MU-NLPC/Calc-aqua_rat huggingface dataset:
It would take one machine 7 hours to complete a large production order and another machine 6 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order? Options:  A) A 13/42  B) B 12/42  C) C 11/42  D) D 10/42  E) E 42/13

Solution: The rate of the first machine is 1/7 job per hour;   The rate of the second machine is 1/6 job per hour;   Thus, the combined rate of the machines is 1/7+1/6=13/42 job per hour, which means that it takes 1/(13/42)=42/13 hours both machines to do the job.   Answer: D 10/42.
Answer: D
If each term in the sum W=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
Choose the correct choice.
A) 38
B) 39
C) 40
D) 41
E) 42

Solution: Min value of 'n' can be 10 i.e 4*22+6*12 =W=> 22+22+22+22+2+2+2+2+2+2= 
22+22+22+22+2+2+2+2+2+2 = 100
100   Since we don't have 10 in the options proceed further, (10-1)+22/2=> 20 digits, which is again not in the options    (20-1) + 22/2= 
 (20-1) + 22/2 = 30
30 digits ( not in options)   (30-1) + 22/2= 
(30-1) + 22/2 = 40
40 digits   Hence 40.
Answer: C
A furniture dealer purchased a desk for $120 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?  Choose the correct choice from the following options
A) 70
B) 66.67
C) 65
D) 75
E) 80

Solution: Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $150 but instead, 40% of Selling price which is obtained by adding mark up to $120.   So if selling price is S,   120 + 40% of S = S   S = 200   Profit = 80 which is calculated on cost price in % terms. So 80/120 * 100 = 66.67% is profit.   66.67
Answer: B
In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
Choose the correct option:
A) 975	B) 1150	C) 1175	D) 1243	E) 1525

Solution: Failed in 1st subject = 34*2500/100= 
34*2500/100 = 850
850   Failed in 2nd subject= 42*2500/100= 
42*2500/100 = 1_050
1050   Failed in both= 15*2500/100= 
15*2500/100 = 375
375   Failed in 1st subject only= 850-375= 
850-375 = 475
475   Failed in 2nd subject only= 1050-375= 
1050-375 = 675
675   Passed in either subject but not in both= 675+475= 
675+475 = 1_150
1150   Answer is 1150
Answer: B
If sy > 0 and yz < 0, which of the following must be negative:
Choose the correct choice from the following choices.
A) syz	B) sy(z^2)	C) s(y^2)z	D) x(y^2)(z^2)	E) (x^2)(y^2)(z^2)

Solution: sy > 0 means that sy is positive.   yz < 0 means that yz is negative.   s(y^2)z = (sy)(yz) = positive*negative = negative. Thus option s(y^2)z is always negative.
Answer: C
The water level in a reservoir has been dropping at the rate of 12 inches per day. Exactly 5 days ago, the water level was at w inches. What will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same?
Choose the correct answer:
A) w − 108	B) w − 56	C) w − 14	D) w + 14	E) w + 126

Solution: Drop=12 inches/day   5 Days ago=w, means now it's equal w-60 and in 4 days = w-60-48=w-108   w − 108nswer w − 108
Answer: A
A cyclist rides a bicycle 8 km at an average speed of 11 km/hr and again travels 11 km at an average speed of 8 km/hr. What is the average speed for the entire trip?	Choose the correct choice from the following options
A) 8.58
B) 8.76
C) 9.04
D) 9.12
E) 9.25

Solution: distance = 19 km   time = 8/11 + 11/8 = (64 + 121) / 88 = 185 / 88 hours   average speed = (19 * 88) / 185 = 9.04 km/h   The answer is 9.04.
Answer: C
A boy was asked to find 7/9 of a x. But he divided the x by 7/9, Thus he got 32 more than theanswer. Find the x.  Answers:
A) 60  B) 41  C) 51  D) 63  E) 56

Solution: x/7/9 = 9x/7 = 32 + y   Actualy he should do 7x/9 = y   y = (9x/7) - 32   y = (9x - 224)/7   (9x - 224)/7 = 7x/9   81x - 2016 = 49x   81x - 49x = 2016   32x = 2016   x = 63   63
Answer: D
Of the 120 passengers on Flight 750, 45% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?	Answers
A) 44 B) 48 C) 46 D) 52 E) 56

Solution: Number of passengers on flight = 120   Number of female passengers= .45*120= 
.45*120 = 54
54   Number of passengers in first class= (10/100)* 120= 
(10/100)* 120 = 12
12   Number of passengers in coach class= (90/100)* 120= 
(90/100)* 120 = 108
108   Number of male passengers in first class= 1/3 * 12= 
1/3 * 12 = 4
4   Number of female passengers in first class= 12-4= 
12-4 = 8
8   Number of female passengers in coach class= 54 - 8= 
54 - 8 = 46
46   Answer 46
Answer: C
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is Choose the correct choice from the following choices:	A) 1 hour	B) 2 hour	C) 3 hour	D) 4 hour	E) 5 hour

Solution: Let the duration of the flight be x hours.   Then, 600/x - 600/0.5x = 200   --> 600/x - 1200/(2x+1) = 200   --> x(2x + 1) = 3   --> 2x^2 + x - 3 (2  + 1)= 
(2  + 1) = 3
3   --> 2x^2 + x - 3= 0   --> (2x + 3)(x - 1) = 0   --> x = 1 hr.   1 hournswer : 1 hour.
Answer: A
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Choose the correct choice from the following answers:	A) 12	B) 77	C) 48	D) 54	E) 11

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 1.25 = 2 km = 2250 m.   Required time = 2250 * 3/125= 
2250 * 3/125 = 54
54 sec.   Answer: 54
Answer: D
A school has received 40% of the amount it needs for a new building by receiving a donation of $600 each from people already solicited. People already solicited represent 40% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?	Choose the correct choice from the following options:
A) $200
B) $300
C) $100
D) $400
E) $250

Solution: Let us suppose there are 100 people. 40% of them donated $16000 ( 400 * 40 )   $16000 is 40% of total amount.   So total amount = 16000 * 100/40   Remaining amount is 60% of total amount.   60% of total amount = 16000 * (100/40) * (60/100)= 
16000 * (100/40) * (60/100) = 24_000
24000   This amount has to be divided by 60 ( remaining people are 60 )   So per head amount is  24000 / 60= 
 24000 / 60 = 400
$400   ANSWER:$400
Answer: D
x, a, z, and b are single digit positive integers. x = 1/7 a. z = 1/7 b. (10a + b) – (10x + z) could NOT equal	Select the correct option:
A) 30	B) 36	C) 42	D) 63	E) 66

Solution: a=7x , b =7z therefore(7x.10+7z) - (10x +z) = (7-1) (10x+z) =6.(10x+Z)   number should be divisible by 6   63
Answer: D
The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places) Select.
A) Rs.20043.94	B) Rs.18654.81	C) Rs.20264.46	D) Rs.19612.41	E) None of these

Solution: Let the rate of interest be R% p.a.   (49500)(3)(R)/100 = 17820   495R = 5940   R = 12   CI on Rs.49500 at 12% p.a. for three years   = 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94   when rounded off to two decimal places.   Rs.20043.94NSWER:Rs.20043.94
Answer: A
Two trains are moving in opposite directions @60kmph and 90kmph. Their length are 1.10km and 0.9km. The time taken by the slower train to cross faster train in second is? Select the correct option
A) 25sec B) 30sec C) 48sec D) 36sec E) 40sec

Solution: Relative speed = 60+90= 
60+90 = 150
150*5/18= 125/3 m/s   Distance covered = 1.10+0.9= 
1.10+0.9 = 2
2km= 2000m   Required time= 2000*3/125= 
2000*3/125 = 48
48sec   Answer is 48sec
Answer: C
A man buys an article for $15. and sells it for $20. Find the gain percent?	Select the correct option
A) 33 1/3%	B) 50 1/3%	C) 20 1/3%	D) 15%	E) 30%

Solution: C.P. = $15   S.P. = $20   Gain = $5   Gain% = 5/15 *100 = 33 1/3%   33 1/3%nswer is 33 1/3%
Answer: A
A right circular cylinder has a height of 24 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? Choose the correct option.
A) 500(π – 3) B) 500(π – 2.5) C) 500(π – 2) D) 600(π – 1.5) E) 500(π – 1)

Solution: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?   The square base has sides of sqrt(50) due to the 45-45-90 triangle   24*25*pi - 15*sqrt(50)^2   =600(π – 1.5)   D. 500(π – 1.5)
Answer: D
Two workers can type two pages in two minuets then how many persons can type 18 pages in 6 minuets
Choose the correct choice:	A) 2Workers	B) 3Workers	C) 6Workers	D) 7Workers	E) 8Workers

Solution: 2Worker 2pages 2minutes   1Worker 1page 2minutes   1worker 18pages 36minutes   Therefore to reduce the time by 6 times, workers should be increased by 6 times   ANSWER:6Workers
Answer: C
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 6 letters in its codes, and all letters can be repeated in any one code?  Choose the correct choice from the following choices:
A) A.321272406 B) B.308915776 C) C.11881376 D) D.456976 E) E.17576

Solution: The no of ways in which the company can make codes of 1 letter : 26   # for 2 letters :   26*26= 
  26*26 = 676
676   # for 3 letters :   26 * 26*26= 
  26 * 26*26 = 17_576
17576   # for 4 letters :   26 * 26*26*26= 
  26 * 26*26*26 = 456_976
456976   # for 5 letters :   26 * 26*26*26*26= 
  26 * 26*26*26*26 = 11_881_376
11881376   # for 6 letters :   26 * 26*26*26*26*26= 
  26 * 26*26*26*26*26 = 308_915_776
308915776   The total : By adding all of them , 26+676+17576+456976+11881376+308915776=321272406   A.321272406
Answer: A
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? Choose the correct choice from the following answers.
A) 1178 B) 144 C) 66 D) 8 E) 55

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 6= 
 24 * 6 = 144
144.   Answer: 144
Answer: B
If the sum of 3 consecutive integers is x, which of the must be true?
I. x is even
II. x is odd
III. x is a multiple of 3  Choose the correct choice from the following choices
A) I only
B) II only
C) III only
D) I and III
E) II and III

Solution: sum of 3 consecutive integers   = (n) + (n+1) + (n+2)   =3n + 3   = odd + odd = even   = 3(n+1) = divisible by 3   Hence, x is even and divisible by 3.   Answer: I and III
Answer: D
A and B start from Opladen and Cologne respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between Opladen and Cologne, A and B proceed to their destinations of Cologne and Opladen respectively. A reaches Cologne 40 minutes after the two meet and B reaches Opladen 80 minutes after their meeting. How long did A take to cover the distance between Opladen and Cologne?  Pick
A) 1 hour	B) 1 hour 10 minutes	C) 2 hours 30 minutes	D) 1 hour 20 minutes	E) 2 hours 10 minutes

Solution: v1 and V2 are speeds.   v1.t /80 = v2   v2.t/40 = v1   v1/v2 = 2   which train A would 80. 1/2 mins to cover the same distance     40 + 40= 
  40 + 40 = 80
80 mins (ans 1 hour 20 minutes)
Answer: D
The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?	Choose the correct answer:
A) 8
B) 9
C) 7
D) 5
E) 2

Solution: 3x + 5x + 7x = 45   x =3   3x = 9   Answer: 9
Answer: B
A certain bridge is 4,024 feet long. Approximately how many minutes does it take to cross this bridge at a constant speed of 40 miles per hour? (1 mile = 5,280 feet)
Choose the correct choice from the following answers:
A) 1  B) 2  C) 4  D) 6  E) 7

Solution: Distance: 4024 feet. This is (4024/5280) miles = 0.76 miles   Speed: 40 miles per hour   Time: (Distance / Speed) (0.76/40) {This will come in Hours}. Multiply by 60 to get answer in minutes. It is 1.14 minutes.   1nswer to be 1 minutes.
Answer: A
An investment of Rs.800 doubled in 4 years when compounded annually. How many more years will it take to get another Rs.1600 compound interest?
Choices:
A) 1 years
B) 6 years
C) 4 years
D) 5 years
E) 3 years

Solution: Explanatory Answer   Rs.800 invested in compound interest becomes Rs.1600 in 4 years.   The amount will double again in another 4 years.   i.e., the amount will become Rs.1600 in another 4 years.   So, to earn another Rs.1600 interest, it will take another 4 years.   Answer 4 years
Answer: C
3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?	Choose one:
A) 50 B) 40 C) 30 D) 20 E) 10

Solution: Explanation :   Work done by 4 men and 6 women in 1 day = 1/8   Work done by 3 men and 7 women in 1 day = 1/10   Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as   4m + 6w = 1/8	---(1)   3m + 7w = 1/10	---(2)   Solving equation (1) and (2) , we get m=11/400 and w=1/400   Amount of work 10 women can do in a day = 10 × (1/400) = 1/40   Ie, 10 women can complete the work in 40 days   Answer : Option 40
Answer: B
What is the probability of getting exactly 2 heads in a single throw of five fair coins?  Choices
A) 1/4  B) 3/8  C) 3/16  D) 5/16  E) 11/32

Solution: One possible case is HHTTT.   P(HHTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32   There are 5C2 = 10 possible cases.   P(2 heads) = 10*1/32 = 5/16   The answer is 5/16.
Answer: D
If −y ≥ x, and −x < −6, then which of the following must be true?	Choose the correct choice from the following answers.
A) y = −6  B) y > −6  C) −y > 6  D) y ≤ −6  E) y ≥ −6

Solution: −y ≥ x, and −x < −6   y <= -x < -6   As '-x' is less than '-6' and Y is less than or equal to '-x'   we have y < -6 which is similar to -y > 6.   −y > 6) -y>6
Answer: C
Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 8100
interest only for the period. The principal amount borrowed by her was  Pick.
A) Rs. 22500 B) Rs. 10000 C) Rs. 15000 D) Rs. 20000 E) None of these

Solution: Explanation :   Principal = Rs. (100×8100 / 12×3)   => Rs. 22500.   Rs. 22500nswer : Rs. 22500
Answer: A
Johnny makes $4.75 per hour at his work. If he works 6 hours, how much money will he earn?	Options
A) $30
B) $54
C) $28.50
D) $12
E) $9.60

Solution: 4.75*6=28.50. Answer is $28.50.
Answer: C
A man spends 3/5 of his expenditure on house rent,2/5 of his expenditure on food and 1/6 of his expenditure on conveyence.if he spent total 12000 rs.,find his expenditure on food.
Pick one
A) 4800 B) 4000 C) 3500 D) 7500 E) 2800

Solution: expenditure=12000 rs.   expenditure on food =12000*2/5= 
12000*2/5 = 4_800
4800 rs.   answer 4800
Answer: A
The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.50, in which year will commodity X cost 90 cents more than the commodity Y?	Options
A) 2010	B) 2011	C) 2012	D) 2013	E) 2014

Solution: The cost of commodity X increases by 10 cents per year relative to commodity Y.   The price of X must gain 30 + 90 = $1.20 cents on commodity Y, which will take 12 years.   The answer is 2013.
Answer: D
A began business with 12500 and is joined afterwards by B with 25000. When did B join, if the profits at the end of the year are divided equally?  Choices.
A) 8 months
B) 9 months
C) 6 months
D) 5 months
E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 12500 : (12 – x) × 25000   or 12 : 2(12 – x)   Since profit is equally divided so   12 = 2(12 – x) or x = 6. Thus B joined after 8 months.   Answer 6 months
Answer: C
The area of a square is equal to seven times the area of a rectangle of dimensions 25 cm * 343 cm. What is the perimeter of the square? Choose the correct choice from the following:
A) 810 cm
B) 800 cm
C) 980 cm
D) 718 cm
E) 860 cm

Solution: Area of the square = s * s = 7(343 * 25)   => s = 5 * 7 * 7= 
5 * 7 * 7 = 245
245 cm   Perimeter of the square= 4 * 245= 
4 * 245 = 980
980 cm.   Answer: 980 cm
Answer: C
A cistern is normally filled in 4 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in? Choose the most appropriate option.
A) 33 B) 88 C) 40 D) 99 E) 12

Solution: 1/4 - 1/x = 1/6   x = 12   Answer: 12
Answer: E
Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?  Choose the most appropriate option:
A) 120  B) 126  C) 252  D) 1200  E) 1260

Solution: My ans is 10C3 = 120   120
Answer: A
A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?  Select the correct option:
A) Rs.10000	B) Rs.12800	C) Rs.6000	D) Rs.8000	E) Rs.13000

Solution: 16*8: x*4 = 5:2   x = 12.8 => Rs.12800   ANSWER:Rs.12800
Answer: B
On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.5, what is the probability that Malachi will return home at the end of the day on the following Monday?
Choose the correct choice from the following answers
A) 0.008
B) 0.125
C) 0.128
D) 0.512
E) 0.64

Solution: Re-phrasing the question:   What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain   Probability of rain = 0.5   Therefore, probability of no rain = 0.5   0.5*0.5*0.5= 
0.5*0.5*0.5 = 0.125
0.125   Hence 0.125
Answer: B
If 12 : 18 :: x : 9, then find the value of x  Choose the correct choice.
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Explanation:Treat 12:18 as 12/18 and x:9 as x/9, treat :: as = So we get 12/18 = x/9=> 18x = 108=> x = 6 Option 6
Answer: C
A reduction of 21% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg? Choose the correct choice from the following choices:
A) s.2.66
B) s.2.4
C) s.2.5
D) s.2.2
E) s.2.1

Solution: 100*(21/100)= 
100*(21/100) = 21
21 --- 10   ? --- 1=> Rs.2.1   100 --- 79   ? --- 2.1 => Rs.2.66   s.2.66nswer:s.2.66
Answer: A
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?	Select the correct option
A) 7 B) 8 C) 9 D) 6 E) 2

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer: 8
Answer: B
The product of x and y is a constant. If the value of x is increased by 50%, by what percentage must the value of y be decreased?
Choose the most appropriate option
A) 50%	B) 40%	C) 33 1⁄3%	D) 25%	E) 12 1⁄2%

Solution: Product of x and y = xy   If the value of x is increased by 50% , value of y needs to be = xy/(1.5 x ) = 2/3 y   Decrease in value of y = y - 2/3 y = 1/3 y   % decrease in value of y = (1/3 y)/y * 100%   =33 1⁄3%   Answer 33 1⁄3%
Answer: C
The average of marks obtained by 120candidates was 35. If the avg of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the no.of candidates who passed the examination is? Choose the correct choice
A) 50 B) 80 C) 100 D) 110 E) 130

Solution: Let the number of candidate who passed = y   Then, 39y + 15(120 - y) =120 x 35   ⇒ 24y= 4200 -1800= 
4200 -1800 = 2_400
2400 / 24= 
2400 / 24 = 100
100   100
Answer: C
If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,710 minutes earlier? (Assume standard time in one location.)
Choices:
A) 6:22
B) 6:24
C) 6:27
D) 6:30
E) 6:32

Solution: 6:27minus 2,880,710in any way must end with 7, the only answer choice which ends with 7 is C.   Answer: 6:27.
Answer: C
The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.60 per metre.	Select.
A) 2399 B) 3888 C) 2999 D) 5808 E) 6072

Solution: Explanation:   Area = (13.86 x 10000) sq.m = 138600 sq.m   Circumference =   Cost of fencing = Rs. (1320 x 4.60) = Rs. 6072.   Answer: 6072) 6072
Answer: E
The average of five results is 46 and that of the first four is 45. The fifth result is? Choose the correct choice.
A) 50  B) 88  C) 77  D) 66  E) 51

Solution: 5 * 46 – 4 * 45   = 50   50nswer: 50
Answer: A
By selling a house for Rs.45000, it was found that 1/2 of the outlay was gained, what ought the selling to price to have been in order to have lost 2 p.c?
Choose the correct choice from the following options:
A) 38020  B) 38000  C) 38028  D) 29400  E) 38192

Solution: CP + CP/2 = 45000   CP = 30000   SP = 30000*(98/100)= 
30000*(98/100) = 29_400
29400   Answer:29400
Answer: D
A is a set containing 8 different positive odd numbers. B is a set containing 7 different numbers, all of which are members of A. Which of the following statements CANNOT be true?	Choose the correct choice from the following
A) The range of B is even.	B) The mean of A is even.	C) The mean of B is even.	D) The range of A is equal to the range of B.	E) The median of B is equal to the mean of B.

Solution: Given: A is a set containing 8 different positive odd numbers   Easily inferred: B is a set containing 7 differentoddnumbers   (A) The range of B is even. - Always even, since it is a difference of two odd numbers   (B) The mean of A is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number   (C) The mean of B is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.   (D) The range of A is equal to the range of B.   (E) The median of B is equal to the mean of B   Option The mean of B is even..
Answer: C
Find unit digit of N when N = 63^1!+2!+...+63! + 18^1!+2!+...+18! + 37^1!+2!+...37!	Select
A) 2  B) 4  C) 6  D) 8  E) 0

Solution: 3,8 and 7 have a power cycle of 4, i.e. the units digit in each case will repeat after every 4th power.   For eg : 3^1 = 3, 3^2 = 9 , 3^3 = 27 , 3^4 = 81, 3^5 = 243   All the powers given(1!+2!+....), are multiples of 4. It is so because the last 2 digits of the total sum will be 00,for each one of them, which make them divisible by 4.   Thus, the given problem boils down to 3^4+8^4+7^4=1+6+1= 
1+6+1 = 8
8   Thus, the units digit is 8.   ANSWER:8
Answer: D