + 1/5   = 71/105   ANSWER:71/105
Answer: C
The area of a square field is 4802 m(power)2 the length of its diagonal is: Select the correct option:
A) 98m  B) 102m  C) 95m  D) 105m  E) 96m

Solution: Let the diagonal be d metres,   Then 1/2 d(power)2 = 4802   d2 = 9604   d = √9604   d = 98 m   98mnswer is 98m.
Answer: A
The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum Q of all the digits of the integers from 0 to 99 inclusive?
Choices.
A) 450  B) 810  C) 900  D) 1000  E) 1100

Solution: We want the sum of the digits from 0 to 99, so I approximated:   0-9 ->45-> (9+0)*10/2   40-49 ->85(13+4)*10/2   90-99 ->135(18+9)*10/2   We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just Q=900:the answer is 900.
Answer: C
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank ? Choose the correct option.
A) 10 hours  B) 15 hours  C) 17 hours  D) 18 hours  E) 20 hours

Solution: Explanation:   Suppose, first pipe alone takes x hours to fill the tank .   Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.   As per question, we get   1/x+1/x−5=1/x−9   =>x−5+x/x(x−5)=1/x−9   =>(2x−5)(x−9)=x(x−5)   =>x2−18x+45=0   After solving this euation, we get   (x-15)(x+3) = 0,   As value can not be negative, so x = 15   Option 15 hours
Answer: B
X starts a business with Rs.54000. Y joins in the business after 9 months with Rs.27000. What will be the ratio in which they should share the profit at the end of the year?	Choose the correct choice from the following choices:
A) 1 : 2  B) 2 : 1  C) 8 : 3  D) 3 : 5  E) 8 : 1

Solution: Explanation :   Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   = 54000 * 12: 27000 * 3   = 54 * 12: 27 * 3   = 2*4: 1   = 8:1. Answer : Option 8 : 1
Answer: E