MU-NLPC/Calc-aqua_rat huggingface dataset:
A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.  Choose the correct choice from the following choices:
A) 110 meter
B) 120 meter
C) 100 meter
D) 90 meter
E) 105 meter

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 6= 
  (50/3) * 6 = 100
100 meter   Answer:100 meter
Answer: C
Two cubes of their volumes in the ratio 64 : 343. The ratio of their surface area is:  Answers.
A) 1.5:5 B) 2:5 C) 3:5 D) 1:5 E) 4:7

Solution: The ratio of their surface area is   64 : 343   4 : 7   Answer is 4:7.
Answer: E
A person took some amount with some interest for 4 years, but increase the interest for 1%, he paid Rs.160/- extra, then how much amount he took? Answers:
A) Rs.5500/-	B) Rs.6000/-	C) Rs.4000/-	D) Rs.7000/-	E) None of these

Solution: Explanation:4 years = Rs.160/-year = 160/4Rate of Interest = 1%100/1% × 160/4 = Rs.4000/-P = Rs.4000/- Answer: Option Rs.4000/-
Answer: C
A shopkeeper sold an article at $100 with 10% profit. Then find its cost price?	Pick one
A) $120  B) $100  C) $91  D) $72  E) $69

Solution: cost price = selling price *100/(100+profit)   C.P. = 100*100/110 = $91(approximately)   Answer is $91
Answer: C
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Answers:
A) 2
B) 3
C) 3.5
D) 4
E) 4.5

Solution: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3   All the three pipes together will fill the tank in 3 hours.   ANSWER 3
Answer: B
The difference between the place values of 8 and 3 in the number 587435 is Answers.
A) 75200  B) 79970  C) 75460  D) 24580  E) None

Solution: Sol.= (Place value of 8) – (place Value of 3)= (80000 - 30)= 
(80000 - 30) = 79_970
79970 Answer 79970
Answer: B
Car Dealership X, the total profit from sales increased by 10 percent over the previous years, while the number of cars sold decreased by 10 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year. Choose the correct choice from the following choices:
A) 18% B) 20% C) 22% D) 23% E) 25%

Solution: Let Profit be x and cars sold be y   Originally Profit/22%ar = x/y   Now it is 1.1x / 0.9 y = 11/9 (x/y)   Increase in profit per car = ((2/9) (x/y)) / (x/y) * 100 = 22.22%   Answer = 22%
Answer: C
At Parkins gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class? Options.
A) 20  B) 24  C) 36  D) 48  E) 96

Solution: We are given that Parkins gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:   G/8 = integer and G/12 = integer   This means that G is a multiple of both 8 and 12.   We are asked to determine the lowest number of students in the class, or the lowest value for variable “G”. Because we know that G is a multiple of 8 and of 12, we need to find the least common multiple of 8 and 12. Although there are technical ways for determining the least common multiple, the easiest method is to analyze the multiples of 8 and 12 until we find one in common.   Starting with 8, we have: 8, 16, 24, 32   For 12, we have: 12, 24   For the multiples of 12, we stopped at 24, because we see that 24 is also a multiple of 8. Thus, 24 is the least common multiple of 8 and 12, and therefore we know that the lowest possible number of students in the gym class is 24.   Answer 24.
Answer: B
In a 1300 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?  Choose the correct choice.
A) 65 sec.	B) 50 sec	C) 25 sec	D) Data not sufficient	E) None of these

Solution: Speed of Shiny = 50/ 10= 
50/ 10 = 5
5m/s   Time taken by shiny to complete the race is B= 1300/5= 
1300/5 = 260
260 sec.   Time taken by Baley to complete the race is D= 1300/4= 
1300/4 = 325
325 sec.   Hence, D-B= 65 sec   65 sec.NSWER:65 sec.
Answer: A
If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before? Choose the correct choice from the following choices
A) 11 1/0%
B) 11 1/5%
C) 11 1/9%
D) 11 2/9%
E) 11 1/4%

Solution: 100 – 10 = 90   90------10   100------? => 11 1/9%   Answer: 11 1/9%
Answer: C
If a man buys 40 purse for $110 and sold them for $3 dollars each determine his gain.
Pick one
A) $ 20
B) $ 10
C) $ 30
D) $ 5
E) $ 25

Solution: Cost of 40 purse = $110   Sold each purse for $3   So he sold 40 purse for $(40 × 3) = $120   Loss = $(120 – 110) = $10   Therefore, gain = $ 10.   Answer:$ 10
Answer: B
How many such letter-pairs are there in the word BONAFIDE having same number of letters left between them as they have in the series?	Choose the correct choice from the following options:	A) 2	B) 3	C) 4	D) 1	E) None of these

Solution: BF,NO,AD,ANone of these,DF,DNone of these 6 POSSIBILITNone of theseS ARNone of these THNone of theseRNone of these   so none of these   ANSWNone of theseR:None of these
Answer: E
A rectangular field is 72 yards long and 33 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.)	Choices.
A) 630 ft
B) 830 ft
C) 430 ft
D) 828 ft
E) 830 ft

Solution: 72 + 33 + 72 + 33= 
72 + 33 + 72 + 33 = 210
210 yds. for   outside of field.   33 + 33= 
33 + 33 = 66
66 yds. for dividing sections    210+ 66= 
 210+ 66 = 276
276 yds. of fencing   276 x 3= 828 ft. of fencing   correct answer 828 ft
Answer: D
Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.	Answers:	A) 15km/hr	B) 6 km/hr	C) 4.28 km/hr	D) 9 km/hr	E) 4.12 km/hr

Solution: Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.   The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.   Because we are dealing with a round trip here, Winson would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour   3.75km/52.5 = .07 km/minute   .07km/minute*60 minutes = 4.28 km/hour.   Answer: C. 4.28 km/hr
Answer: C
In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is? Choose the correct choice:
A) 82%  B) 58%  C) 52%  D) 22%  E) 42%

Solution: Total = 100   T= 40 NT= 60   40*(60/100)= 
40*(60/100) = 24
24 60*(40/100)=24   24 + 24= 
24 + 24 = 48
48=> 100 - 48= 
100 - 48 = 52
52%   Answer: 52%
Answer: C
At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and John get lockers with the numbers 200, 400, 150, and 420, respectively, who is the most popular student?  Choose the correct choice:
A) Johanna
B) John
C) Brianna
D) Jamal
E) They have equal popularity

Solution: Distinct prime factors of 200 (Johanna) : 2, 5   Distinct prime factors of 400 (Jamal): 2 and 5.   Distinct prime factors of 150 (Brianna): 2,3, and 5   Distinct prime factors of 420 (John): 2,3,5 and 7.   So most popular student - John   Answer John
Answer: B
In a company of 148 employees, 92 are females. A total of 78 employees have advanced degrees and the rest have a college degree only. If 31 employees are males with college degree only, how many employees are females with advanced degrees?	Choose the most appropriate option:  A) 50  B) 51  C) 52  D) 53  E) 54

Solution: The number of males is 148-92= 
148-92 = 56
56.   The number of males with advanced degrees is 56-31= 
56-31 = 25
25.   The number of females with advanced degrees is   78-25= 
  78-25 = 53
53.   The answer is 53.
Answer: D
There are 8 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 8 points?
Select the correct option
A) 26	B) 28	C) 30	D) 32	E) 34

Solution: 8C6=28   The answer is 28.
Answer: B
If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ? Choose the correct choice from the following.
A) Two	B) Three	C) Four	D) Six	E) Eight

Solution: n=4p   since n = 4p then even divisors are:   4p/4p = 1   4p/2p  4 /4= 
 4 /4 = 1
1   4p/2p = 2   4p/4 4 /2= 
4 /2 = 2
2   4p/4= p   4p/2 = 2p   so the answer is (Four)4 /2= 
4 /2 = 2
2p   so the answer is (Four)
Answer: C
What is the tens digit of 7^1415? Choose the correct option.
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: 7^1 = 7   7^2 = 49   7^3 = 343   7^4 = 2401   7^5 = 16807   7^6 = 117649   We should see this as pattern recognition . We have a cycle of 4 . (We can multiply the last 2 digits only as we care about ten's digit )   0 , 4 , 4 , 0 .   1415= 4*353 + 3   The ten's digit will be 4 .   Answer 4
Answer: E
If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 8 days ? Choose the correct choice from the following:
A) X-1/8
B) X-1/32
C) X-1/64
D) X-1/128
E) X-1/256

Solution: LET NO OF LEAVES IX X ..IST DAY X/2 ..2ND DAY X/4 ..3RD DAY X/8 , FOURTH DAY X/16 , 5TH DAY X/32 , 6TH DAY X/64 SO ON SO FOURTH.   FINALLY ON LX-1/256AVX-1/256 WILL BX-1/256 LX-1/256FT ..SO ON 3RD DAY LX-1/256AVX-1/256 LOST IS X-1/256 ANSWX-1/256R X-1/256
Answer: E
Which of the following are/is prime?
I. 145
II. 147
III. 149
Pick one.
A) II only
B) III only
C) III
D) IIII
E) I, II,III

Solution: 1) 143 = 13*11 so we know it is not prime quickly eliminate all options having 1 as a choice   which leaves us with 2 ) and 3) as possible answers   From here on we find 147 = 3* 49 so we eliminate 147 which leaves us with 149 as the only possible solution   III
Answer: C
A football coach must choose 4 freshers from a team of 12players. How many different ways can the coach choose the freshers?
Pick one:
A) 495 B) 650 C) 729 D) 800 E) 890

Solution: Choose 4 starters from a team of 12 players. Order is not important.   \inline {\color{Black} 12C_{4}}= 495   495
Answer: A
The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places?
Choices
A) 187.89 cm
B) 178.29 cm
C) 123.98 cm
D) 149.98 cm
E) 146.89 cm

Solution: Calculated average height of 35 boys = 180 cm.   Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm   = 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm   = 180 cm - 1.71 cm = 178.29 cm.   Answer: 178.29 cm
Answer: B
Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share? Choose the correct choice from the following options:
A) 177	B) 169	C) 199	D) 540	E) 123

Solution: A+B+C = 1170   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1170 = Rs.540   Answer: 540
Answer: D
Mahesh visited his cousin Akash during the summer vacation. In the mornings, they both would go for swimming. In the evenings, they would play tennis. They would engage in at most one activity per day, i.e. either they went swimming or played tennis each day. There were days when they took rest and stayed home all day long. There were 32 mornings when they did nothing, 18 evenings when they stayed at home, and a total of 28 days when they swam or played tennis. What duration of the summer vacation did Mahesh stay with Akash?
Choose the correct choice:
A) 46 days
B) 36 days
C) 39 days
D) 58 days
E) None

Solution: Explanation :   Let, the duration of Mahesh's vacation be 'n' days.   Acording to the question, he was free on 32 mornings and on 18 evenings and on total 28 days they either went for swimming or tennis together.   Thus, they were together on (n−32) mornings and (n−18) evenings.   =>(n−32)+(n−18)=28.   =>x=39.   Hence, the require number of days is 39.   Answer : 39 days
Answer: C
ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $51.50. If profit is revenue from sales minus manufacturing costs, and the company producessells 987 sets of horseshoes, what was their profit?	Choose the correct choice from the following
A) $19,887.25
B) $30,943.25
C) $41,308.50
D) $51,817.50
E) $53,624.25

Solution: its $19,887.25   since options are not so close we can solve this by uniting calculation and guessing   total sales will be bit lower than 51500   from that initial outlay will get deducted 11500 so we left with 40000   variable cost say 20 X 1000 = 20000 will be deducted so finally we left with 20000   since we have considered the price greater than it actually is, the correct answer will certainly not cross the threshold of 20000.
Answer: A
Ravi purchased a T.V. and a mobile phone for Rs. 30000 and Rs. 10000 respectively. He sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent. Overall he make a.	Choose the correct choice.
A) loss of Rs. 500  B) loss of Rs. 100  C) profit of Rs. 100  D) profit of Rs. 200  E) None of these

Solution: Total C.P. = 30000+10000= 
30000+10000 = 40_000
40000   S.P. of TV= 30000/100*95= 
30000/100*95 = 28_500
28500   S.P. of Mobile= 10000/100*110= 
10000/100*110 = 11_000
11000   Total S.P.= 28500 + 11000= 
28500 + 11000 = 39_500
39500   Tota. C.P. - Total S.P.= 40000 - 39500= 
40000 - 39500 = 500
500   loss of Rs. 500nswer : loss of Rs. 500
Answer: A
If the average (arithmetic mean) of a and b is 35 and the average of b and c is 80, what is the value of c − a?
Answers.
A) 25 B) 50 C) 90 D) 140 E) It cannot be determined from the information given.

Solution: -(a + b = 70)   b + c=160   c-a=90   C. 90
Answer: C
If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 12/15 Find P(B|A)
Choose one:  A) 1/2  B) 2/3  C) 3/2  D) 4/5  E) 6

Solution: P(B|A) = P(A âˆª B)/P(A)   P(B|A) = (12/15)/(2/15)= 
(12/15)/(2/15) = 6
6.   6
Answer: E
Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in
Options.
A) 7.5 hr B) 8 hr C) 8.5 hr D) 10 hr E) None of these

Solution: Solution:   Work done by all the tanks working together in 1 hour.   1/10+1/12−1/20=2/15   Hence, tank will be filled in 15/2= 
15/2 = 15/2 = around 7.5
7.5 hour   Option(7.5 hr)
Answer: A
If a fair coin is flipped four times in a row, what is the probability that there will be at least one head and one tail? Choose the correct choice
A) 3/4	B) 7/8	C) 15/16	D) 31/32	E) 63/64

Solution: The number of possible outcomes is 2^4 = 16   There is one way to get no heads and one way to get no tails.   Thus there are 14 outcomes with at least one head and one tail.   P(at least one head and one tail) = 14/16 = 7/8   The answer is 7/8.
Answer: B
If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 27, Find x and y ?
Select: A) x=4,y=8 B) x=4,y=9 C) x=4,y=7 D) x=4,y=9 E) x=9,y=27

Solution: 9+27= 
9+27 = 36
36   when reversed 63   63-36= 
63-36 = 27
27   x=9,y=27   ANSWx=9,y=27R:x=9,y=27
Answer: E
A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?  Pick one.
A) 2 hours	B) 7 hours	C) 9 hours	D) 5 hours	E) 3 hours

Solution: |-----------20--------------------|   50 40   D = 20   RS = 50 – 40 = 10   T = 20/10= 
20/10 = 2
2 hours   2 hoursnswer: 2 hours
Answer: A
If f(x) = 2x^2 + y, and f(2) = 100, what is the value of f(5)?  Select the correct option.
A) 104
B) 60
C) 52
D) 50
E) 142

Solution: f(x) = 2x^2 + y   f(2) = 100   => 2*(2)^2 + y = 100   => 8 + y = 100   => y = 92   f(5)= 2*(5)^2 + 92   = 142   Answer 142
Answer: E
In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 70 percent of the Republicans and 25 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?
Answers:  A) 2%  B) 4%  C) 8%  D) 10%  E) 15%

Solution: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 60:40 represents the number ratio of Republicans:Democrats. If 70% of Republicans (which is (60*0.7)= 
(60*0.7) = 42
42) and 25% of Democrats (40*0.25= 10) voted for candidate X, means that out of total of 100 voters; 52 (42 +10) voters voted for candidate X and 48 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 4 (52-48) votes. Therefore candidate X is expected to win the election by (4/100) votes which is equivalent to 4%.   I think the answer is 4%.
Answer: B
What Is The Next Number
12 13 15 17 111 113 117 119 123 129 ?  Options:
A) 154 B) 220 C) 129 D) 131 E) 224

Solution: 131.   These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1   Answer : 131
Answer: D
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders T when the order of the divisors is reversed.	Choose the correct choice
A) 8,5,3	B) 4,2,1	C) T=3,2,1	D) T=6,4,2	E) None of above

Solution: My approach would be   Three Divisors: 3, 5, 8   Three Remain: 1, 4, 7   Start from the bottom of the last column i.e. from the third remainder:   Go up diagonally and multiply by the second divisor:  5*7= 
 5*7 = 35
35   Go down and add the second remainder:   35 + 4= 
  35 + 4 = 39
39   Go up diagonally and multiply by the first divisor:  39* 3= 
 39* 3 = 117
117   Go down and add the first remainder:  117 + 1= 
 117 + 1 = 118
118   Divide 118 by 8, 5, 3   118/8 gives quotient= 14 and remainder = 6   14/5 gives quotient = 2 and remainder = 4   2/3 gives quotient = 0 and remainder = 2   Ans is D i.e. 6,4,2
Answer: D
On a partly cloudy day, john decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
Pick.
A) 1/8  B) 1/7  C) 1/6  D) 1/5  E) 1/4

Solution: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is 2/14 = 1/7. Answer: 1/7
Answer: B
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?  Choose the correct choice from the following answers: A) 81:121 B) 81:126 C) 81:221 D) 86:121 E) 81:131

Solution: Ratio of the sides = ³√729 : ³√1331   = 9:11   Ratio of surface areas = 92 : 112   = 81:121   81:121nswer: 81:121
Answer: A
In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 5 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?  Choose the correct choice from the following answers:
A) d= (p-0.18)/1.05	B) d = (p-0.05)/1.18	C) d = p/1.23	D) d = p-0.23	E) d = p/1.05 - 0.18

Solution: Let dealers price (d) be 1. so adding 5% to dealers price is d+ 5% of d. i.e. 1 + 5% of 1 which is1 + 0.05. then add 0.18 to the value.   Now 1.05 + 0.18. this is now 1.23. you have the gasoline stations price (p) as 1.23 dollars.   Now sub 1.23 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.   PS: always remember to start from E upwards.   d= (p-0.18)/1.05nswer : d= (p-0.18)/1.05
Answer: A
Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:  Pick one
A) 1/6 B) 2/7 C) 3/7 D) 4/6 E) None of them

Solution: Original share of 1 person = 1/7   New share of 1 person = 1/6   Increase = (1/6 - 1/7	= 1/42)   Therefore, Required fraction = (1/42)/(1/7)	= (1/42)x (7/1)	= 1/6   1/6nswer is 1/6.
Answer: A
A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?	Choose the correct choice from the following choices
A) 3/8
B) 1/4
C) 3/16
D) 1/8
E) 1/16

Solution: no of ways of getting P(GGBB) is 4!/2!*2!;   Total no of ways is 2^n =2^4 =16;   6/16 = 3/8;   We can consider this question to a coin that is flipped for 4 times . what is the probability of getting exactly two heads .   P(all out comes) = 1/2 *1/2 *1/2 *1/2 =1/16;   P(favorable outcomes) = 4!/(2! * 2!) = 6/16 =3/8;   3/8NSWER:3/8
Answer: A
At a small company, 58 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?
Choose the correct choice from the following answers:
A) 5/16
B) 1/3
C) 9/20
D) 7/10
E) 41/58

Solution: Lets take total employees are 100.   Given that,Total Women= 58 and Total Married = 60.   Total Men = 100 - 58= 
100 - 58 = 42
42 and Single men= 2/3*42= 
2/3*42 = 28
28.   Married men= total men - single men = 47 - 28= 
47 - 28 = 19
19.   Married women= Total married - Married men = 60 - 19= 
60 - 19 = 41
41.   Fraction of women are married= Married women / Total Women = 41 / 58 = 5/7. ANS 41/58
Answer: E
here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
Select:
A) 1235  B) 4510  C) 1203  D) 1800  E) 4512

Solution: 5 subjects can be arranged in 6 periods in 6P5 ways.   Any of the 5 subjects can be organized in the remaining period (5C1 ways).   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements   = 6P5× 5C1 /2!=1800   Ans: 1800
Answer: D