MU-NLPC/Calc-aqua_rat huggingface dataset:
If a class of 10 students has eight men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other? Select:
A) 8!7!
B) 5!5!
C) 4!4!
D) 10!
E) 10!/5!

Solution: for no two men to sit together, either all are in even or odd position.   fix one at any one position then rest four can be fixed in 7! ways...   also rest five position of women can be fixed in 8!..   total ways 8!7!   8!7!
Answer: A
If a boat is rowed downstream for 500 km in 5 hours and upstream for 240 km in 6 hours, what is the speed of the boat and the river? Select:
A) 70 , 30
B) 30 , 70
C) 70 , 70
D) 30 , 30
E) 80 , 50

Solution: Explanation:   If x: speed of boats man in still water   y: speed of the river   Downstream speed (Ds) = x + y   Upstream speed (Us) = x â€“ y   x = (Ds + Us) / 2   y = (Ds â€“ Us) / 2   In the above problem Ds = 100 ; Us = 40   x = (100 + 40) / 2 = 140/2= 
140/2 = 70
70 km/hr   y= (100 - 40)/2 = 60/2= 
60/2 = 30
30 km/hr   70 , 30NSWER: 70 , 30
Answer: A
In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent L of her bushes have only yellow roses? Choose the correct option:
A) 20 B) 30 C) 50 D) 70 E) 80

Solution: let, the number of bushes with only yellow flowers be x   so, number of bushes with only yellow flowers will be 1.5x   if total number of bushes of flowers= T   then total number of bushes with yellow flowers= 0.8T   we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers   so,L= 0.8T+x=T   x=0.2T   so, 1.5x=0.3T   30% flowers are yellow flowers   OA 30
Answer: B
If |x – 9/2| = 5/2, and if y is the median of a set of q consecutive integers, where q is odd, which of the following must be true?
I. xyq is odd
II. xy(q^2 + q) is even
III. x^2y^2q^2 is even Pick:
A) I only is true	B) II only is true	C) I and III	D) II and III	E) I, II, and III

Solution: given:   q is Odd   y is the median of odd numbers, hence y is Odd   x = solving the modulus you get 7 and 2. Hence x is Even or Odd   Therefore: q = O, y = O and x = O or E   Statement I = x*y*q = y*q*x = O x O x O/E = O x O/E = Odd or even. So False   Statement II = xy(q^2 + q) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true   Statement III. x^2y^2q^2 is even. E/O x O x O = Odd or even. Hence False.   Answer =II only is true.
Answer: B
A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? Choices: A) 39:40 B) 39:49 C) 39:42 D) 39:47 E) 39:41

Solution: Explanation:   3: 4   39:40 = 3/7*210= 
3/7*210 = 90
90   390: 400   39:40   39:40nswer:39:40
Answer: A
The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 10,000? Choose one.
A) 50,000  B) 750,000  C) 850,000  D) 7,500,000  E) 3,000,000,000

Solution: number of cars sold = x=800000-50y   y=10000   x=800000-500000= 
800000-500000 = 300_000
300000   revenue from 300000 cars=10000*300000= 
10000*300000 = 3_000_000_000
3000000000 3,000,000,000
Answer: E
What is the sum of all even numbers from 1 to 501?
Choose the correct option.
A) 122821 B) 281228 C) 281199 D) 62750 E) 128111

Solution: Explanation:   500/2= 
500/2 = 250
250   250 * 251= 
250 * 251 = 62_750
62750   Answer: 62750
Answer: D
A, B and C enter in partnership. A invests some money at the beging, B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit be Rs 39,000/-, C’s Share is: Select the correct option: A) Rs. 12655/- B) Rs. 13,000/- C) Rs. 9000/- D) Rs. 10800/- E) None of these

Solution: Explanation:   Suppose A, B, C invest Rs. X, Rs. 2x and Rs. 3x respectively   A : B : C = (x * 12) : (2x * 6) : (3x * 4)   = 12x : 12x : 12x (3  * 4)= 
(3  * 4) = 12
12x : 12x : 12x= 1: 1: 1   C’ Share = Rs. (39000 * 1/3) =Rs. 13000/-   Answer: Option Rs. 13,000/-
Answer: B
A student finds the sum 1 + 2 + 3 + ... as his patience runs out. He found the sum as 575. When the teacher declared the result wrong, the student realized that he missed a number. What was the number the student missed? Choose the correct choice from the following
A) 16	B) 18	C) 14	D) 20	E) 22

Solution: Explanation :   Sum of 1st 10 natural numbers (1 – 10) = 1 + 2 + …10 = 55.   Sum of next 10 natural numbers (11 – 20) = 10 + 11 + 12 +…20 = 100 + 55= 
100 + 55 = 155
155.   Sum of next 10 natural numbers (31 – 40)= 255.   Sum of numbers from 31 – 40 = 355 and so on and on.   So, we have here   55 + 155 + 255= 
  55 + 155 + 255 = 465
465.   If we add 355 to 465, it will be way more than 575.   So, we can add one by one.   465 + 31 + 32 + 33= 
465 + 31 + 32 + 33 = 561
561.   465 + 31 + 32 + 33 +34= 
465 + 31 + 32 + 33 +34 = 595
595.   Thus, the sum should be 595 instead of 575, and the missing number is 20.   Answer : 20
Answer: D
5 men are equal to as many women as are equal to 8 boys. All of them earn $90 only. Men’s wages are? Choose the correct choice from the following choices:  A) $4  B) $6  C) $7  D) $9  E) $3

Solution: B   $6   5M = xW = 8B   5M + xW + 8B ----- $90 Rs.   5M + 5M + 5M ----- $90 Rs.   15M ------ $90 => 1M = $6.
Answer: B
10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3312, how much was it in the beginning?
Choose the correct option:	A) A)3800	B) B)4200	C) C)4400	D) D)4500	E) E)4600

Solution: X * (90/100) * (80/100) = 3312   X = 4600   ANSW4600R:4600
Answer: E
Aniket deposited two parts of a sum of 25000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year he got 4050 as the total interest. What was the amount deposited at the rate of 18% per annum?  Choose the correct choice from the following choices.
A) 9000
B) 18000
C) 15000
D) Data inadequate
E) None of these

Solution: Let the amount deposited at the rate of 15% per annum be x.   15% of x + 18% of (25000 – x) = 4050   or, 15% of x + 18% of 25000 – 18% of x = 4050   or, 3% of x = 4500 – 4050 = 450 ⇒ x = 15000   \ Amount deposited at 18% = (25000 – 15000 ) = 10000   Answer None of these
Answer: E
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 108 kmph. In how much time will the trains cross each other?  Choose the correct option:	A) 80/8	B) 80/7	C) 80/5	D) 80/3	E) 80/11

Solution: Relative speed = (90 + 108)* 5/18 = 11 * 5= 
11 * 5 = 55
55 mps.   The time required= d/s = (100 + 100 + 200)/55   = 400/55 = 80/11 sec.   Answer: 80/11
Answer: E
If a 3-number code is formed of the integers from 1 to 17 inclusively, and each of the numbers in the code is different, how many possible codes are there? Choose the most appropriate option:
A) 3970
B) 4080
C) 4190
D) 4200
E) 4310

Solution: 17*16*15= 
17*16*15 = 4_080
4080   The answer is 4080.
Answer: B
A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
Choose the correct choice from the following: A) 71.12 B) 71.19 C) 71.11 D) 71.132 E) 71.16

Solution: Total time taken = (160/64 + 160/8) = 9/2 hrs.   Average speed = 320 * 2/9 = 71.11 km/hr.   Answer:71.11
Answer: C
Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?  Choose the most appropriate option:
A) 22 days  B) 68 days  C) 77 days  D) 11 days  E) 88 days

Solution: (5 + x)/20 + 5/25 = 1 => x = 11 days   Answer: 11 days
Answer: D
When the stock market opened yesterday, the price of a share of stock X was 10 1/2. When the market closed, the price was 11 1/4. Of the following, which is closest to the percent increase in the price of stock X? Choose the correct choice from the following options.
A) 0.5%
B) 1.0%
C) 6.7%
D) 7.1%
E) 7.5%

Solution: General formula for percent increase or decrease, (percent change):   percent=Change/Original∗100   So, the percent increase in the price of stock X is (45/4−21/2)/(2/12)∗100=50/7   Answer: 7.1%.
Answer: D
The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $70,000?  Choose the correct answer:	A) $38,796.	B) $40,000.	C) $38,976.	D) $39,679.	E) $68,208.

Solution: 70,000 *1.16*.84= Unit and tens digit of the expression is 6 and 7 respectively.   Only option $68,208. fulfills the condition and hence is the answer
Answer: E
If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 60?	Choose the correct choice
A) 10	B) 12	C) 14	D) 18	E) 24

Solution: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.   The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.   60=2*3*5*2 is divisible by 12. therefore the greatest common divisor is 12   12
Answer: B
P is 10% more efficient than Q. P can complete a work in 21 days. If P and Q work together, how many days will it take to complete the same work? Choose the correct choice from the following choices:
A) 7	B) 9	C) 11	D) 13	E) 15

Solution: The work done by P in 1 day = 1/21   Let work done by Q in 1 day = q   q × (110/100) = 1/21   q = 100/(21×110) = 10/(21×11)   The work done by P and Q in 1 day = 1/21 + 10/(21×11) = 21/(21×11)= 1/11   P and Q together can do the work in 11 days.   The answer is 11.
Answer: C
A train running at the speed of 126 km/hr crosses a pole in 9 seconds. Find the length of the train.
Choose the correct option
A) 150 meter  B) 286 meter  C) 186 meter  D) 315 meter  E) 265 meter

Solution: Speed = 126*(5/18) m/sec   = 35 m/sec   Length of Train (315 meteristance)   = Speed * Time     (35) * 9= 
  (35) * 9 = 315
315 meter   Answer:315 meter
Answer: D
There are two cars. One is 60 miles north of the other. Simultaneously, the car to the north is driven westward at 15 miles per hour and the other car is driven eastward at 25 miles per hour. How many miles apart are the cars after 2 hours?	Answers
A) 60  B) 80  C) 100  D) 120  E) 140

Solution: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:   The right triangle will have a base of 60 and a height of 80. The hidden pattern here is a 3/4/5 right triangle (the 60 lines up with the '3' and the 80 lines up with the '4'). In this way, you can deduce that each side is '20 times' bigger than it's corresponding side:   3/4/5 becomes   60/80/100   Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...   Final Answer: 100
Answer: C
X and Y are two towns. Ganesh covers the distance from X to Y at an average speed of 60 Km/hr. However, he covers the distance from Y to X at an average speed of 30 Km/hr. His average speed during the whole journey in km/hr. is :	Choose the correct answer: A) 34 B) 43 C) 40 D) 38 E) 29

Solution: Solution: Average speed = 2XY / X+Y   = 2*60*30 / 60+30   =40   Answer : 40
Answer: C
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?
Choose the correct option:
A) 256 B) 432 C) 512 D) 640 E) None of these

Solution: Explanation:   Let total number of children be x.   Then, x x	1/8x=x/2x 16 x = 64.   Number of notebooks =	1/8x2 = (1/8	x 64 x 64)= 512.   ANSWER IS 512
Answer: C
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?  Choose the correct option:	A) 35	B) 40	C) 45	D) 50	E) 55

Solution: Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.   Then, 4x + 6y =	1/8	and 3x + 7y =	1/10	.   Solving the two equations, we get: x =11/400, y =1/400   1 woman's 1 day's work =	1/400	.   10 women's 1 day's work =	1/400 x 10 =	1/40	.   Hence, 10 women will complete the work in 40 days.   Answer : 40
Answer: B
Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
12 minutes more to walk to work than to ride his bicycle, then x equals	Choose one.
A) 4 B) 7 C) 10 D) 18 E) 20

Solution: The best way would be...   Per km, he takes 40 secs extra if he walks   So he will take 12 mins or 12*60 secs in 12*60/40= 
12*60/40 = 18
18 km   ANSWER:18
Answer: D
What is the unit digit in {(6374)^1793 x (625)^317 x (341^491)}?  Choose one
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Unit digit in (6374)1793 = Unit digit in (4)1793   = Unit digit in [(42)896 x 4]   = Unit digit in (6 x 4) = 4   Unit digit in (625)317 = Unit digit in (5)317 = 5   Unit digit in (341)491 = Unit digit in (1)491 = 1   Required digit = Unit digit in (4 x 5 x 1) = 0.   0)
Answer: A
If y exceeds x by 20%, then x is less than y by?  Select.
A) 86 2/3%  B) 16 2/7%  C) 16 2/3%  D) 16 3/3%  E) 16 2/3%

Solution: X=100	y=120   120------20   100-------? => 16 2/3%   Answer:16 2/3%
Answer: C
A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 6% dividend at the end of the year,then how much does he get ? Choose the most appropriate option:
A) Rs. 500
B) Rs. 600
C) Rs. 650
D) Rs. 720
E) None

Solution: Solution   Number of shares = (14400/120)= 
(14400/120) = 120
120.   Face value= Rs. (100x120 ) = Rs. 12000.   Annual income = Rs.(6/100x12000) = Rs. 720.   Answer Rs. 720
Answer: D
Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 90 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following? Pick one:  A) 45  B) 50  C) 60  D) 75  E) 81

Solution: AnalystsNot AnalystsTotal   MBAx/32x/3x   No MBAy/4   Total2x/350y   We are asked for the value of x.   From the table: 2x/3 = y - 90   y - 90 + (y/4) = 90   5y/4 = 180   y = 144   2x/3 = 144 - 90= 
144 - 90 = 54
54   x= 162/2= 
162/2 = 81
81   Answer: 81
Answer: E
Awordis defined as a sequence of two dots arranged in a row. Each dot is colored any one of the three colours. How many distinct words can be formed?	Select the correct option:  A) 3  B) 5  C) 6  D) 8  E) 9

Solution: Each dot can be coloured any of the three colours, so 3 options for each dot:   3*3= 
  3*3 = 9
9.   Answer: 9
Answer: E
The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
Options:
A) 1/2
B) 3/4
C) 3/5
D) 3/7
E) 4/7

Solution: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D   1 2 3 1 =iXiX71=4;   1 3 Required probability 3/4   3/4
Answer: B
In a mayoral election, Candidate X received 1/2 more votes than candidate Y, and Candidate Y received 2/5 fewer votes than Z. If Z received 25,000 votes how many votes did candidate X received? Choose the correct choice
A) 18000 B) 22500 C) 24000 D) 26000 E) 32000

Solution: Z=25 --> Y received 2/5 fewer votes than Z --> Y=Z- 2/5*Z=15;   X received 1/2 more votes than Y --> X=Y+1/2*Y=22,5.   Answer: 22500.
Answer: B
If the population of a certain country increases at the rate of one person every 20 seconds, by how many persons does the population increase in 1 hour? Choose the correct answer
A) 100	B) 120	C) 150	D) 180	E) 160

Solution: Answer = 3 * 60= 
3 * 60 = 180
180   Answer is 180
Answer: D
Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 40%. What fraction of the original paint was replaced?  Choose the correct choice from the following:
A) 1/30
B) 1/5
C) 2/5
D) 3/4
E) 4/5

Solution: 40% is 15%-points above 25% and 10%-points below 50%.   Thus the ratio of 25%-solution to 50%-solution is 2:3.   2/5 of the original paint was replaced.   The answer is 2/5.
Answer: C
The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 350, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
Choose the correct answer:  A) 60  B) 90  C) 120  D) 150  E) 240

Solution: Let x be the number of timeshare condos available at Playa del Mar.   Then number of timeshare condos available at Sunset Beach = 3/5x   We know, x + 2/5 x = 350   Hence, x = 250. So, number of timeshare condos available at Playa del Mar = 250   the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 2/5x = 3/5x = 3/5(250) = 150   The correct answer is 150
Answer: D
If 'A' means '-', 'B' means '/', 'C' means '+', and 'D' means 'X' then
Find the value of the following:
21 B 7 C 9 D 10 A 13
Choose the correct option
A) 60  B) 70  C) 80  D) 90  E) 100

Solution: Solution:   80   Explanation:   21 B 7 80 9 D 10 A 13   = 21 / 7 + 9 X 10 - 13   = 3 + 90 - 13= 
3 + 90 - 13 = 80
80   Answer 80
Answer: C
Find the average of all prime numbers between 20 and 30	Answers.
A) 15  B) 20  C) 18  D) 32  E) 26

Solution: Prime numbers between 20 and 30 are 23,29   Required average = (23+29)/2 = 52/2= 
52/2 = 26
26   Answer is 26
Answer: E
Ram professes to sell his goods at the cost price but he made use of 700 grms instead of a kg, what is the gain percent?
A. 11%
Choose the correct choice.
A) 11 1/9%	B) 11 1/8%	C) 11 9/9%	D) 11 5/9%	E) 42.85%

Solution: 700 --- 300   100 --- ? => 42.85%   Answer:42.85%
Answer: E
A trader marked the selling price of an article at 60% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of :  Answers
A) 10 %
B) 10.5 %
C) 6.8 %
D) 12.5 %
E) None

Solution: Sol.   Let C.P. = Rs. 100. Then, Marked Price = Rs. 160, S.P. = Rs. 99.   ∴ Discount % = [11/160 * 100] % = 6.8 %   Answer 6.8 %
Answer: C
A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.	Choose the correct answer.
A) 8/15
B) 5/14
C) 7/15
D) 16/7
E) 4/3

Solution: .let S be the sample space   Then n(S)=no of ways of drawing 2 balls out of   (6+4)= 
  (6+4) = 10
10c2=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   Let E=event of getting both balls of same colour   Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)   =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(E)=n(E)/n(S)=21/45=7/15   Ans: 7/15
Answer: C
Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 40 litres of tomato juice? Select:
A) 2.8 liters.  B) 2.5 liters.  C) 5 liters.  D) 2.6 liters.  E) 2.1 liters.

Solution: Answer:   Explanation:   In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.   â‡’â‡’ 10%(40) = 80%(x)   â‡’â‡’ x = 5 liters.   Answer:5 liters.
Answer: C
What will the ratio of simple interest earned by certain amount at the same rate of interest for7 years and that for 9 years.
Answers.
A) 7:5	B) 2:5	C) 2:9	D) 7:9	E) None of these

Solution: Explanation:   Let the principal be P and rate be R   then   ratio = [(P∗R∗7/100) /(P∗R∗9/100)]   =7PR /9PR=7:9   Option 7:9
Answer: D
In how many ways can you seat 8 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?  Choose the correct choice from the following choices:  A) 720  B) 1720  C) 2880  D) 5040  E) 25200

Solution: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 5 chairs to sit. The remaining 7 people can sit in 7! ways. Thus the # of arrangements is 5*7! = 25,200.   Answer: 25200.
Answer: E
A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 40% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
Pick.
A) $37.80
B) $38.50
C) $39.20
D) $44.33
E) $40.60

Solution: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14 0.4* 35= 
 0.4* 35 = 14
$14 on chicken feed, thus he spent the remaining   35-14= 
  35-14 = 21
$21 on goat feed.   Now, since he bought chicken feed at a 40% discount then the original price of it was x*0.6=$14 --> x=$23,33.   Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 23,33+21=$44,33.   Answer: $44.33.
Answer: D
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 238, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
Choose the correct answer.
A) 22 B) 33 C) 55 D) 42 E) 88

Solution: Let f = pure fuji , g = pure gala and c - cross pollinated.   c = 10% of x where x is total trees.   c = .1x   also 3x/4 = f and c+f = 238 => .1x + 3/4x = 238 => x = 280   280 - 238 = pure gala = 42.   Answer 42
Answer: D
If 14 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?  Pick: A) 95 B) 90 C) 85 D) 80 E) 56

Solution: Let x be the number of students in the school. 0.14x students went to the trip and took more than 100$. They compose   (100-75)= 
  (100-75) = 25
25% of all students who went to the trip. Therefore the toal of 0.14x/0.25=0.56x students went to the camping which is 56%.   The answer is 56  0.14 /0.25= 
  0.14 /0.25 = 0.56
0.56x students went to the camping which is 56%.   The answer is 56
Answer: E
In a diving competition, each diver has a 40% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)	Select the correct option:
A) 1/5
B) 1/15
C) 4/25
D) 18/125
E) 61/125

Solution: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)   Given:Probability of Perfect dive = 0.4 = 40/100 = 2/5   i.e. Probability of Non-Perfect dive = 0.6 = 60/100 = 3/5   The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect   Method-1:   i.e. Probability of First two being Imperfect and Third being Perfect dive = (3/5)*(3/5)*(2/5) =18/125   18/125
Answer: D