MU-NLPC/Calc-aqua_rat huggingface dataset:
Laura has a deck of standard playing cards with 14 of the 70 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?  Select the correct option.
A) 1/4 B) 12/42 C) 5/26 D) 1/5 E) 13/42

Solution: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.   If there is no replacement then how is the (P) that the 10th card is 14/70 ??   there are many cases here to be considered here if there is no replacement such as:   H- Denotes heart X-may be any diamond, spade or club.   1. HXXXXXXXXH   2. HHXXXXXXXH   3. HHHXXXXXXH   .   .   .   .   .   9. HHHHHHHHHH   10. XXXXXXXXXH   All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.   For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 14/70 = 1/5 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....   1/5
Answer: D
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is  Pick:
A) 288  B) 278  C) 245  D) 397  E) 252

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X   = 245 m.   Answer:245
Answer: C
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?	Select:
A) 3/4	B) 1/3	C) 7/19	D) 8/21	E) 9/21

Solution: 7C1/21C1=7/21=1/3   ANSWER:1/3
Answer: B
If |z|/w = 2, which of the following must be true?
Choose the correct choice from the following choices:	A) z = -2w	B) z = 2w	C) z^2 = 4w^2	D) z^2 = 4w^3	E) z^3 = 8w^3

Solution: |z|/w = 2.   |z| = 2w.   Then z = 2w or -2w and so z^2 = 4w^2.   The answer is z^2 = 4w^2.
Answer: C
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
Choose the most appropriate option: A) 15 kmph B) 17 kmph C) 75 kmph D) 18 kmph E) 87 kmph

Solution: 90 * 10/60= 
90 * 10/60 = 15
15 kmph   15 kmphnswer: 15 kmph
Answer: A
The ratio of the ages of Mona and Sona is 4:5. Twelve years hence, their ages will be in the ratio of 5:6. What will be Sona's age after 6 years?
Choose the most appropriate option: A) 8 B) 10 C) 12 D) 14 E) 66

Solution: Let their present ages be 4x & 6x   Then (4x + 12)/(5x + 12) = 5/6 ; x=12   Sona's age after 6 years = (5x +6) = 66 years   ANSW66R:66
Answer: E
Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised? Choices
A) 11.
B) 12
C) 13
D) 14
E) 14.5

Solution: Let the Candy and Soda before the increase be C and S respectively   so Increased price of can = C(1+ 25/100) =10 -----------> C= 8   Increase price of soda : S(1+1/2) = 6 -----------> S=4   Hence total = 8+4 =12.. hence answer: 12
Answer: B
Find the odd man out
864, 420, 200, 85, 40, 16, 6	Choices.
A) 420	B) 85	C) 16	D) 40	E) 6

Solution: 6x2+4=16   16x2+8=40   40x2+12=92   92x2+16=200.. and so on. 85   ANSWER:85
Answer: B
On a counter of a donuts store, there are only 16 identical donuts, 11 filled with chocolate and 5 filled with jelly, but the seller tells me that the donuts are randomly placed on the counter. If would want to buy two, what is the probability that I choose one donuts of each flavor? Options:
A) 2/16
B) 1/32
C) 11/12
D) 11/48
E) 11/24

Solution: We are told that we have 16 donuts, 11 of chocolate and 5 of jelly. The donuts are picked simultaneous and randomly, D1 and D2, in different flavors. There are two acceptable outcomes: 1) D1 is chocolate and D2 is jelly; 2) D1 is jelly and D2 is chocolate. Let's go: 1) D1 = (11/16)(5/15)= 11/48 chance of this happening. 2) D2 = (5/16)(11/15) = 11/48 chance of this happening. Then: (11/48)+(11/48)= 11/24, chance of getting the result that you wanted. Answer 11/24.
Answer: E
Bob bikes to school every day at a steady rate of d miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
Choose one:
A) (d + y) / t	B) 2(d + t) / dy	C) 2dyt / (d + y)	D) 2(d + y + t) / dy	E) x(y + t) + y(x + t)

Solution: If we choose for d (distance): 10 miles, for d 10 and for y 5.   t would be 90 minutes or 1,5 hours.   If I try this for answer choice 2dyt / (d + y) it fits.
Answer: C
A can complete a certain job in 16 days. B is 60% more efficient than A. In how many days can B complete the same job?	Choose the correct choice:
A) 6	B) 6.25	C) 7	D) 7.5	E) 10

Solution: Let, Total Work Unit = 160 Units   A can finish in 16 days = 160 unit work   i.e. A can finish in 1 days = 10 unit work   i.e. B can finish in 1 days = 10+(60/100)*10= 
10+(60/100)*10 = 16
16 unit work   Days in which B will complete the work alone= 160/16= 
160/16 = 10
10 days   Answer: Option 10
Answer: E
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?	Choose the correct option:
A) 12  B) 10  C) 11  D) 9  E) 8

Solution: Explanation :   speed of the bus excluding stoppages = 54 kmph   speed of the bus including stoppages = 45 kmph   Loss in speed when including stoppages = 54 - 45= 
54 - 45 = 9
9kmph=> In 1 hour, bus covers 9 km less due to stoppages   Hence, time that the bus stop per hour = time taken to cover 9 km   =distance / speed= 9 / 54 hour = 1/6 hour = 60/6= 
60/6 = 10
10 min   Answer : 11
Answer: C
A train covers a distance of 12 km in 10 min. If it takes 4 sec to pass a telegraph post, then the length of the train is?  Answers.
A) 20
B) 110
C) 120
D) 80
E) 60

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 4= 
20 * 4 = 80
80 m.   Answer: Option 80
Answer: D
A factory makes 134,341 jam packets which need to be placed in boxes and each box can contain at most 9 packets.How many packets will be in the last unfilled box?	Choose the correct choice from the following options
A) 1 packet
B) 2 packets
C) 3 packets
D) 4 packets
E) 5 packets

Solution: In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 134,341 = 16 and 9 is divisible by 9.   Hence,we need to add 2 to this number for it to be divisible by 9   Correct Option: 2 packets
Answer: B
A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit	Choose the correct choice from the following
A) Rs.1200	B) Rs.1230	C) Rs.1260	D) Rs.1290	E) None of these

Solution: Explanation:   Let the new S.P. be x, then.   (100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)   =>(95/1140=105/x)=>x=1260   Option Rs.1260
Answer: C
If two numbers are in the ratio 4:3. If 10 is added to both of the numbers then the ratio becomes 5:4 then find the biggest number.  Select the correct option
A) 60	B) 80	C) 70	D) 40	E) 100

Solution: 4:3   4x + 20 : 3x + 20 =5 : 4   4[4x + 20] =5[3x + 20]   16x + 80 = 15x + 100   16x -15x = 100 - 80= 
100 - 80 = 20
20   Then biggest number is= 4x   4x = 80   80
Answer: B
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?  Options:
A) 1.6	B) 1.5	C) 1.2	D) 1.9	E) 1.3

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer:1.5
Answer: B
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 50 cms?	Select the correct option:
A) 187 B) 476 C) 119 D) 208 E) 276

Solution: Area of the room =3.5 * 8.5= 
3.5 * 8.5 = 29.75
29.75   Area of the tile= 0.5 *0.5= 
0.5 *0.5 = 0.25
0.25   No. of tiles= 29.75/0.25= 
29.75/0.25 = 119
119   Answer : 119
Answer: C
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 13 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is  Choose the correct choice from the following options:  A) 345600  B) 153400  C) 153600  D) 154000  E) 154200

Solution: Perimeter = Distance covered in 8 min. = 18000 x 8 m = 2400 m.   60   Let length = 3x metres and breadth = 2x metres.   Then, 2(3x + 2x) = 2400 or x = 240.   Length = 720 m and Breadth = 480 m.   Area = (720 x 480) m2 = 345600 m2.   345600
Answer: A
If n = 3 x 4 x p, where p is a prime number greater than 3, how many different positive non-prime divisors does n have, excluding 1 and n? Pick.
A) Six	B) Seven	C) Eight	D) Nine	E) Ten

Solution: N=Xa∗Yb where X and Y are prime,   then number of factors of N are given by the formula (a+1)(b+1) { Notice I have simply increased the powers of X and Y by one and then multiplied them. Also Make sure X and Y are DISTINCT primes)   So, in your question, n = 3 x 4 x p, where p is prime.   I can n=31∗22∗p^1   or number of factors = (1+1) * (2+1) * (1+1)= 
(1+1) * (2+1) * (1+1) = 12
12.   But Notice we need to find Non prime and Other than 1 and n, so we have three prime numbers (2,3,p) , 1 and N.   Excluding these, we have 12-5= 
12-5 = 7
7 such factors.   Hence Answer is Seven
Answer: B
A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?  Choose the correct choice from the following answers:
A) 66 sec
B) 46 sec
C) 48 sec
D) 65 sec
E) 64 sec

Solution: D = 540 + 180= 
540 + 180 = 720
720   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 720/15= 
720/15 = 48
48 sec   Answer:48 sec
Answer: C
A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds. If the typical dosage is 2 cubic centimeters per 10 pounds of the body weight, by what percent was the prescribed dosage lesser than the typical dosage? Pick
A) 8%	B) -37.5%	C) 11%	D) 12.5%	E) 14.8%

Solution: Typical dosage per 10 pound of the body weight = 2 c.c   Typical dosage per 120 pound of the body weight = 2 *(120/10)   = 2 * 12= 
2 * 12 = 24
24 c.c   Dosage prescribed by doctor for 120 pound patient= 18 c.c   % prescribed dosage greater than the typical dosage = (18-24/16) *100%   =(-6/16) *100%   = -37.5%   Answer -37.5%
Answer: B
Ganesh ,Ram and Sohan together can do a work in 16 days. If Ganesh and Ram together can do a the same work in 24 days then, how long will take Sohan to do the same work?
Select:
A) 48  B) 58  C) 68  D) 78  E) 100

Solution: Solution:   Work done by three of them together in 1 day= 1/16............(1)   Work done by Ganesh and Ram together in 1 day= 1/24.....(2)   So,work done by Sohan in one day=(1)- (2)=(1/16) - (1/24)=1/48   =>Total days taken by Sohan to complete the work alone= 48 days.   48nswer 48
Answer: A
Five boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?	Pick
A) A)4^30	B) B)2^30	C) C)1^30	D) D)3^30	E) E)5^30

Solution: 5^30ach Mango can be given to any one of the four people or in other words..1 mango can be divided into 5 ways...so all 30 can be divided in 5^30 ways   ANS:5^30
Answer: E
The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 40/kg. how much did a kg of coffee cost in june ?  Choose the correct choice from the following options
A) 40 B) 60 C) 80 D) 100 E) 120

Solution: Let the price of tea and coffee be x per kg in June.   Price of tea in July = 1.2x   Price of coffee in July = 0.8x .   In July the price of 1/2 kg (400gm) of tea and 1/2 kg (400gm) of coffee (equal quantities) = 40   1.2x(1/2) + 0.8x(1/2) = 40   => x =40   Thus proved...option 40.
Answer: A
A florist is making a bouquet of flowers. The florist has 12 different flowers to choose from to make the bouquet. The bouquet will be made of 6 different flowers. What is the probability the florist will choose a rose, a tulip, and a lilie? Choose the correct choice.
A) 1/2
B) 3/55
C) 111/112
D) 1/5
E) 3/308

Solution: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.   Total number possible = 12C6 - 12!/(6!(12 - 6)!) = 924   Number rose possible = 1C1 = 1   Number tulip possible = 1C1 = 1   Number lilie possible = 1C1 = 1   Number other possible = 9C1 = 9   Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)   P(RTL) = (1C1)(1C1)(1C1)(9C1)/12C6 = 9/924 = 3/308   Answer: 3/308
Answer: E
If two sides of a triangle are 6 and 13, respectively, which of the following could NOT be the area of this triangle?
Choose the correct choice from the following answers:  A) 40  B) 6  C) 17  D) 29  E) 38

Solution: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 6 and 12.   We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)13 * 6 -or- (.5)6 * 13 will result in a maximum area of 39 for the triangle; therefore, the triangle could never have an area of 40.   40
Answer: A
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 136, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?	Choose the correct choice from the following choices:	A) 24	B) 33	C) 55	D) 77	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 = 136 => .1x + 3/4x = 136 => x = 160   160 - 136 = pure gala =24.   24
Answer: A
Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 8 minutes 30 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
Choose the correct answer
A) 3% B) 15% C) 8% D) 10% E) 12%

Solution: Bob's time = 600 secs.   His sis' time = 510 secs.   Percent increase needed = (640-510/600) * 100 = 90/600 * 100= 
90/600 * 100 = 15
15%. Ans (15%).
Answer: B
An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?
Select the correct option:
A) 1/12
B) 1/2
C) 3/4
D) 1/6
E) 1/9

Solution: S={1,2,3,4,5,6}   P(E)=n(E)/n(S)   n(s)=Total numbers in a die=6   Let E be the event of getting the multiple of 3   then ,E={3,6}   P(mutliple of 3) = 2/6 = 1/3   Let E be the event of getting the multiple of 4   then ,E={4}   P(multiple of 4) = 1/6   P(multiple of 3 or 4) = 1/3 + 1/6 = 1/2   ans 1/2
Answer: B
Rectangular Floors X and Y have equal area. If Floor X is 18 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
Select the correct option
A) 13 1/2 B) 18 C) 18 3/4 D) 21 E) 36

Solution: The area of a rectangle is: Area = length x width   We are given that floor X is 12 feet by 18 feet and that floor Y is 9 feet wide. So we can say:   length of X = 18   width of X = 18   width of Y = 9   length of Y = n   We also can say:   Area of Floor X = Area of Floor Y   (length of X)(width of X) = (length of Y)(width of Y)   (18)(18) = 9n   (18)(2) = n   36 = n   Answer 36.
Answer: E
Mahesh and suresh are ranked 31th and 32th respectively form the top in a class of 41 Students. What will be their respective ranks from the bottom ?	Options:
A) 9th and 10th	B) 11th and 12th	C) 12th and 13th	D) 10th and 11th	E) 10th and 12th

Solution: 1-----41   2-----40   3-----39   4-----38   .   .   .   .   31---11   32---10   33---9   34---8   35----7   36---6   37---5   38----4   39----3   40---2   41----1   so....from bottom mahesh suresh ranks are 11th and 10th   ANSWER:10th and 11th
Answer: D
find the smallest number in GP whose sum is 38 and product is 1728  Answers:
A) 5  B) 6  C) 7  D) 8  E) 9

Solution: Let x,y,z be the numbers in geometric progression?   y^2=xz   x+y+z=38   xyz=1728   xyz = xzy = y^2y = y^3 = 1728   y = 12   y^2=xz=144   z=144/x   x+y+z = x+12+144/x = 38   x^2+12x+144=38x   x^2-26x+144=0   (x-18)(x-8)=0   x=8,18   If x =8, z = 38-8-12= 
38-8-12 = 18
18   The numbers are 8,12, 18   Their sum is 38   Their product is 1,728   The smallest number is 8   ANSWER:8
Answer: D
If YWUSQ is 25 - 23 - 21 - 19 - 17 then MKIGF is	Choose the correct answer:
A) 9 - 8 - 7 - 6 - 5
B) 1 - 2 - 3 - 5 - 7
C) 7 - 8 - 4 - 5 - 3
D) 13 - 11 - 9 - 7 - 6
E) None

Solution: In alphabet has 26 words coresponding as   A position 1   E position 5   Z position 26   similarly as given in question Y=25 ;W=23; U=21;S=19; Q=17   for M=13 ;K=11;I=9 and so on   ANSWER:13 - 11 - 9 - 7 - 6
Answer: D
David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?  Choose the correct answer:
A) 75
B) 276
C) 87
D) 165
E) 11

Solution: Explanation:   Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5= 
375/5 = 75
75.   75nswer:75
Answer: A
If it is assumed that 62 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?  Answers:	A) 400	B) 420	C) 480	D) 483.8	E) 600

Solution: Minimum no of mail to be sent for getting 300 responses at 62%   = 300/0.62 = 483.8   Option 483.8
Answer: D
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? Choose the correct choice from the following answers:
A) 79.5 B) 79.0 C) 79.4 D) 79.2 E) 79.3

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer: 79.2
Answer: D
A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $550.00. What would be the approximate hourly charge to rent computer B?  Choose the correct choice from the following:
A) $7.85 B) $11.30 C) $13.20 D) $17.80 E) $22.10

Solution: Pa = price of $7.85   Pb = price of B   Ta = time for $7.85 to complete the job   Tb = time for B to complete the job   Given   Pa = 1.4 Pb   Ta+20 = Tb   Pa*Ta = Pb*Tb=550   1.4Pb * (Tb-20) = Pb*Tb   1.4 Pb Tb - Pb Tb = 1.4 Pb * 20   0.4PbTb = 28Pb   Tb = 28/0.4= 
28/0.4 = 70
70   Pb=550/70 ~ 7.85   $7.85
Answer: A
Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 6 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?	Choose the correct choice from the following choices
A) R-4
B) R/(R+4)
C) R/(R-12)
D) 8/(R-8)
E) 2R - 4

Solution: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.   In T hours Alex will cover 4T miles;   Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);   We want the distance covered by Brenda to be twice as much as that of Alex: 2*6T=R(T-1) --> 12T=RT-R -->T=R/(R-12).   Answer: R/(R-12).
Answer: C
A train covers a distance of 90 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?	Choose one
A) 675  B) 680  C) 685  D) 690  E) 695

Solution: Speed = (90/20 * 60) km/hr = (270 * 5/18) m/sec = 75 m/sec.   Length of the train = 75 * 9= 
75 * 9 = 675
675 m.   675nswer: Option 675
Answer: A
Jane and Thomas are among the 7 people from which a committee of 3 people is to be selected. How many different possible committees of 3 people can be selected from these 7 people if at least one of either Jane or Thomas is to be selected?  Choose the most appropriate option:
A) 20 B) 25 C) 30 D) 35 E) 40

Solution: The total number of ways to choose 3 people from 7 is 7C3 = 35.   The number of committees without Jane or Thomas is 5C3 = 10.   There are  35-10= 
 35-10 = 25
25 possible committees which include Jane and/or Thomas.   The answer is 25.
Answer: B
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?  Choose the correct choice from the following answers: A) 20/9 sec B) 20/2 sec C) 20/7 sec D) 40/9 sec E) 20/1 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed   = (54 + 72)*5/18   = 7*5= 
7*5 = 35
35 mps.   The time required= d/s   = 100/35 = 20/7 sec.   Answer: 20/7 sec
Answer: C
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 answer
A) 12/455  B) 24/455  C) 9/31  D) 48/75  E) 89/121

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   = (Â²Câ‚)(â´Câ‚‚)/Â¹âµCâ‚ƒ   = (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455   12/455NSWER 12/455
Answer: A
How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
Choose the most appropriate option
A) 50 sec
B) 77
C) 55
D) 44
E) 11

Solution: Answer: Option A   Explanation:   The distance to be covered = Sum of their lengths = 200 + 300= 
200 + 300 = 500
500 m.   Relative speed= 72 -36= 
72 -36 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 mps.   Time required= d/s = 500/10= 
500/10 = 50
50 sec.   50 secnswer: 50 sec
Answer: A
Sam invested $1000 @20% per annum for one year. If the interest is compounded half yearly, then the amount received by Sam at the end of the year will be?  Pick.
A) $1542
B) $1145
C) $1210
D) $1642
E) $1020

Solution: P = $1000   R = 20%   p.a. = 10%   T = 2 half years   Amount = 1000 * (1 + 10/100)^2 = 1000* 11/10 * 11/10= 
1000* 11/10 * 11/10 = 1_210
$1210   Answer is $1210
Answer: C
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:  Choices:
A) 3500  B) 4000  C) 4050  D) 5000  E) 6000

Solution: Explanation:   Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 x 2) = 10100 .... (i)   Q + R = (6250 x 2) = 12500 .... (ii)   P + R = (5200 x 2) = 10400 .... (iii)   Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)   Subtracting (ii) from (iv), we get P = 4000.   P's monthly income = Rs. 4000.   Answer: 4000
Answer: B