MU-NLPC/Calc-aqua_rat huggingface dataset:
A number is to be multiplied by the fraction 4/5.But amit, by mistake multiplied it by 5/4 and obtained the number 81 more than the correct value.what was the original number?	Choose the correct choice from the following
A) 200	B) 240	C) 180	D) 120	E) 100

Solution: let the no. be x.   x*5/4 - x*4/5 =81. solving this we get 180   ANSWER:180
Answer: C
The ratio of the adjacent angles of a parallelogram is 6 : 9. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
Choose the correct answer: A) 168° B) 228° C) 156° D) 224° E) None of these

Solution: The measures of the adjacent angles of a parallelogram add up to be 180°   Given   So, 6x + 9x = 180°   Or, 15x = 180°   Or, x = 12°   Hence the angles of the parallelogram are 72° and 108°   Further it is given   We know sum of all the four angles of a quadrilateral is 360°   So, 5y + 6y + 7y + 12 y = 360°   Or, 5y + 6y + 7y + 12 y = 360°   Or, 30y = 360°   Or, y = 12°   Hence the angles of the quadrilateral are 60° , 72, 84° and 144°   Will be 72° + 84° = 156°   Answer : 156°72  + 84= 
72  + 84 = 156
156°   Answer : 156°
Answer: C
What is x if x + 2y = 10 and y = 3? Choose one.
A) 2  B) 4  C) 5  D) 8  E) 9

Solution: Substitute y by 3 in x + 2y = 10   x + 2(3) = 10   x + 6 = 10   If we substitute x by 4 in x + 6 = 10, we have 4 + 6= 
4 + 6 = 10
10. Hence   x= 4   correct answer 4
Answer: B
If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 7 (B + G) is ?
Pick:  A) more than 7  B) Less than 3  C) More than 3  D) Less than 1/3  E) none of these

Solution: Let number of boys = x   Let number of girls = y   Therefore x/y = B and y/x = G   7(B + G) = 7[(x/y) + (y/x)] = 7[(x2 + y2)/xy] > 7   more than 7NSWER:more than 7
Answer: A
10% of the inhabitants of village having died of cholera, a panic set in during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.	Pick:
A) 5000
B) 6000
C) 4000
D) 8000
E) 9000

Solution: Let the total number of orginal inhabitants be x.   ((75/100))*(90/100)*x)=4050 ==> (27/40)*x=4050   ==> x=((4050*40)/27)= 
((4050*40)/27) = 6_000
6000.   Answer 6000.
Answer: B
The cost of a Washing machine was $400 in 1985. In 2014, the cost had increased to $800. What was the percent increase in the cost of Washing machine? Choose one
A) 10
B) 40
C) 60
D) 200
E) 100

Solution: Increase = 800 - 400= 
800 - 400 = 400
400   % increase= 400*100/400= 
400*100/400 = 100
100%   Answer: option 100
Answer: E
A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 3%. What is the cost price? Choose the correct choice from the following choices
A) 1000	B) 2876	C) 1077	D) 2778	E) 2711

Solution: 90%   103%   --------   13% ---- 140   100% ---- ? => Rs.1077   Answer: 1077
Answer: C
At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party? Options
A) 384
B) 258
C) 215
D) 120
E) 72

Solution: Five times as many females as males --> F = 7M.   Three times as many adults as children --> (F + M) = 2C.   The number of people at the party = F + M + C = 2C + C = 3C.   The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C.   Answer: 215.
Answer: C
Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?	Choose the correct choice from the following.
A) 26,000  B) 83,20  C) 23,320  D) Data inadequate  E) 39,309

Solution: Answer: Option D   Explanation:   Let the original earnings of A and B be Rs. 4x and Rs. 7x.   New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x   New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4   6x:21x/4 = 8:7   This does not give x. So, the given data is inadequate.   Answer:Data inadequate
Answer: D
Village P’s population is 1150 greater than Village Q's population. If Village Q’s population were reduced by 200 people, then Village P’s population would be 4 times as large as Village Q's population. What is Village Q's current population?  Choices.
A) 600  B) 625  C) 650  D) 675  E) 700

Solution: P = Q+1150.   P=4(Q-200).   4(Q-200)=Q+1150.   3Q=1950.   Q=650.   The answer is 650.
Answer: C
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?  Choose one:
A) 18 B) 76 C) 24 D) 20 E) 12

Solution: Let the present ages of Sameer and Anand be 5x and 4x years respectively.   Then, (5x + 3)/(4x + 3) = 11/9   9(5x + 3) = 11(4x + 3) => x = 6   Anand's present age = 4x = 24 years.Answer:24
Answer: C
A and B invests Rs.6000 and Rs.12000 in a business. After 6 months, A withdraws half of his capital and B withdraws two-third of his capital. In what ratio should they share the profits at the end of the year?
Choose the correct choice from the following
A) 27:32  B) 25:32  C) 32:27  D) 27:29  E) 27:31

Solution: 27:32 : B   (6000*6)+(3000*6) : (12000*6)+(4000*6)   54000 : 96000   27 : 32   27:32nswer: 27:32
Answer: A
On 5th Mar, 2012 Monday falls. What day of the week was it on 5th Mar, 2011?
Options
A) Saturday	B) Sunday	C) Monday	D) Tuesday	E) Wednesday

Solution: Explanation:   5th Mar 2012 – 5th Mar 2011 = 52 weeks 1 day. So Mar 5th 2011 is behind one day = Sunday   Answer: Sunday
Answer: B
A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary? Options: A) 5000 B) 2999 C) 2878 D) 2990 E) 2771

Solution: Income = Rs. 100   Expenditure = Rs. 80   Savings = Rs. 20   Present Expenditure 80*(20/100) = Rs. 96   Present Savings = 100 – 96 =Rs. 4   100 ------ 4   ? --------- 200 => 5000   5000nswer: 5000
Answer: A
A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 30% melted chocolate and 70% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?  Answers.
A) 1.5
B) 2.14
C) 3
D) 4.5
E) 5

Solution: Yes, we assume that the mix is homogeneous. Otherwise, we will not be able to solve the question.   You have 15 cups of sauce with 30% chocolate. You also have unlimited amount of pure chocolate sauce. Now you need to mix these two in such a way that you get total 15 cups of sauce with 50% chocolate.   Using scale method:   w1/w2 = (100 - 50)/(50 - 30) = 5/2   w1 - Amount of 30% chocolate sauce   w2 - Amount of pure chocolate sauce   So for every 5/2 cups of 30% chocolate sauce, we need 2 cup of pure chocolate sauce. This will give us 7 cups of 50% chocolate sauce. But we need 15 cups of 50% chocolate sauce.   So we need to mix 5*15/7 = 12.5 cups of 40% chocolate sauce with 1*15/7 = 2.14 cups of pure chocolate sauce.   Answer (2.14)
Answer: B
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is: Choose the correct choice from the following answers:
A) 45m B) 50m C) 54m D) 72m E) 70m

Solution: Explanation:   2 kmph =	(	2 x5/18)m/sec =	5/9m/sec.   4 kmph =(4x5/18)m/sec =10/9m/sec.   Let the length of the train be x metres and its speed by y m/sec.   Then,	(x/y-5/9)=9and(x/y -	10/9)=10.   9y - 5 = x and 10(9y - 10) = 9x   => 9y - x = 5 and 90y - 9x = 100.   On solving, we get: x = 50.   Therefore Length of the train is 50 m.   ANSWER IS 50m
Answer: B
A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.  Choose the correct choice:	A) 9	B) 10	C) 7	D) 12	E) 13

Solution: 213ab may be written as   213ab = 21300 + 10a + b   When 213ab is divide by 100, the reminder is 10a + b. The only way for the remainder to be less that 10 is that a = 0. Hence the sum of the digits is   2 + 1 + 3 + 0 + b = 13   Solve for b   b = 7   correct answer 7
Answer: C
If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?
Select the correct option.
A) Rs 10  B) Rs 12  C) Rs 14  D) Rs 16  E) Rs 18

Solution: Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]   = [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400   = Rs. [(1/6)8(1/100)*8400] = Rs. 14.   ANSWER Rs 14 14
Answer: C
For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <4>*<2>?	Answers:	A) 60	B) 116	C) 360	D) 263	E) 478

Solution: Since <x></x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.   Hence <4> is the sum of all integers from 1 to  2*4</x>= 
 2*4 = 8
8 and <2> is the sum of all integers from 1 to  2*2= 
 2*2 = 4
4 --> <4>=36 and <2>=10 --> <3>*<2>=36*10= 
36*10 = 360
360.   Answer: 360.
Answer: C
If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/12 then b= ?
Choose the correct choice
A) -1/6  B) 1/6  C) 6  D) -6  E) 3

Solution: f(a) = -1/2 = -1/a, and thus a = 2   f(ab) = 1/12, and thus ab = -12   2b = -12   b = -6   The answer is -6.
Answer: D
The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $50,000, how much profit did the business make?
Pick
A) $80,000  B) $100,000  C) $120,000  D) $150,000  E) $200,000

Solution: Let P be the total profit.   P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 50000   P = $80,000   The answer is $80,000.
Answer: A
Using only the digits from 0 to 6 , how many 5 digit codes can be constructed, if the first digit can not be 4 and no digits is used more than once ?  Pick one:
A) 1080	B) 2160	C) 777	D) 720	E) 620

Solution: code can be contain zero,(ex 0122---, 0731---)   sw, we can consider 0 at first place.   so it should be  6*6*5*4*3= 
 6*6*5*4*3 = 2_160
2160   ANSWER:2160
Answer: B
A, Band C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?  Pick:
A) 7 days B) 8 days C) 9 days D) 10 days E) 11 days

Solution: (A+8 days)'s 1 day's work = 1/11+1/20 = 31/220   (A+C)'s 1 day's work = 1/11+1/55 = 6/55   work done in 2 day's = 31/220+6/55 = 55/220 = 1/4   1/4th work done in 2 days   work done= 4*2= 
4*2 = 8
8 days   ANSWER:8 days
Answer: B
L is a positive integer and 225 and 216 are both divisors of L. If L=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?  Choose the correct answer: A) 4 B) 5 C) 6 D) 8 E) 7

Solution: Lets make factorization of 225 and 216 ..   225 = 5 X 5 X 3 X 3 X 3   216 = 2 X 2 X 2 X 3 X 3 X 3   L would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2= 
3 + 3 + 2 = 8
8(8) (answer) ...
Answer: D
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?	Select:
A) 123600 m  B) 141600 m  C) 153600 m  D) 161600 m  E) 165600 m

Solution: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 1600 or x = 160.   Length = 480 m and Breadth = 320 m.   Area = (480 x 320) m2 = 153600 m   153600 m
Answer: C
If a and b are each greater than x and y, which of the following must be true?
I. ab > xy
II. |a| + |b| > |x| + |y|
III.a + b > x + y	Choose the correct choice from the following options:
A) I only B) II only C) I and II D) I and III E) I, II and III

Solution: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.   II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.   III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.   Answer: II only.
Answer: B
If a boat goes 5 km upstream in 50 minutes and the speed of the stream is 3 kmph, then the speed of
the boat in still water is	Answers: A) 9 kmph B) 13 kmph C) 14 kmph D) 15 kmph E) None of these

Solution: Explanation:   Rate upstream = (5/50)*60= 
(5/50)*60 = 6
6 kmph.   Speed of stream= 3 kmph.   Let speed in still water is x km/hr   Then, speed upstream = (x ï¿½3) km/hr.   x-3 = 6 or x = 9 kmph   9 kmphnswer: 9 kmph
Answer: A
The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even? Choices
A) a  B) b  C) a + b  D) ab - a  E) a + b^2

Solution: ab+a is odd   a and b are integers   If a were even "ab+a" would be even despite any value of b.   B can't be odd, so "b" must be even.   Ans : b
Answer: B
The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?	Choose one
A) 1987 sq m  B) 7867 sq m  C) 1897 sq m  D) 4783 sq m  E) 4312 sq m

Solution: Let the radii of the smaller and the larger circles be s m and l m respectively.   2∏s = 264 and 2∏l = 352   s = 264/2∏ and l = 352/2∏   Difference between the areas = ∏l2 - ∏s2   = ∏{1762/∏2 - 1322/∏2}   = 1762/∏ - 1322/∏   = (176 - 132)(176 + 132)/∏   = (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m   Answer:4312 sq m
Answer: E
If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE Select the correct option.
A) 110 B) 112 C) 114 D) 118 E) 120

Solution: Total no'of arrangements 5P5 = 5! = 120   no'of arrangements start with AE = 1 × 6 = 6   no'of arrangements which do not start with AE = 120 - 6= 
120 - 6 = 114
114.   114
Answer: C
What is the difference between the C.I. on Rs. 8000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?  Pick: A) s.3.26 B) s.2.08 C) s.2.02 D) s.2.83 E) s.2.42

Solution: C.I. when interest is compounded yearly   = [8000 * (1 + 4/100) * (1 + (1/2 * 4)/100]   = 8000 * 26/25 * 51/50 = Rs. 8486.4   C.I. when interest is compounded half-yearly   = [8000 * (1 + 2/100)2]   = (8000 * 51/50 * 51/50 * 51/50)   = Rs. 8489.66 Difference   = (8489.66 - 8486.4   = Rs.3.26.   s.3.26nswer: s.3.26
Answer: A
If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum V of the 3 greatest of these temperatures, in degrees Fahrenheit, could be Choose one.
A) 6x  B) V=4x  C) V=5x/3  D) 3x/2  E) 3x/5

Solution: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)   But what about C,D,E? Any ideas why these could be wrong?   Note that we have 5positivetemperatures.   Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<sum<5x --=""> only option B fits.   Answer: V</sum<5x>=4x.
Answer: B
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Choose the correct choice from the following answers
A) 6  B) 7  C) 8  D) 5  E) 3

Solution: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.   Part to be emptied = 2/5   Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15   1/15 : 2/5 :: 1 : x   x = (2/5 * 1 * 15)= 
(2/5 * 1 * 15) = 6
6 min.   So, the tank will be emptied in 6 min. 6nswer: 6
Answer: A
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?	Choose the correct choice:
A) 9/10	B) 6/10	C) 2/10	D) 3/10	E) 5/10

Solution: Explanation:   Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20   Let E = event of getting a multiple of 4 or 15   =multiples od 4 are {4, 8, 12, 16, 20}   And multiples of 15 means multiples of 3 and 5   = {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}.   = the common multiple is only (15).   => E = n(E)= 6   Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10.   Answer is 3/10
Answer: D
There are 2 couples. If they will sit 4 chairs in a row such that each couple sits side by side, how many possible cases are there?	Choose the correct option.
A) 120  B) 8  C) 1,200  D) 2,460  E) 3,840

Solution: Tie the couples. Then we have 2 persons that have to be arranged in 2 places. 2! ways.   Now the couples can change position with each other. 2! ways.   2! * (2!)^2 = 2 *4= 
2 *4 = 8
8   Answer is 8.
Answer: B
A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?	Choices: A) 10 min B) 20 min C) 30 min D) 40 min E) 60 min

Solution: Sol. 40 ministance between Ramgarh and 40 minevgarh =(50*44)/60=110/3   Average speed of the bus is increased by 5 km/hr then the   speed of the bus = 55 km/hr   Required time = 110/3*60/55= 
110/3*60/55 = 40
40 min   40 min
Answer: D
A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream. Choose the correct choice from the following options.
A) 2.5 km/hr  B) 12.5 km/hr  C) 1 2.6 km/hr  D) 22.5 km/hr  E) 22.6 km/hr

Solution: Given that, time taken to travel upstream = 2 × time taken to travel downstream   When distance is constant, speed is inversely proportional to the time   Hence, 2 × speed upstream = speed downstream   Let speed upstream = x   Then speed downstream = 2x   we have, 1/2(x+2x) = speed in still water   ⇒1/2(3x)=7.5   3x = 15   x = 5   i.e., speed upstream = 5 km/hr   Rate of stream = 1/2(2x−x)=x/2=5/2= 
5/2 = 5/2 = around 2.5
2.5 km/hr   2.5 km/hrnswer is 2.5 km/hr
Answer: A
The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations Q of soloists can appear in the liner notes?  Choose the correct choice from the following choices:
A) 5!	B) 10!/(5!5!)	C) 10!/5!	D) 10!	E) 10!*5!

Solution: Total Soloists to choose from = 10   Soloist Required = 5   Question : How many different combinations Q of soloists can appear in the liner notes?   The language of the question clearly mentions that only the combinations need to be calculated   i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)   Method-1:   Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)   Method-2:   No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6   Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,   Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)   Answer: Option 10!/(5!5!)
Answer: B
What is the place value of 0 in the numeral 2074?	Options.
A) 0	B) 1	C) 2	D) 5	E) 6

Solution: Note : The place value of zero (0) is always 0. It may hold any place in a number,   its value is always 0.   0
Answer: A
A boat running downstream cover a distance of 24km in 6 hr while covering the same distance upstream it takes 8 hr then the speed of the boat still in the water  Choose the most appropriate option.
A) 4.5km/hr  B) 9.5km/hr  C) 3.5km/hr  D) 25.6km/hr  E) 12.3km/hr

Solution: rate down stream=(24/6)= 
(24/6) = 4
4kmph   rate upstream=(24/8)= 
(24/8) = 3
3kmph   speed still water=1/2(4+3)kmph=3.5km/hr   Answer(3.5km/hr)
Answer: C
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 12, how many more dollars, in terms of x, will it cost per person? Pick
A) x/6 B) x/16 C) x/40 D) 3x/40 E) 3x/80

Solution: Choose x as a multiple of 16, I chose 64:   So for 10 people, that's 6.4 each and for 12 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is x/40.
Answer: C
A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500?
Select
A) 1991 B) 2991 C) 3991 D) 4521 E) 5991

Solution: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009.   Required sale = Rs. [ (4500 x 6) - 24009 ]   = Rs. (27000 - 24009)   = Rs. 2991   Answer: Option 2991
Answer: B
On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $5, the second $500, and the third $5000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. What is the probability that a contestant will win more than $5000? Choose one:
A) 1/9
B) 4/6
C) 3/6
D) 1/2
E) 1/6

Solution: Let's call the boxes that contain $5, $500, and $5000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.   We want to know the probability of winning more than $5000. Notice that if the distribution of keys is:   Box A = Key B   Box B = Key A   Box C = Key C   then the contestant wins exactly $5000, not more than $5000. The only configuration that leads to winning more than $1000 is:   Box A = Key A   Box B = Key B   Box C = Key C   i.e., getting all three keys correct. That's the only way to be more than $5000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?   Well, for a set of three items, the number of possible permutations is 3! = 3*2*1= 
3*2*1 = 6
6.   Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is   Probability= 1/6   Answer: 1/6
Answer: E
Working simultaneously and independently at an identical constant rate, 30 machines of a certain type can produce a total of x units of product P in 3 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 10 days?	Select.
A) 41	B) 44	C) 45	D) 47	E) 50

Solution: The rate of 30 machines is rate=job/time=x/3 units per day --> the rate of 1 machine 1/30*(x/3)=x/90 units per day;   Now, again as {time}*{combined rate}={job done}   then 10*(m*x/90)=5x --> m=45.   Answer: 45.
Answer: C
Five different books (A, B, C, D and E) are to be arranged on a shelf. Books A , B ,C and D ARE to be arranged first and second starting from the right of the shelf. The number of different orders in which books E may be arranged is  Pick one:	A) 5!	B) 6!	C) 8!	D) 1!	E) 12!

Solution: Solution   Since books A, B,C and D is arranged first and second, only book E will change order. Therefore it an arrangement problem involving 1 items and the number of different order is given by   1!   Answer 1!
Answer: D