MU-NLPC/Calc-aqua_rat huggingface dataset:
If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:  Choose the correct choice from the following answers:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.   x = 2.   Answer 2) 2.
Answer: B
In a division, divident is 690, divisior is 36 and quotient is 19. Find the remainder. Pick one:
A) A)4	B) B)3	C) C)2	D) D)5	E) E)6

Solution: 6xplanation:   690 = 36 x 19 + r   690 = 684 + r   r = 690 - 684= 
690 - 684 = 6
6   Answer: Option 6
Answer: E
A present value of a machine is $900. Its value depletiation rate is 25% per annum then find the machine value before 2 years? Choose the correct answer.
A) $1500
B) $1200
C) $1600
D) $1000
E) $1350

Solution: P= $900   R = 25%   T = 2 years   Machine value before 2 years = P/[(1-R/100)^T]   =900*4/3 * 4/3= 
900*4/3 * 4/3 = 1_600
$1600   Answer is $1600
Answer: C
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 30, the dividend is: Options:
A) A)5322 B) B)5330 C) C)2280 D) D)5340 E) E)5342

Solution: Divisor = (5 * 30)= 
(5 * 30) = 150
150= 10 * Quotient = Divisor   => Quotient = 150/10= 
150/10 = 15
15   Dividend= (Divisor * Quotient) + Remainder   Dividend = (150 * 15) + 30= 
(150 * 15) + 30 = 2_280
2280.   2280
Answer: C
The length of the bridge, which a train 200 metres long and travelling at 60 km/hr can cross in 30 seconds, is? Select the correct option:
A) 720 B) 470 C) 270 D) 370 m. E) 570

Solution: Speed = [60 X 5/18] m/sec = [50/3] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30   = 50/3 => (130 + x)/30   = 370=> x   = 370 m.   Answer:370 m.
Answer: D
4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%? Select the correct option:
A) 3299 B) 2690 C) 2800 D) 2692 E) 2981

Solution: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144   3x/100 + 200 – 5x/100 = 144   2x/100 = 56 è x = 2800.Answer: 2800
Answer: C
There are 30 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall? Choose the correct answer:
A) 6	B) 12	C) 15	D) 24	E) 27

Solution: 30*2/3 *3/4= 
30*2/3 *3/4 = 15
15   Answer: 15
Answer: C
96% of the population of a village is 23040. The total population of the village is?	Choose the correct choice from the following
A) 16800  B) 1689  C) 6795  D) 24000  E) 12654

Solution: Explanation:   X * (96/100) = 23040   X = 240 * 100= 
240 * 100 = 24_000
24000   Answer: 24000
Answer: D
Value of
(256)5/4 Choose one
A) 1012
B) 1024
C) 1048
D) 525
E) None of these

Solution: Explanation:   =(256)5/4=(44)5/4=4(5)=1024   Option 1024
Answer: B
A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour? Pick one
A) 100 miles / hour B) 90 miles / hour C) 70 miles / hour D) 60 miles / hour E) 30 miles / hour

Solution: We first convert the time of 4 hours 41 minutes in minutes   4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes   Average speed S is given by distance / time. Hence   S = 281 miles / 281 minutes = 1 mile / minute   = 60 miles / hour   correct answer 60 miles / hour
Answer: D
The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is  Choose the correct choice from the following options.
A) 90  B) 99  C) 92  D) 94  E) 97

Solution: The average score in an examination of 10 students of a class is 60 --> the total score = 10*60= 
10*60 = 600
600;   The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores= 275.   From above, the total score of the 5 largest scores = 600 - 275= 
600 - 275 = 325
325.   Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:   a + b + c + d + e= 55 + 56 +57 + 58 + e = 325;   e = 99.   Answer: 99.
Answer: B
A student is ranked 21th from right and 11th from left. How many students are there in totality ?
Choose the correct choice.
A) 18  B) 19  C) 20  D) 31  E) 22

Solution: From right 21 , From left 11   Total = 21+11-1= 
21+11-1 = 31
31   ANSWER:31
Answer: D
In the formula V = 1/(3r)^4, if r is halved, then V is multiplied by Choose the correct choice from the following answers.
A) 64 B) 8 C) 16 D) 1/8 E) 1/64

Solution: Say r=2 => V1 = 1/1296   when r=1; V2 = 1/81   V2 = 16*V1.   Answer=1616* 1.= 
16* 1. = 16
16=16
Answer: C
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Choose the correct choice from the following answers:  A) 76 seconds  B) 18 seconds  C) 40 seconds  D) 19 seconds  E) 45 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (2/25)= 
500 * (2/25) = 40
40 seconds   Answer: 40 seconds
Answer: C
In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
Choose the most appropriate option.
A) 50
B) 45.
C) 40.
D) 30.
E) 25.

Solution: Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.   Now here 90% are Boys and 10% are Girls.   Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..   If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.   Now boys are 95% and girls are 5%. ( out of 100 students = 95 boys + 5 girls ).   50nswer: option 50 is correct.
Answer: A
At the end of year X, automobile installment credit accounted for 43% of all outstanding consumer installment credit. At that time automobile finance companies extended $50 billion of credit, or 1/4 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
Choices: A) 450 B) 465.12 C) 475 D) 500.15 E) 200

Solution: System of Equations   a = (43/100) c   (1/4) a = 50 --> a = 200   Substitution   200 = (43/100) c   c = (100/43) 200   Calculate   200/43 * 100   - The the correct answer is 465.12. The correct answer is 465.12.
Answer: B
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 45 more revolutions than gear P?  Options:
A) 45
B) 80
C) 90
D) 100
E) 120

Solution: Gear Q makes 30 more revolutions each 60 seconds.   The time to make 45 = 30*1.5 more revolutions is 60*1.5= 
60*1.5 = 90
90 seconds.   The answer is 90.
Answer: C
A cistern is filled by pipe A in 12 hours and the full cistern can be leaked out by an exhaust pipe B in 18 hours. If both the pipes are opened, in what time the cistern is full? Choose the correct choice.
A) 50hrs	B) 60hrs	C) 36hrs	D) 80hrs	E) 90hrs

Solution: time taken to full the cistern=(1/12-1/18)hrs   =1/36   =36hrs   ANSWER:36hrs
Answer: C
A 72 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Select:
A) 8  B) 12  C) 18  D) 14  E) 16

Solution: Amount of salt = 7.2   Assume x gallons of water are added.   7.2 / 72 + x = 8/100   720 = 8x + 576   8x = 144   x = 18   18orrect Option: 18
Answer: C
A pet shop sells 50 rabbits for Rs. 2000 at a profit of Rs. 12 per rabbit. Find the cost price for one rabbit? Choose the correct choice from the following answers:  A) 20  B) 52  C) 28  D) 40  E) 15

Solution: SP per rabbit = 2000/50 = Rs. 40Profit per rabbit = Rs. 12 CP per rabbit = 40 - 12= Rs. 28Answer: 28
Answer: C
A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 62 unique alphanumeric case sensitive characters. Answers.
A) 63^4 B) 62^5 C) 62(62^4) D) 63(62^4) E) 63(62^6)

Solution: Total number of passwords = number of 4 character password +number of 5 character password   = 62^4 + 62^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )   =62^4(1+ 62)   =62^4 * 63   Answer 63(62^4)
Answer: D
A can do a work in 20 days. B is 30% more efficient than A. How many days does B alone take to do the same job? Choose the correct answer.
A) 121/23	B) 129/12	C) 198/13	D) 200/13	E) 199/18

Solution: Ratio of times taken by A and B = 130:100 = 13:10   suppose B alone to take x days to do the work   then, 13:10::20:x   13x= 10*20= 
10*20 = 200
200/13 days   correct option is 200/13
Answer: D
Harry is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 10 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain? Choose the correct choice from the following options:
A) 5.5
B) 5.8
C) 6.0
D) 6.3
E) 6.6

Solution: to calculate average of 2 speeds a and b when distance is constant   Formula - 2ab/(a+b)   Here Harry's uphill speed = 5 mph   Harry's downhill speed = 10 mph   2*5*10/(5+10) = 100/15 = 6.6   Correct answer - 6.6
Answer: E
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?  Choose the correct answer:
A) 1 : 8 B) 1 : 0 C) 1 : 2 D) 1 : 1 E) 1 : 5

Solution: Ratio of investments of P and Q is 2 : 5   Total salary claimed by P = 12 * 5000 = Rs. 60000   Total profit = Rs. 2 lakhs.   Profit is to be shared = Rs. 140000   Share of P = (2/7) * 140000 = Rs. 400000   Share of Q = Rs. 100000   Total earnings of P = (60000 + 40000) = Rs. 100000   Ratio of their earnings = 1 : 1   Answer: 1 : 1
Answer: D
When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction f of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
Choose the correct option:
A) 11/14
B) 13/18
C) 4/7
D) 3/7
E) 3/14

Solution: If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.   2/9 of the votes on a certain resolution have been counted--> 4 counted and  18-4= 
 18-4 = 14
14 votes left to be counted;   3/4 of those counted are in favor of the resolution--> 3 in favor and 1 against;   Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of   18*2/3= 
  18*2/3 = 12
12 people who voted against, so in the remaining 14 votes there should be   12-1= 
  12-1 = 11
11 people who voted against. Thus f=11/14 of the remaining votes must be against.   11/14nswer: 11/14.
Answer: A
Twelve participants are participating in a competition. In how many ways can the first three prizes be won?
Choose the correct option:
A) 1320 B) 680 C) 820 D) 720 E) 620

Solution: Out of 12 participants, the first three prizes can be won in,   12P3 = 12! / (12 - 3)!   = 12 X 11 X 10   = 1320 ways   1320NSWER:1320
Answer: A
X,Y and Z can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:
Answers
A) 24/7days  B) 3/7days  C) 35/7days  D) 12/24days  E) 45/35days

Solution: X+Y+Z day work = 1/24+1/6+1/12 = 7/24   X,Y,Z complete the work in 24/7 days   24/7daysNSWER 24/7days
Answer: A
The last day of the century cannot be: Choose the correct choice from the following choices
A) Sunday  B) Wednesday  C) Friday  D) Saturday  E) Tuesday

Solution: SOLUTION :   100 years have 5 odd days. Hence the last day of 1st century is a Friday.   200 years have 10 odd days or 1 week + 3 odd days. Hence, the last day of the 2nd century is a Wednesday.   300 years have 15 odd days or 2 week + 1 odd day. Hence, the last day of the 3rd century is a Monday.   400 years have 0 odd days. Hence, the last day of the 4th century is a Sunday.   ANSWER IS Saturday
Answer: D
The average of seven numbers is 9. The average of first three numbers is 7 and the average of last three numbers is 11. What is the middle number? Options
A) 7	B) 8	C) 9	D) 11	E) 10

Solution: The total of seven numbers = 7X9 = 63   The total of first 3 and last 3 numbers is = 3 X 7+3 X 11 = 54   So, the middle number is  (63 - 54 )= 
 (63 - 54 ) = 9
9   9
Answer: C
The first train leaves the station at 6:00 am with a speed of 60 km/hr. The second train leaves at 7:00 am, in the same direction from the same station, with a speed of 80 km/hr. What time will the second train catch the first train?	Choose the correct option
A) 9:00 am B) 10:00 am C) 11:00 am D) 12:00 noon E) 1:00 pm

Solution: In one hour, the first train travels 60 km.   The second train catches the first train with a relative speed of 20 km/h.   The second train will catch the first train at 10:00 am.   The answer is 10:00 am.
Answer: B
A family consists of two grandparents, two parents, and four grandchildren. The average age of the grandparents is 66 years, the average age of the parents is 40 years, and the average age of the grandchildren is 7 years. What is the average age (in years) of the family?	Choose the correct option
A) 26	B) 28	C) 30	D) 32	E) 34

Solution: Total age of the grandparents = 66 Ã— 2 = 132   Total age of the parents = 40 Ã— 2 = 80   Total age of the grandchildren = 7 Ã— 4 = 28   Average age of the family = (132+80+28)/8 = 240/8= 
240/8 = 30
30 years   The answer is 30.
Answer: C
At a baseball game, 10% of the fans did not wear ball caps, 60% of the remaining fans wore ball caps for the home team. What percentage of the fans wore ball caps for the visiting team?	Choices
A) 64% of the attendees wore ball caps for the visiting team.	B) 36% of the attendees wore ball caps for the visiting team.	C) 44% of the attendees wore ball caps for the visiting team.	D) 54% of the attendees wore ball caps for the visiting team.	E) None of these.

Solution: Explanation:Let total number of fans be 100,Then, number of fans not wearing ball caps = 10.Number of fans with home team ball cap= 60% of 90 = 54.Total number of fans with visitor team ball cap = 100 – (10 + 54) = 36.Thus, 36% of the attendees wore ball caps for the visiting team.Answer: Option 36% of the attendees wore ball caps for the visiting team..
Answer: B
Two trains 180 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?  Select the correct option.
A) 10.24 sec	B) 18.8 sec	C) 14.24 sec	D) 12.24 sec	E) 11.84 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 180 + 160= 
180 + 160 = 340
340 m.   Required time= 340 * 9/250 = 306/25= 
306/25 = 306/25 = around 12.24
12.24 sec.   Answer: 12.24 sec
Answer: D
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?	Choose the correct choice from the following:
A) 12/477 B) 12/487 C) 12/455 D) 12/416 E) 12/419

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   When three marbles are drawn, the probability that one is yellow and two are red   = (²12/455₁)(⁴12/455₂)/¹⁵12/455₃   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)   = 12/455   Answer: 12/455
Answer: C
A 10-meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
Choose the correct choice from the following.
A) 2/3
B) 3/4
C) 1/5
D) 2/5
E) 3/5

Solution: The longer wire will form a square with an area more than 4 if the wire is cut at a point within two meters of either end. The probability of this is 4/10 = 2/5.   The answer is 2/5.
Answer: D
5 - [5 - {5 - 5(5 + 5)}] = ?
Answers.
A) 5
B) -45
C) 45
D) 50
E) 60

Solution: Explanation:   => ? = 5 - [5 - {5 - 5 × 10}] = 5 - [5 - (-45)]   = 5 - (50) = - 45   Answer: Option -45
Answer: B
A class consists of 5 boys and 5 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?	Choose one:  A) 9  B) 18  C) 32  D) 40  E) 240

Solution: Easiest way is to treat it like an arrangements question in the following manner:   From the boys we need to select 2 to be clown and pet: This can be done in 5*4 ways   Similarly for the girls, we have 4*5 ways.   Thus total = 20+20= 
20+20 = 40
40 ways. Thus 40 is the correct answer.
Answer: D
There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 7:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?  Choose the correct choice from the following choices.
A) 59:31	B) 3:2	C) 118:126	D) 193:122	E) 201:132

Solution: 7:3=>7x+3x=10x   2:17 +3= 
7 +3 = 10
10x   2:1=>2y+1y=3y   3:22 +1= 
2 +1 = 3
3y   3:2=>3z+2z=5z   10x3 +2= 
3 +2 = 5
5z   10x=3y=5z   Take LCM of 10,3,5=30   Or simply;   x=3   y=10   z=6   So,   Ratio of Milk:Water= (7x+2y+3z)/(3x+y+2z)=59/31   59:31ns:59:31
Answer: A
Ravi and sunil are partners in a business. Ravi invests Rs.18,000 for 8 months and Sunil invested Rs.10000 for 10 months then after one year ratio of their profits will be Answers.
A) 1:3
B) 36:25
C) 3:2
D) 4:5
E) 20:45

Solution: =(18000*8):(10000*10)   =144000:100000   =36:25   ANSWER:36:25
Answer: B
Two pipes A and B can separately fill a tank in 16 and 18 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 18 minutes. What is the capacity of the tank?	Choose the correct choice from the following options:  A) 590 liters  B) 720 liters  C) 740 liters  D) 860 liters  E) 620 liters

Solution: 1/16 + 1/18 - 1/x   = 1/18   x = 16   16 * 45= 
16 * 45 = 720
720   Answer:720 liters
Answer: B
the population of a country is increased by 2% in one year and 3% in next year.what is the combined growth of population in these two year Select:
A) 4.06% B) 5.06% C) 6.06% D) 7.06% E) 8.06%

Solution: concept of successive percentage, total percentage= x+y+xy/100   put x=2 and y=3   combined growth= 2+3+2*3/100   = 5+0.06= 
5+0.06 = 5.06
5.06%   ANSWER:5.06%
Answer: B
A number, x is chosen at random from the set of positive integers less than 10. What is the probability that (7/x) > x? Options:
A) 1/5  B) 7/9  C) 1/3  D) 2/3  E) 2/9

Solution: Number x has to be chosen from numbers 1-9   (7/x) > x   => 7 > x^2   =>x^2 - 7 < 0   x can have 2 values only 1 , 2   Therefore , probability = 2 / 9   Answer 2/9
Answer: E
Debony normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Debony averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?  Choose the correct choice
A) 135 B) 105 C) 95 D) 75 E) 45

Solution: Debony normally drives to work in 45 minutes at an average speed of 40 miles per hour.   Use formula 75 = RT   Car:   T1: 45 min   R1: 40 mph   751: [(40*45)/60= 
(40*45)/60 = 30
30 miles   Bike:   T1:?   R2: 12 - 16 mph   752: 08*751= 24 miles   T1: [(24*60)/12= 
(24*60)/12 = 120
120 min (Only 12 mph speed yields an answer given in the choices)   Therefore, 75eb has to leave 120 min - 45 min= 75 min early   ANSWER: 75
Answer: D
What is the area inscribed by the lines y =6, x = 3, y = 2x-4 on an xy-coordinate plane? Choose the correct choice from the following answers.
A) a) 1	B) b) 2	C) c) 4	D) d) 8	E) e) 16

Solution: First, let's graph the lines y = 6 and x = 3   At this point, we need to find the points where the line y = 2x-4 INTERSECTS the other two lines.   For the vertical line, we know that x = 3, so we'll PLUG x = 3 into the equation y = 2x-4 to get y = 2(3)-4 = 2   Perfect, when x = 3, y = 2, so one point of intersection is (3,2)   For the horizontal line, we know that y = 6, so we'll PLUG y = 6 into the equation y = 2x-4 to get 6 = 2x-4. Solve to get: x = 5   So, when y = 6, x = 5, so one point of intersection is (5,6)   Now add these points to our graph and sketch the line y = 2x-4   At this point, we can see that we have the following triangle.   The base has length 2 and the height is 4   Area = (1/2)(base)(height)   = (1/2)(2)(4)   = 4   Answer:   c) 4
Answer: C
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
Choices
A) 228  B) 2769  C) 278  D) 502  E) 131

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85   5x/100 + 90 – 6x/100 = 85   x/100 = 5   => x = 500   Answer: 502
Answer: D
Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many R women are currently in the room?	Pick one
A) 12 B) 14 C) 15 D) 24 E) 36

Solution: the number of women doubled means that they have become 24 from 12..   and we have to tell the current strength so 24 is the answer..   let the number be 4x and 5x..   given 4x+2=14.. so x=3..   women number=5*3-3= 
5*3-3 = 12
12, then doubled=24..   ans 24
Answer: D
In how many ways can the letters of the word "VENUS" be arranged? Choose the correct choice from the following answers:
A) 60
B) 80
C) 100
D) 120
E) 140

Solution: The total ways of arranging the letters = 5! = 120   The answer is 120.
Answer: D
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 3 letters in its codes, and all letters can be repeated in any one code? Choose one.
A) 15600 B) 16226 C) 17576 D) 18278 E) 28572

Solution: 1-letter codes   26 letters, so there are 26 possible codes   2-letter codes   There are 26 options for the 1st letter, and 26 options for the 2nd letter.   So, the number of 2-letter codes = (26)(26) = 26²   3-letter codes   There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.   So, the number of 3-letter codes = (26)(26)(26) = 26³   So, the TOTAL number of codes = 26 + 26² + 26³=18278   ANSWER:18278
Answer: D