MU-NLPC/Calc-aqua_rat huggingface dataset:
A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)] Choose the correct choice from the following answers.
A) 1/4	B) 7/12	C) 2/3	D) 7/8	E) 8/7

Solution: Let there be g geese, of which 0.3g are male and 0.7g are female   Lets say m geese migrated, 0.2m are male and 0.8m are female   Migration Rate Male = 0.2m / 0.3g = (2/3)*(m/g)   Migration Rate Female = 0.8m / 0.7g = (8/7)*(m/g)   Ratio of migration rates = (2/3) / (8/7) = 7/12   Answer is (7/12)
Answer: B
In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd? Choose the correct choice from the following answers.
A) 5/18 B) 13/36 C) 3/8 D) 5/8 E) 23/36

Solution: player begins with containing tiles 1 to 10 and have equal probability of selecting means   Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.   Next , player draws one title , if number is even player stops or otherwise title is odd without replacement   player draws second title.   If second title is even , player stops or title is odd without replacement player draws third title.   in third title , without replacement of first and second title, player draws and stops it.   the sum of tilte probability is odd. here two conditions are possible.   1st condition is   1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.   Here are we are not selecting 1st condition as even stops because sum of tile is odd.   Here 5 odd numbers are there we can select 1out of 5 odd numbers.   without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.   here we are selecting one number out of remaining 9 numbers. so probability is 5/18.   we are selecting 1 even number out of 5.   2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.   Then probability is 5/10*4/9*3/8=1/12.   Finally sum of probability of two conditions is 5/18+1/12   =5/18.   so option 5/18 is correct.
Answer: A
At a certain amateur bands rock show the ratio of freaks to nerds to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yellsrock on!will be a nerds?  Select:
A) 1
B) 1/2
C) 1/4
D) 1/3
E) 1/6

Solution: Another approach is to assign some nice values for the number of freaks, nerds and geeks.   Given: the ratio of freaks to nerds to geeks is 1:2:3   So, let's say there is: 1 freak, 2 nerds and 3 geeks for a TOTAL of 6 people.   P(next person who yells rock on!is a nerds) = (# of nerds in the crowd)/(TOTAL # of people in the crowd)   =2/6   = 1/3   Answer:   1/3
Answer: D
There is one highland where planes get fuel. A plan can cover the half of the world with full tank. A plane can transfer fuel from one plane to the other in the air. How many planes are required to make one plane cover the entire world once. Starting point of the travel is the Highland and coming back to the same Highland. All the other planes giving fuels to this Plane should also come back to the same highland and they don't have to cover the entire world.	Choose the correct choice from the following options:
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: Divide the world as 6 parts.   To cover 1/6 th of the distance 1/3 rd of fuel is required.   1 plane, B, can start in same direction of target flight say A.   It can travel 1/6 th of the distance and give 1/3rd of fuel to A and return home with 1/3rd fuel. Now A can cover 4/6th world with that full tank.   Let C and D start from home at opposite direction.   Let C cover 1/6th dist and give 1/3rd fuel to D. Now D travels 1/3 rd more distance and meets A and gives 1/3rd fuel. Both are now 1/6th distance away from home. Let E take fuel and bring one plane home and F take fuel and bring home A. Now excluding A.. 5 supporting planes are required.   ANSWER:5
Answer: D
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?  Select
A) 225 sq.m B) 360 sq.m C) 720 sq.m D) 480 sq.m E) None of these

Solution: Explanation:   Consider the rhombus ABCD. Let the diagonals intersect at E. Since   diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = âˆš(625 - 225)= 
(625 - 225) = 400
âˆš400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   ANSWNone of theseR IS None of these
Answer: E
Given a square of 10cm each side with the four semi circles inside as shown in the above
diagram, find the area of the shaded portion  Choose the correct choice from the following answers
A) 54	B) 55	C) 56	D) 57	E) 58

Solution: area quadra circle- area of triangle   area of triangle =1/8(area of square)   required area=((pie*5*5/4)-(10*10/8))*8=57   ANSWER:57
Answer: D
A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 m3. The emptying capacity of the pump is 10m3 per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.	Choose the correct choice from the following answers
A) 45 m3/min
B) 40 m3/min
C) 50 m3/min
D) 55 m3/min
E) None of these

Solution: 2400/x - 2400/x+10=8,solving this we get x,   =50m3/min   Answer: 50 m3/min
Answer: C
The total circumference of two circles is 64. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?  Pick one: A) 5.7 B) 6.0 C) 6.7 D) 10.2 E) 18.0

Solution: Let r= Radius of smaller circle. Let R = Radius of larger circle   Therefore:   2πr + 2πR = 64   where 2r = R   Thus:   2πr + 4πr = 64   6πr = 64   r = approx 3.4   πR + 2Rπ = 64   3πR = 64   R = approx 6.8   r + R = approx 10.2   Answer 10.2
Answer: D
The events A and B are independent. The probability that event A occurs is u and the probability that event B occurs is v. Which of the following is equal to the probability that exactly one of the events A and B occurs?	Choose the correct answer.
A) u − 2uv B) v − uv C) u + v − 2uv D) u + v − uv E) u + v

Solution: Probability of A occuring = u , Probability of A NOT occuring = 1-u   Probability of B occuring = v , Probability of B not occurring = 1-v   Probability of atleast of one of A and B occuring = 1-(1-u)(1-v) =u+v -uv   u + v − uv
Answer: D
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 18, Find x and y ?  Answers:
A) x=4,y=8
B) x=4,y=9
C) x=4,y=7
D) x=4,y=64
E) x=5,y=8

Solution: 4+64= 
4+64 = 68
68   when reversed 86   86-68= 
86-68 = 18
18   x=4,y=64   ANSWER:x=4,y=64
Answer: D
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is  Choose the correct choice from the following
A) 100 B) 250 C) 260 D) 416 E) None

Solution: Sol.   Let the number of boys and girls be 8x and 5x respectively.   Then, 5x = 160 ⇔ x = 32.   ∴ Total number of students = 13x = (13 x 32) = 416.   Answer 416
Answer: D
The calendar of the year 2032 can be used again in the year?
Choices:
A) 2060	B) 2050	C) 2040	D) 2033	E) 2034

Solution: Explanation:   Given year 2032 when divided by 4, leaves a remainder 0.   NOTE: When remainder is 0, 28 is added to the given year to get the result.   So, 2032 + 28 = 2060   2060nswer: 2060
Answer: A
Find the perimeter and area of the rectangle of length 19 cm and breadth 13 cm. Choose the most appropriate option.
A) 71 cm2 B) 121 cm2 C) 141 cm2 D) 171 cm2 E) 247 cm2

Solution: length = 19 cm, breadth = 13 cm   Perimeter of rectangle = 2 (length + breadth)   = 2 (19 + 13) cm   = 2 × 32 cm   = 64 cm   We know that the area of rectangle = length × breadth   = (19 × 13) cm22   = 247 cm2   ANSW247 cm2R : 247 cm2
Answer: E
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?	Choose the correct choice:
A) 4 months  B) 6 months  C) 7 months  D) 9 months  E) 10 months

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5= 
12 -5 = 7
7   ANSWER:7 months
Answer: C
A will states that the estate would be divided among six sons with the remainder donated to charity. One stipulation in the will is that no one among the sons can receive an amount within 12% of another's amount. If one of the beneficiaries received $30,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the six sons? Select.
A) $4096  B) $14043  C) $7892  D) $17736  E) $15336

Solution: 1st - 30,000.   2nd - 0.88*30,000 = 26,400   3rd - 0.88*26,400 = 23,232   4th - 0.88*23,232 = 20,444.16   5th - 0.88*20,444.16 = ~17,990.86   6th - 0.88*17,990.86 = ~15,831.96   Range = 30,000 - 15,831 = 14,168   Answer: $14043.
Answer: B
Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 4/5 of the juniors is equal to 1/2 of the seniors, what fraction of the students in the room are juniors?  Pick one: A) 13/20 B) 11/3 C) 5/13 D) 12/17 E) 17/20

Solution: Let total number of juniors= J   total number of seniors =S   (4/5) J = (1/2) S   => S = 8/5 J   Total number of students = J+S = (13/5) J   Fraction of the students in the room are juniors = J/(J+S) = J/[(13/5) J]   =5/13   Answer 5/13
Answer: C
5x + y = 19 , and x + 3y = 1. Find the value of 3x + 2y Pick one
A) 20	B) 18	C) 11	D) 10	E) 5

Solution: Add these two equations   6x + 4y = 20   Divide by 2 ( to Get 3x + 2y)   Answer will be D. 10
Answer: D
A card is drawn from a pack of 52 cards. The probability of getting a queen of spade or an ace of club is:
Choose the correct choice from the following answers
A) 1/13 B) 1/26 C) 2/13 D) 1/52 E) 1/48

Solution: Explanation :   Total outcomes = 52   Favourable outcomes (getting a queen of spade or an ace of club) = 2   Probability = 2/52 = 1/26.   Answer : 1/26
Answer: B
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Pick
A) 45 km/hr
B) 50 km/hr
C) 54 km/hr
D) 55 km/hr
E) 59 km/hr

Solution: Speed of the train relative to man =	125	m/sec   10   =	25	m/sec.   2   =	25	x	18	km/hr   2	5   = 45 km/hr.   Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.   x - 5 = 45 x = 50 km/hr.   ANSWER:50 km/hr
Answer: B
There is a train and car. The ratio between the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 320 km in 5 hours. The speed of the bus is 4/5th of the speed of the train. How many kilometers will the car cover in 7 hours? Choose the correct choice from the following options.
A) 375  B) 425  C) 475  D) 525  E) 575

Solution: The speed of the bus is 320/5= 
320/5 = 64
64 km/hr   The speed of the train is  (64*5)/4= 
 (64*5)/4 = 80
80 km/hr   The speed of the car is   80/16 * 15= 
  80/16 * 15 = 75
75 km/hr   The distance covered by the car in 7 hours is 75 × 7= 525 km   The answer is 525.
Answer: D
In a 5 digit ID number, what is the probability of exactly 4 digits are the digit 2? Choose the correct choice from the following choices:
A) 0.81 B) 1 C) 11/22500 D) 0.0081 E) .144

Solution: Total number of 5 digit numbers = 9 * 10 * 10 * 10 * 10 = 90,000   No. of ways of arranging 4 digits as 2 = 5C4=5.   Arrangements are as follows. Here X can be any digit other than 2   1) 2222X = no. of ways = 9   2) 2X222 = no. of ways = 9   3) 22X22 = no. of ways = 9   4) X2222 = no. of ways = 8   5) 222X2 = no. of ways = 9   Probability = (9+9+9+9+8)/90000   =11/22500   Ans - 11/22500
Answer: C
If S = {8, 16, 24, 32, 40, 48}, what is the product of mean and median of the numbers in S?  Choose the correct choice from the following options
A) 652	B) 589	C) 456	D) 620	E) 784

Solution: Mean = (8 + 16 +24 + 32 + 40 + 48)/6= 
(8 + 16 +24 + 32 + 40 + 48)/6 = 28
28   Median= (24+32)/2= 
(24+32)/2 = 28
28   Product= 28*28= 
28*28 = 784
784   Option 784
Answer: E
There are 10 boxes numbered from 1 to 10. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done? Choose the correct option
A) 46
B) 49
C) 52
D) 55
E) 58

Solution: 1 green ball: 10 ways   2 green balls: 9 ways   3 green balls: 8 ways   4 green balls: 7 ways   5 green balls: 6 ways   6 green balls: 5 ways   7 green balls: 4 ways   8 green balls: 3 ways   9 green balls: 2 ways   10 green balls: 1 way   The total number of ways is   10*11/2= 
  10*11/2 = 55
55   The answer is 55.
Answer: D
If A = x% of y and B = y% of x, then which of the following is true?
Choose the correct choice:
A) None of these	B) A is smaller than B.	C) Relationship between A and B	D) If x is smaller than y, then cannot be determined. A is greater than B.	E) A is greater than B.

Solution: Explanation :   None of these = (x/100)y = xy/100.................(Equation 1)   B = (y/100)x = yx/100.................(Equation 2)   From these equations, it is clear that None of these = B   None of thesenswer : Option None of these
Answer: A
Several students are studying together for an exam. 60% of the students who studied less than 10 hours a week feel unprepared. 80% of students who studied 10 hours or more each week feel prepared. If 75% of the students studied less than 10 hours per week, what percent of the students feel prepared for the exam? Choose the correct choice from the following choices:
A) 20
B) 25
C) 30
D) 35
E) 50

Solution: Let's say there are 100 students.   Students who studied <10 hrs = 75% = 75   So students who studied =>10hrs = 25   Given: 60% of the students who studied less than 10 hours a week feel unprepared.   So 40% of 75 (=30) feel prepared   Given: 80% of students who studied 10 hours or more each week feel prepared.   So 80% of 25 (= 20) feel prepared   Total   (30 + 20)= 
  (30 + 20) = 50
50 out of 100 feel prepared. 50% feel prepared   ANSW50R:50
Answer: E
Mary charges $8.50 per hour to clean a house. If she works 27 hours, how much
does she earn in one week?	Choose the correct choice from the following answers
A) $619.50  B) $122.50  C) $229.50  D) $429.50  E) $312.50

Solution: Multiply 27 hours x $8.50 =   Answer: $229.50   correct answer $229.50
Answer: C
For 1rs 4p interest
wat will be for 2000rs?	Choose the correct choice
A) 45Rs	B) 80Rs	C) 40Rs	D) 30Rs	E) 48Rs

Solution: For 1rs , 4p interest   for 2000rs, x   x= 2000/1 * 4p ==> 8000 paise   To express in rs, 8000/100 = 80rs   ANSWER:80Rs
Answer: B
Find the total number of divisors of 1728(including 1 and 1728) Pick:
A) 28	B) 29	C) 30	D) 31	E) 32

Solution: 1728=2^6*3^3   no. of divisors = (6+1)*(3+1)= 
(6+1)*(3+1) = 28
28   28NSWER:28
Answer: A
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half? Choose the correct choice from the following.
A) 10 min.  B) 40 min.  C) 30 min.  D) 20 min.  E) 15 min.

Solution: Part filled by (A + B) in 1 minute =1/60+1/40=1/24	.   Suppose the tank is filled in x minutes.   Then,	x /2	(1/24+ 1/40)= 1   x/2 x 1/15=1   x/30=1   x = 30 min.   Answer is 30 min.
Answer: C
If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2240 less than the principal. What was the principal? Select the correct option:
A) 1500  B) 2500  C) 2507  D) 2800  E) 11500

Solution: P - 2240 = (P*5*4)/100   P = 2800   Answer: 2800
Answer: D
Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 50 years. The age of E is?	Choices:
A) 50 B) 47 C) 48 D) 49 E) 46

Solution: Solution   5 years ago average age of A,B,C,D = 45 years   => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years   => Total present age of A, B, C, D = 180 + 5x4 = 200 years   If E's present age is x years = 200+x/5= 50   x=50 years. 50nswer 50
Answer: A
A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio E of students per class?
Choose the correct choice from the following choices
A) E=3
B) 4
C) 6
D) 8
E) 12

Solution: Another way to look at the problem...   Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)   we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)   (ii)-(i)....   C=10R+10 = 10(R+1).......   so # of classes has to be multiple of 10   AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..   so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3   E=3
Answer: A
A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a women alone in 18 days, how long will a boy take to complete the work?
Choose one.
A) 6days B) 8days C) 9days D) 7days E) 5days

Solution: Explanation:   (1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3   1 man’s 1 day work = 1/6   1womans 1 day’s work = 1/18   (1 Man + 1 woman) ‘s 1 day’s work = 1/6 + 1/18 = 2/9   Therefore, 1 boys 1 day’s work = 1/3 – 2/9 = 3-2/9 = 1/9   Therefore, the boy alone can finish the work in 9 days.   Answer: Option 9days
Answer: C
If n is an integer and 5^n > 50,000,000, what is the least possible value of n?  Choose the correct choice from the following choices.
A) 12  B) 8  C) 9  D) 10  E) 11

Solution: When you seperate the 50000000 into factors of 5 and 2 you get - > 10^7 x 5^1 = 5^8 x 2^7   2 to the ^ 7 = 128 so its 128 x 5^8   that means 5^8 x 5^x must be greater   5^x > 128   5^1=5   5^2=25   5^4= 625   - > so x must be at least 4   5^(8+4)= 5^12   12
Answer: A
If a coin is tossed twice, what is the probability that the coin lands on tails on both tosses?	Choose the most appropriate option
A) 1/6
B) 1/3
C) 1/4
D) 1/2
E) 1

Solution: P(2 tails) = 1/2*1/2=1/4   The answer is 1/4.
Answer: C
The price of a certain painting increased by 20% during the first year and decreased by 15% during the second year. The price of the painting at the end of the 2-year period was what percent of the original price? Choose the correct choice from the following.
A) 102%  B) 105%  C) 120%  D) 135%  E) 140%

Solution: 102%ssume that price is 100   Price at the end of yr 1: 100+ 20 = 120   Price at the end of year 2 = 120 - 120*0.15 = 120*0.85= 
120*0.85 = 102
102   Hence required answer= (102/100)*100= 
(102/100)*100 = 102
102%   102%nswer is 102%.
Answer: A
Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 55 km more than the other. What is the distance between the two stations?  Select:  A) 540 km  B) 495 km  C) 276 km  D) 178 km  E) 176 km

Solution: Explanation:   Let us assume that trains meet after 'x' hours   Distance = speed * Time   Distance traveled by two trains = 20x km and 25x km resp.   As one train travels 55 km more than the other,   25x â€“ 20x = 55   5x = 55   x = 11hours   As the two trains are moving towards each other, relative speed = 20 + 25= 
20 + 25 = 45
45 km/hr   Therefore, total distance= 45*11= 
45*11 = 495
495 km.   ANSWER: 495 km
Answer: B
A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 80 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period? Choose the correct choice from the following options
A) 79	B) 89	C) 95	D) 90.91	E) 97.2

Solution: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6   A1+A2+A3+A4+A5+A6 = 100*6= 
100*6 = 600
600   The year before , the 5 courses be B1, B2 , B3 , B4 , B5   B1+B2+B3+B4+B5= 80*5= 
80*5 = 400
400   Student's average= (600+400)/11 = 90.91   Answer 90.91
Answer: D
In 2005, 20 percent of the math department’s 45 students were female, and in 2007, 40 percent of the math department’s 705 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?	Choose one
A) 85%
B) 130%
C) 211.1%
D) 220%
E) 260%

Solution: Female students in 2005 = 20% of 45 = 9   Female students in 2007 = 40% of 70 = 28   Percentage increase = [(28 - 9)/9] *100 % = 211.1%   211.1%orrect Option: 211.1%
Answer: C
Find the average of the series : 130, 160, 328, 180 and 162? Choose the correct choice from the following choices: A) 186 B) 196 C) 190 D) 198 E) 192

Solution: Average = (130 + 160 + 328 + 180 + 162)/5   = 960/5= 
960/5 = 192
192   Answer: 192
Answer: E
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a red and the second card is black is?  Choose the correct choice from the following choices:
A) 1/4  B) 1/52  C) 1/26  D) 1/13  E) 1/169

Solution: Probability of a queen = 4/52 = 1/2   Probability of a red card = 26/52 = 1/2   Probability of both = P1*P2 = 1/(2*2) = 1/4   1/4nswer is 1/4.
Answer: A
A certain sum amounts to Rs.1725 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?  Choices.
A) 4%	B) 5%	C) 2%	D) 9%	E) 1%

Solution: 3 --- 1725   5 --- 1875   --------------   2 --- 150   N = 1 I = 75 R = ?   P = 1725 - 225= 
1725 - 225 = 1_500
1500   75= (1500*1*R)/100   R =5%   Answer:5%
Answer: B
A box contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 25/36. How many marbles are in the bag? Pick one
A) 24	B) 48	C) 60	D) 72	E) 84

Solution: ok let me see if i can explain what went on in the previous post   lets say i have x marbles in the bag in total --> out of them 12 are red   so the probability of pulling a non-red marble is (x -12) / x   now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x   probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n   so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]   this is given as 25/36   -->(x-12)^2= 25/36   x^2   square rooting u have x-12/x = 5/6 or x = 72   84
Answer: E
Platinum is 19 times as heavy as bronze and silver is 9 times as heavy as bronze. In what ratio these two metals be mixed so that the alloy is 15 times as heavy as bronze is Answers.
A) 2:1 B) 3:2 C) 1:2 D) 2:3 E) 3:4

Solution: Let the proportion of weight of platinum in the mixture = x   then the proportion of weight of silver in the mixture = 1 - x   According to the question   19 X x + 9 (1 - x) = 15 X 1   19x + 9 - 9x = 15   10x = 15 - 9= 
15 - 9 = 6
6   x= 6/10 = 3/5   Therefore the proportion of weight of platinum in the mixture = x = 3/5   and the proportion of weight of silver in the mixture = 1 - x = 1 - 3/5 = 2/5   The required ratio of platinum : silver = 3/5 : 2/5   = 3 : 2   ANSWER:3:2
Answer: B