MU-NLPC/Calc-aqua_rat huggingface dataset:
N= 1!+2!+3!.....+10!. what is the last digit of N^N? Choose the correct choice.
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: as you see 5! till 10 ! each unit digit is zero.   so 1!+2!+3!+4! =33   so unit digit   3+ 0= 
  3+ 0 = 3
3   N=3   N^N= 3^3=27   so last digit is 7.   ANSW7R:7
Answer: E
In the xy-coordinate system, if (m, n) and (m 1 2, n 1 k) are two points on the line
with the equation x 5 2y 1 5, then k 5
Choose the correct answer:
A) 1/2
B) 1
C) 2
D) 5/2
E) 4

Solution: Step 1: Analyze the Question   For any question involving the equation of a line, a good   place to start is the slope-intercept form of the line,   y = mx 1 b. Remember that if you have two points on a   line, you can derive the entire equation, and if you have an   equation of the line, you can calculate any points on that   line.   Step 2: State the Task   We are solving for k, which is the amount by which the   y-coordinate increases when the x-coordinate increases   by 2.   Step 3: Approach Strategically   The slope of a line is the ratio between the change in y and   the change in x. In other words, every time the x-coordinate   increases by 1, the y-coordinate increases by the amount   of the slope.   The equation of the line in the question stem is defined as   x = 2y + 5. We must isolate y to have slope-intercept form:   So the slope of this line is 1/2 . This means that for every   change of +1 in the x direction, there is a change of + 1/2   in the y direction. Then we know that, because there is an   increase in 2 units in the x direction when moving from   m to m + 2, there must be a change of 1 unit in the y   direction when moving from n to n + k. So k = 1.   Since there are variables that eventually cancel (m and n   are not part of the answers), we can Pick Numbers. Let’s   say that you choose the y-coordinate of the point (m, n) to   be 0 to allow for easier calculations. Using the equation   we’re given to relate x- and y-coordinates, we can calculate   the x-coordinate:   So (m, n) is the point (5, 0).   Now we’ll plug our values of m and n into the next point:   (m + 2, n + k). That yields (7, k). All we have to do is plug   an x-coordinate of 7 into the equation to solve for k, the   y-coordinate:   Answer is 1
Answer: B
Sarah is driving to the airport. After driving at 20 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 50 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all? Choose the most appropriate option.
A) 140
B) 175
C) 210
D) 70
E) 280

Solution: After driving at 20 miles per hourfor one hour, this distance left to cover is d-20. Say this distance is x miles.   Now, we know that the difference in time between covering this distance at 20 miles per hour and 50 miles per hour is 1+ 1/2 = 3/2 hours.   So, we have that x/20 - x/50 = 3/2 --> 5x/100 - 2x/100 = 3/2 --> 3x/100 = 3/2 --> x = 50.   Total distance = x + 20 = 70 miles.   Answer: 70
Answer: D
If the price of an item is decreased by 50% and then increased by 20%, the net effect on the price of the item is
Choose the correct option:  A) A decrease of 99%  B) A decrease of 40%  C) A decrease of 1%  D) A increase of 1%  E) none

Solution: initially assume 100 rupees   50% discount in 100 gives price of 50 rupees   then 20% raise in 50 is only 10 rupees.   therefore total price =60 rupees.   hence 40% is the loss   ANSWER:A decrease of 40%
Answer: B
What distance will be covered by a bus moving at 72 kmph in 30 seconds?  Answers:
A) 700 m B) 500 m C) 800 m D) 600 m E) 400 m

Solution: 600 m   600 m   72 kmph = 72 * 5/18= 
72 * 5/18 = 20
20 mps   600 m= Speed * time = 20 * 30= 
20 * 30 = 600
600 m.
Answer: D
Some men can do a work in 10 days. with 10 less than original no of men it takes 10 more days to complete the work. what is the original no of men? Choose the correct option:
A) 20 men
B) 25 men
C) 30 men
D) 35 men
E) 40 men

Solution: let the no. of men be x   x men can do in 10 days,so one man can do in 10*x days   now (x-10) men can do in (10+10=20 days),so one man can do in 20*(x-10)days   10x=20(x-10)   or x=2x-20   or x=20 men   20 menNSWER:20 men
Answer: A
The tax on a commodity is diminished by 19% and its consumption increased by 15%. The effect on revenue is?  Choose the correct choice from the following choices
A) 2%	B) 8.85%	C) 5.85%	D) 6.85%	E) 1%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   81 * 115= 
81 * 115 = 9_315
9315   -----------   10000-----------685   100-----------?=> 6.85% decrease   Answer: 6.85%
Answer: D
70 percent of the members of a study group are women, and 40 percent of those women are lawyers. If one member of the study group is to be selected at random, what is the probability that the member selected is a woman lawyer? Choose the correct choice from the following answers.
A) 0.28  B) 0.27  C) 0.25  D) 0.32  E) 0.35

Solution: Say there are 100 people in that group, then there would be 0.7*0.40*100= 
0.7*0.40*100 = 28
28 women lawyers, which means that the probability that the member selected is a woman lawyer is favorable/total=28/100.   0.28nswer: 0.28
Answer: A
When 20 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?	Choose one
A) 3 : 4  B) 2 : 1  C) 3 : 2  D) Data inadequate  E) None of these

Solution: Let the first and the second numbers be x and y respect then   y + 20% of x = 140% of y   or, y + 0.2x = 1.4y   or, 0.2x = 0.4y   ∴ x : y = 0.4 : 0.2 = 2 : 1   Answer 2 : 1
Answer: B
If x is divided by 7, the remainder is 5. What is the remainder if 4x is divided by 7? Choose one:
A) 1 B) 2 C) 4 D) 6 E) 8

Solution: x=7q+5   4x=7*4q+20   4x=7*4q+7*2+6   4x=7(4q+2)+6   4x=7k+6 (k=4q+2)   Answer 6
Answer: D
Complete the series
13, 9, 5, 1, -3...  Options:	A) -4	B) 0	C) 3	D) -7	E) 3

Solution: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option -7) -7
Answer: D
Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 1 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?
Choices:
A) 560 B) 561 C) 562 D) 563 E) 673

Solution: Total price of 8 t-shirts= 8*526= 
8*526 = 4_208
4208   Total price of 7 t-shirts=7*505= 
7*505 = 3_535
3535   Total price of 1 t-shirts=4208-3535= 
4208-3535 = 673
673   Average price of 3 t-shirts=673   Correct option Answer:673
Answer: E
The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 49 kg more than the weight of the third boy, what is the weight of the lightest boy?	Choose the correct choice from the following answers.
A) 87 kg  B) 39.2 kg  C) 98.2 kg  D) 65.2 kg  E) 87.2 kg

Solution: Let the weights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 49   => 5k = 49=> k = 9.8   Therefore the weight of the lightest boy   = 4k = 4(9.8) = 39.2 kg.   Answer:39.2 kg
Answer: B
Bob can eat 27 chocolates in an hour. Alice can eat 2 chocolates in 10 minutes, and Kelly can eat 7 chocolates in 20 minutes. How long will it take them to share and eat a large box of 120 chocolates whilst watching a movie? Choose the correct choice:
A) 2 hrs	B) 1 hrs	C) 3 hrs	D) 4 hrs	E) 6 hrs

Solution: Bob can eat 27 chocolates in a hour,   Alice can eat 2 chocolates in 10 minutes or 12 choc in 1 hr   , and Kelly can eat 7 chocolates in 20 minutes or 21 chocs in 1 hr.   Three together can eat   27+12+21= 
  27+12+21 = 60
60 choclates in 1 hr .   it take them 2 hrs to share and eat a large box of 120 chocolates whilst watching a movie   2 hrsNSWER:2 hrs
Answer: A
The cost price of a TV is Rs.1500 and it was sold for Rs.1230, find the loss %?	Pick one: A) 20% B) 18% C) 16% D) 21% E) 13%

Solution: 18%   18%   1500 ---- 270   100 ---- ? => 18%
Answer: B
Due to fall in manpower , the production in a factory decreases by 40%, By what percentage should the working hours be increased to restore the original level of production?	Options
A) 66 2/3 %
B) 46 1/3 %
C) 25%
D) 40%
E) 33 1/3 %

Solution: 2/3*3/5*5/6 =1/3   1/3 x/ x*100 = 100/3 = 33 1/3 %   ANSW33 1/3 %R:33 1/3 %
Answer: E
The ages of two person differ by 20 years. If 4 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively Choose the correct choice from the following choices.
A) 30, 10  B) 25, 5  C) 29, 9  D) 50, 30  E) 20,10

Solution: Let their ages be x and (x + 20) years.   Then, 5(x - 4) = (x + 20 - 4)   => 4x = 36   =>x =9   Their present ages are 29 years and 9 year.   ANSWER:29, 9
Answer: C
How many times in a day, are the hands of a clock in straight line but opposite in direction? Choose one: A) 20 B) 22 C) 24 D) 48 E) 50

Solution: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).   So, in a day, the hands point in the opposite directions 22 times.   Answer: Option 22
Answer: B
Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 10% ?  Choose the correct choice from the following answers:
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Let n be the number of man. Probability = n/10 * (n-1)/9= n(n-1)/90.   For the probability to be less than 10%, n(n-1) < 9.   Maximum number that satisfies this condition is 3. For 4, it is > 9. Hence the answer is 3.
Answer: D
A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds. The length of the train (in metres) is:	Choose the correct choice from the following choices.
A) 184	B) 176	C) 175	D) 96	E) None of these

Solution: Explanation:   Let the length of train be L m.   Acc. to question   (276+L)/20 = L/8   2208+8L=20L   L= 2208/12= 
2208/12 = 184
184 m   184nswer 184
Answer: A
Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 2?	Choose the correct choice from the following choices
A) y = -1/2*x + 3 B) y = 1/2*x - 2 C) y = 1/2*x + 3 D) y = 2x + 3 E) y = 2x − 3

Solution: Since our line has to perpendicular to y = − 2x + 3   Slope of this line , m = -2   Slope will be required line L = 1/2 ( Product of slope of perpendicular lines = -1)   y-intercept of line L is same as y intercept of line y = 2x − 2   y - intercept of line L = -2   Required line = 1/2* x - 2   Answer y = 1/2*x - 2
Answer: B
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 66 km downstream?	Answers:
A) 30/83 hours
B) 33/13 hours
C) 31/13 hours
D) 30/13 hours
E) 30/14 hours

Solution: Speed downstream = 20 + 6= 
20 + 6 = 26
26 kmph.   Time required to cover 66 km downstream= d/s = 66/26   = 33/13 hours.   Answer:33/13 hours
Answer: B
A rectangular grass field is 60 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?	Choose one
A) 1350	B) 1200	C) 9676	D) 1679	E) 2691

Solution: Area = (l + b +2d) 2d   = (60 + 55 +2.5 * 2) 2*2.5 => 600   600 * 2 = Rs.1200   Answer:1200
Answer: B
The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bought, then the probability, to the nearest thousandth, that 7 devices function properly is  Pick.
A) 0.057  B) 0.478  C) 0.001  D) 0  E) None

Solution: Solution   Let q being the probability a device does not function properly and p = 1 - q = 0.9 the probability that a device functions properly. Since there are only two possible results, it is a binomial distribution. The P probability that 7 out of 10 devices function properly is given by   C(10,7)*0.9 7*0.1 3 , where C(10,7) is the number of ways that 7 items are selected from 10 and is given by   P = C(10,7) = 10! / (7!3!)   0.057 calculation of P gives   P = 0.057   0.057nswer 0.057
Answer: A
What is the smallest positive perfect square that is divisible by 12, 14, and 42?  Select:
A) 900
B) 1089
C) 1600
D) 1764
E) 2025

Solution: The number needs to be divisible by 2^2*3, 2*7, and 2*3*7.   The smallest such perfect square is 2^2*3^2*7^2 = 1764   The answer is 1764.
Answer: D
If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?	Choices
A) 16 2/3% B) 16 4/3% C) 16 7/3% D) 16 6/3% E) 16 2/3%

Solution: Let the price of the article be Rs. 100.   20% of 100 = 20.   New price   = 100 + 20 = Rs. 120   Required percentage   = (120 - 100)/120 * 100   = 20/120 * 100   = 50/3   = 16 2/3%.   16 2/3%nswer:16 2/3%
Answer: A
4 dice are thrown simultaneously on the board. Find the probability show the same face.	Select:
A) 1/211  B) 2/211  C) 1/216  D) 3/211  E) 4/215

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
15 people entered a theater before Sujit. 7 people entered the theater between Sujit and Suraj and 20 people entered the theater after Suraj. How many people are there in the theater?	Pick:
A) 28
B) 36
C) 44
D) 40
E) Cannot be determined.

Solution: Explanation:   If Sujit entered before Suraj then the number of people will be 15 + 1(Sujit) + 7 + 1(Suraj) + 20 = 44.   If Suraj entered before Sujit then number of people will be 7 + 1(Suraj) + 7 + 1(Sujit) + 12 = 28.   So, the number of people in the theater cannot be determined.   ANSWCannot be determined.R IS Cannot be determined.
Answer: E
Z is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Z, and y is the minimum value of the sum of k distinct members of Z, what is x + y? Select the correct option:
A) kn	B) kn + k^2	C) kn + 2k^2	D) 2kn – k^2	E) 2kn

Solution: Probably the easiest way to solve this question would be to assume some values for n and k.   Say n=3, so Z, the set of the first n positive odd numbers would be: Z={1, 3, 5};   Say k=1, so X, the maximum value of the sum of K distinct members of Z would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of Z would simply be 1.   X+Y=5+1= 
5+1 = 6
6.   Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1= 
2*3*1 = 6
6.   Answer: 2kn.
Answer: E
The average age of 30 students of a class is 20 years. Out of these, the average age of 10 students is 16 years and that of the other 19 students is 22 years. The age of the 30th student is:  Choose the correct choice from the following choices
A) 22 years	B) 24 years	C) 15 years	D) 16 years	E) None of these

Solution: Explanation :   Age of the 30th student = [30 x 20 - (10 x 16 + 19 x 22)] = (600 - 278) = 22 years.   22 yearsnswer : 22 years
Answer: A
The volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options.
A) 4:5
B) 4:9
C) 4:2
D) 5:2
E) 2:8

Solution: The volume of the cone = (1/3)πr2h   Only radius (r) and height (h) are varying.   Hence, (1/3)π may be ignored.   V1/V2 = r1^2 . h1/r2^2. h2 => 1/20   = (1)^2h1/(2)^2h2   => h1/h2 = 4/5   i.e. h1 : h2 = 4:5   4:5nswer: 4:5
Answer: A
25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Choose the correct option:  A) None of these  B) 600  C) 12  D) 24  E) 42

Solution: Explanation :   He can go in any bus out of the 25 buses.   Hence He can go in 25 ways.   Since he can not come back in the same bus that he used for travelling,   He can return in 24 ways.   Total number of ways = 25 x 24 = 600. Answer : Option 600
Answer: B
A shipment of 8 TV sets contains 1 black and white sets and 7 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set? Choose the correct choice from the following choices:
A) 1/7  B) 1/4  C) 5/14  D) 11/28  E) 13/28

Solution: 7/8 * 6/7 = 3/4   1-(3/4) = 1/4   Answer 1/4
Answer: B
How long is an IPv6 address?
Pick:
A) 32 bits	B) 128 bits	C) 64 bits	D) 128 bytes	E) 28 bytes

Solution: An IPv6 address is 128 bits long.   Answer:128 bits
Answer: B
A certain industrial loom weaves 0.127 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?	Select the correct option.
A) 114
B) 115
C) 116
D) 117
E) 118

Solution: Let the required number of seconds be x   More cloth, More time, (direct proportion)   Hence we can write as   (cloth) 0.127: 15 :: 1 : x   =>0.127*x=15   =>x=15/0.127   =>x=118   ANSW118R:118
Answer: E
A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident
Choose the correct choice from the following options
A) 30%	B) 35%	C) 40%	D) 45%	E) None of these

Solution: Explanation:   Let A = Event that A speaks the truth   35% = Event that 35% speaks the truth   Then P(A) = 75/100 = 3/4   P(35%) = 80/100 = 4/5   P(A-lie) = 1-3/4 = 1/4   P(35%-lie) = 1-4/5 = 1/5   Now   A and 35% contradict each other =   [A lies and 35% true] or [35% true and 35% lies]   = P(A).P(35%-lie) + P(A-lie).P(35%)   [Please note that we are adding at the place of OR]   = (3/5*1/5) + (1/4*4/5) = 7/20   = (7/20 * 100)= 
(7/20 * 100) = 35
35%   Option 35%
Answer: B
The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 507 sq meters, then what is the width (in meters) of the rectangular plot? Choose the correct choice from the following options:
A) 11	B) 12	C) 13	D) 14	E) 15

Solution: Area = L*W = 3W^2 = 507   W^2 = 169   W = 13   The answer is 13.
Answer: C
If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?  Choose one: A) 33 B) 27 C) 72 D) 69 E) 22

Solution: (3 * 4)/48 = (9 * 2)/ x   x = 72 kg   Answer:72
Answer: C
If 125(5^y) = 1 then y=	Answers:  A) –2  B) –1  C) 0  D) 1  E) -3

Solution: 5^x = 1/125   5^x = 1/5^3   5^x= 5^-3   x = -3   -3
Answer: E
How long does a train 105 m long running at the speed of 68 km/hr takes to cross a bridge 90 m length?  Choose the correct choice from the following options.
A) 13.9 sec	B) 10.7 sec	C) 17.9 sec	D) 61.9 sec	E) 47.98 sec

Solution: Speed = 68 * 5/18 = 19m/sec   Total distance covered = 105 + 90 = 205 m.   Required time = 205/19 = 10.7 sec.   Answer:10.7 sec
Answer: B
In Parkin's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?  Select the correct option
A) 43.0  B) 45.5  C) 46.0  D) 49.0  E) 50.0

Solution: In Parkin's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2=43.0(43 +43 )/2= 
(43 +43 )/2 = 43
43.0
Answer: A
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Choose the correct choice from the following answers:	A) 720	B) 620	C) 520	D) 820	E) 420

Solution: The word 'LEADING' has 7 different letters.   When the vowels EAI are always together, they can be supposed to form one letter.   Then, we have to arrange the letters LNDG (EAI).   Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.   The vowels (EAI) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   720nswer is 720.
Answer: A
A driver just filled the car's gas tank with 36 liters of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If the car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance?	Choose the correct option:
A) 1 B) 1.5 C) 2 D) 2.5 E) 3

Solution: Let x be the number of liters of ethanol added to the gas tank.   0.05(36) + x = 0.1(36+x)   0.9x = 3.6 - 1.8= 
3.6 - 1.8 = 1.8
1.8   x= 2 liters   The answer is 2.
Answer: C
In a class, the average age of 42 boys is 12 years and the average of 28 girls is 10 years. what is the average age of the whole class?  Answers.
A) 11.2 Years	B) 12.6 Years	C) 13 Years	D) 13.5 Years	E) 14 Years

Solution: Total age of 70 students   (42X 12+28 X 10) = 784   11.2 Yearsverage = 784/70= 
784/70 = 56/5 = around 11.2
11.2 Years   11.2 Years)
Answer: A
A child crawls 20 ft towards north , turns right and crawls 30 ft, turns right again and crawls 35 ft. He turns left now and crawls 15 ft. He turns left again and crawls 15 ft . Finally he turns to his left to crawl another 15 ft. how far is he from his starting point and in which direction? Choose the correct choice:	A) 45 ft north-east	B) 30 ft east	C) 30 ft west	D) 15 ft west	E) None

Solution: Considering every move of a child straight one, if in (x,y) coordinates, starting point is (0,0), then given 6 moves can be represented as:   1) 20 ft. towards north ---> (0,20)   2) 30 ft. towards right ---> (30,20)   3) 35 ft. towards right ---> (30,-15)   4) 15 ft. towards left ---> (45,-15)   5) 15 ft. towards left ----> (45, 0)   6) 15 ft. towards left ----> (30, 0)   So child is at 30 ft. from his starting point towards east.   ANSWER:30 ft east
Answer: B
In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet? Choices:
A) 168.
B) 80.
C) 56.
D) 48.
E) 16.

Solution: ways to select one shelf = 2   ways to select one bed = 4   ways to select one of the following: a chair or a closet = 7+3= 
7+3 = 10
10   ways to select all of them together= 2*4*10= 
2*4*10 = 80
80   Hence, 80. is the answer.
Answer: B
In how many ways can the letters of the word SPHERICAL be arranged such that all the vowels always appear together? Options.
A) 9!*6!  B) 9!  C) 7!*3!  D) 9!*3!  E) 6!*3!

Solution: The 9 letters can be grouped into 6 consonants and one set of 3 vowels.   The number of ways to arrange 7 units is 7!   Then, for each arrangement, the 3 vowels can be arranged in 3! ways.   The total number of arrangements is 7!*3!   The answer is 7!*3!.
Answer: C
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 2.5 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?  Choose the correct choice from the following answers:	A) 5729	B) 5760	C) 2889	D) 3600	E) 2799

Solution: 1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 2.5= 
 24 * 60 * 2.5 = 3_600
3600.Answer: 3600
Answer: D
In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is : Choices.
A) 5 B) 6 C) 7 D) 10 E) 12

Solution: Let no of cows be x, no of hens be y.   So heads=x+y   Legs=4x+2y   Now, 4x+2y = 2(x+y)+ 14   2x = 14   x = 7.   ANSWER:7
Answer: C
Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
Pick.
A) 12
B) 16
C) 14
D) 13
E) 17

Solution: 1/20 + 1/30 = 1/12   1 + 1/3 = 4/3   1 --- 12   4/3 --- ?     4/3 * 12= 
  4/3 * 12 = 16
16 hrs.Answer: 16
Answer: B