MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain roller coaster has 6 cars, and a passenger is equally likely to ride in any 1 of the 6 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 6 times, what is the probability that the passenger will ride in each of the 6 cars? Choose the correct choice from the following options:	A) 3/1944	B) 1/96	C) 2/96	D) 1/1944	E) 1

Solution: If he is to ride 6 times and since he can choose any of the 6 cars each time, total number of ways is   = 6 * 6 * 6 * 6 * 6 * 6= 
6 * 6 * 6 * 6 * 6 * 6 = 46_656
46656   Now the number of ways if he is to choose a different car each time is= 6 * 5 * 4 * 3 * 2 * 1= 
6 * 5 * 4 * 3 * 2 * 1 = 720
720   So the probability is= 720/46656 = 3/1944   3/1944nswer : 3/1944
Answer: A
For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(99) – g(97)? Choose the correct option
A) 98  B) 100  C) 0  D) 99  E) 97

Solution: g(99) = 1*3*5*7*9*...*99   g(97) = 1*3*5*7*9*...*97   g(99) - g(97) = 1*3*5*7*9*...*99 - 1*3*5*7*9*...*97 = 1*3*5*7*9*...*97*(99 - 1) = 1*3*5*7*9*...*97*98   hence:98.
Answer: A
The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to q% of stall’s revenue and accounted for r% of sales of juice tetra packs. Which of the following expresses q in terms of r? Options
A) 100r/(150 – r)
B) 200r/(250-r)
C) 200r/(300-r)
D) 250r/(400-r)
E) 300r/(500-r)

Solution: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.   Total revenue= Revenue due to A + Revenue due to B   = (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)   = r *1 + (100-r) *1.5   = r + (150-1.5r) --- (1)   2. But we know, revenue due to A = q %. of the total revenue --- (2)   3. To express q in terms of r we need to relate (1) and (2)   4. q % = r / ( r + (150-1.5r))   or q = 100r / 150-0.5r = 200r/(300-r)   200r/(300-r)
Answer: C
The product of all the prime numbers less than 16 is closest to which of the following powers of 10 ?  Choose the correct choice from the following options:
A) 10^9
B) 10^8
C) 10^7
D) 10^6
E) 10^5

Solution: Product of Prime numbers less than 16 is 2*3*5*7*11*13   2*5= 
2*5 = 10
10 .   10*11*3*7*13= 10*10*3*10*10 (approximately) ~ Product will be >10^4 <10^6 i.e. 10^5   10^5 is the answer
Answer: E
Can V and can В are both right circular cylinders. The radius of can V is twice the radius of can B, while the height of can V is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can V with the same brand of gasoline?  Choose the correct choice from the following options: A) $1 B) $2 C) $4 D) $8 E) $16

Solution: Let x be the radius of b and 2h be the height of B. Therefore, radius of V = 2x and height = h   Vol of b = 3.14*x^2*2h   Vol of a = 3.14*4x^2*h   cost to fill half of B = $4 --> cost to fill full B = $8   --> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16   Ans $16
Answer: E
The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 2. What is the radius of circle O?	Choose the correct choice from the following options:
A) –2/pi B) 1 C) 3 D) 4 E) 5

Solution: pi*r^2 + 2r -2*pi*r = 2   Simplifying the equation: pi*r(r-2)+2r=2   Without much algebraic: We can Test the answers quickly, then 1 is the only possible answer that will eliminate pi from equation.   Answer is 1
Answer: B
BCB, DED, FGF, HIH, ___	Choose the correct choice from the following answers.
A) KOP  B) QLM  C) JKJ  D) PSQ  E) IOP

Solution: This series consists of a simple alphabetical order with the first two letters of all segments: B, C, D, E, F, G, H, I, J, K. The third letter of each segment is a repetition of the first letter.   ANSWER:JKJ
Answer: C
All the faces of cubes are painted with red colour.It is then cut into 64 equal small cubes.Find How many small cubes are there whose three faces are coloured ?  Choose the correct answer:
A) 4 B) 8 C) 16 D) 24 E) 2

Solution: There are 64 small cubes,Hence one side side of the big cube is 3√64=4 cm   Number of small cubes having three faces coloured = No. of corners = 8   Answer: 8
Answer: B
Jerry has 3 flavors of ice cream in his parlor. How many options are there for George to pick a one-flavor, two-flavor or three-flavor order?  Answers
A) 2  B) 3  C) 4  D) 7  E) 8

Solution: 3C1 + 3C2+ 3C3 = 7.   Ans 7.
Answer: D
A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? Select the correct option:
A) 229  B) 288  C) 600  D) 888  E) 121

Solution: D = 30 * 5= 
30 * 5 = 150
150   RS= 40 – 30 = 10   T = 150/10= 
150/10 = 15
15   D= 40 * 15= 
40 * 15 = 600
600 km   Answer: 600
Answer: C
In a group of 1 boy and 9 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be selected?	Select:	A) 60	B) 68	C) 76	D) 84	E) 92

Solution: Number of ways to select four children is 10C4 = 210   Number of ways to choose only girls is 9C4 = 126   Number of ways that at least one boy is selected is  210 - 126= 
 210 - 126 = 84
84   The answer is 84.
Answer: D
How much 60% of 50 is greater than 45% of 30?	Select the correct option
A) 18  B) 91  C) 16.5  D) 17  E) 12

Solution: (60/100) * 50 – (45/100) * 30   30 - 13.5= 
30 - 13.5 = 16.5
16.5   Answer: 16.5
Answer: C
The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations R of soloists can appear in the liner notes?	Choose the most appropriate option:  A) 5!  B) 10!/(5!5!)  C) 10!/5!  D) 10!  E) 10!*5!

Solution: Total Soloists to choose from = 10   Soloist Required = 5   Question : How many different combinations R of soloists can appear in the liner notes?   The language of the question clearly mentions that only the combinations need to be calculated   i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)   Method-1:   Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)   Method-2:   No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6   Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,   Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)   Answer: Option 10!/(5!5!)
Answer: B
In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Pick one:
A) 1/80  B) 1  C) 40  D) 1/40  E) 80

Solution: Let the required number of days be x.   Less cows, More days (Indirect Proportion)   Less bags, Less days (Direct Proportion)   Cows	1:40 :: 40 : x   Bags 40:1   1 * 40 * x = 40 * 1 * 40   x = 40.   Answer is 40.
Answer: C
A snooker tournament charges $45.00 for VIP seats and $20.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?  Select:
A) 200 B) 276 C) 230 D) 240 E) 250

Solution: let no of sits in vip enclosure is x then x*45 +20( 320-x) =7500 or 25x = 7500 -6400 , x = 1100/25= 
1100/25 = 44
44   vip=44 general 320-44= 
320-44 = 276
276   276
Answer: B
A bag has 9 green balls and 23 pink balls. How many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1:1?
Choose the correct choice from the following options.
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: Suppose x green balls need to be added.   Then, the number of green balls becomes 9 + x, and the number of pink balls remains the same, 23.   But now the ratio of green and pink balls is 1:1   This means,   (9 + x)/23 = 1/1   Solving this we get x = 14.   Ans 14
Answer: E
A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:  Choose the correct option: A) 24 km/hr B) 25 km/hr C) 26 km/hr D) 23 km/hr E) 22 km/hr

Solution: Speed upstream =8/(24/60)= 
8/(24/60) = 20
20 km/hr   Speed of the stream= 4 km/hr   speed of boat in still water = (20+4)= 
(20+4) = 24
24 km/hr   24 km/hrnswer : Option 24 km/hr
Answer: A
If by reduction of rupee 1 per kg in the price,a person can buy one kg more for Rs.56. find the original price of the per kg?	Choose the correct choice from the following options:
A) 7rs/kg  B) 8rs/kg  C) 9rs/kg  D) 6rs/kg  E) 5rs/kg

Solution: for Rs.56 he can buy = 56/8= 
56/8 = 7
7kg rice. (Original Price)   By reduction of Rs.1 per kg,= 56/7= 
56/7 = 8
8kg rice. (As per reduction)   Original Price(8rs), he can buy= 7kg of rice   ANSWER:8rs/kg
Answer: B
Of the 500 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
Choose the correct option:
A) 65	B) 100	C) 115	D) 130	E) 325

Solution: 300 prefer X (Group 1);   200 prefer Y (Group 2).   City Y needs 375 people: letall 200 who prefer Y (entire Group 2) be relocated there, the rest 175 will be those who prefer X from Group 1;   City X needs 125 people: 300-175= 
300-175 = 125
125 from Group 1 will be relocated to X, which they prefer.   So, the highest possible number of employees who will be relocated to the city they prefer is  200+125= 
 200+125 = 325
325.   Answer: 325.
Answer: E
one kilo gram coffee is Rs. 126 and Rs. 135 are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the 3rd variety per kilo gram is?  Choose the most appropriate option.
A) 150  B) 133  C) 175.5  D) 178  E) 190

Solution: Since first and second varieties are mixed in equal proportions.   So, their average price = Rs. 126 + 135 = Rs. 130.50   2   So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.   By the rule of alligation, we have:   Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind   Rs. 130.50	Mean Price   Rs. 153	Rs. x   (x - 153)	22.50   x - 153	= 1   22.50   x - 153 = 22.50   x = 175.50   175.5
Answer: C
A train covers a distance of 36 km in 12 min. If it takes 7 sec to pass a telegraph post, then the length of the train is?  Choose the correct choice from the following choices:
A) 330	B) 340	C) 350	D) 360	E) 370

Solution: Speed = (36/12 * 60) km/hr = (180 * 5/18) m/sec = 50 m/sec.   Length of the train = 50 * 7= 
50 * 7 = 350
350 m.   Answer: Option 350
Answer: C
Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?  Choose the correct choice from the following choices.
A) 26/36 B) 26/31 C) 26/19 D) 26/33 E) 26/38

Solution: Let ages of Ramu and Shyam be x and y respectively.   x/y = 3/4 => x = 3/4 y   (x- 7)/(y - 7) = 2/3   => 3x - 21 = 2y - 14 => 3x = 2y + 7   But x = 3/4 y   3 * 3/4 y = 2y + 7   9y = 8y + 28 => y = 28years   => x = 21 years   Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.   Answer:26/33
Answer: D
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:  Choose the correct choice from the following answers:  A) 1510  B) 1315  C) 1015  D) 1215  E) 1715

Solution: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7   = 1008 + 7= 
1008 + 7 = 1_015
1015   Answer: Option 1015
Answer: C
15 : 5 seconds :: ? : 10 minutes  Choose the correct option
A) 10 B) 15 C) 30 D) 25 E) 30

Solution: 15*10=5*x   x=30   ANSWER:30
Answer: C
Certain sum becomes 3 times it self at compound interest in 10 years. In how many years it becomes 9 times?
Choose the correct option.
A) 10 Years	B) 20 Years	C) 30 Years	D) 40 Years	E) 45 Years

Solution: P(1 + R/100)10 = 3P   => P(1 + R/100)10 = 3   Let P(1 + R/100)n = 9P   => (1 + R/100)n = 9   => 32 = [(1 + R/100)10]2   => (1 + R/100)n => (1 + R/100)20   => n = 20 Years.   20 Years
Answer: B
Of the 3,600 employees of Company X, 1/6 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical? Options:  A) 25%  B) 22.2%  C) 20%  D) 12.5%  E) 11.7%

Solution: Welcome, just post the question and the choices   Let's see, the way I did it was   1/6 are clerical out of 3600 so 600 are clerical   600 reduced by 1/3 is 600*1/3   so it reduced 200 people , so there is 400 clerical people left   but since 200 people left, it also reduced from the total of 3600 so there are 3400 people total   since 400 clerical left / 3400 people total   you get (A) 11.7%   Answer :11.7%
Answer: E
Two circles are there one with arc area 60digree equal to 45digree of another circle find the area of circle1:circle2 ratio	Choose the correct answer.
A) 3:4 B) 1:4 C) 1:2 D) 2:3 E) 1:3

Solution: area for first circle=(3.14*r^2)/6   area of second circke=(3.14*R^2)/8   therefore, ratio=3:4   3:4NSWER:3:4
Answer: A
A $500 investment and a $1,500 investment have a combined yearly return of 22 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?  Choose the correct choice from the following answers.
A) 29%	B) 20%	C) 27%	D) 25%	E) 12%

Solution: The equation we can form the question :   Return on Total Investment = Sum of individual Investments   (500+1500)(22)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.   Solving the equation, we get x = 27% ( Option 27% )	ANSWER:27%
Answer: C
Robert tossed a fair coin 3 times. What is the probability that the coin landed heads up exactly twice? Choose the correct choice:
A) 0.125  B) 0.250  C) 0.375  D) 0.75  E) 0.875

Solution: Total number of outcomes = 2 * 2 * 2= 
2 * 2 * 2 = 8
8   Out of 3 times we need heads exactly 2 times= 30.3752 = 3   Probability = 3/8= 
3/8 = 3/8 = around 0.375
0.375   The answer is, therefore, (0.375).
Answer: C
Two unbiased coins are tossed. What is probability of getting at most one tail ? Answers.
A) 1/2  B) 1/3  C) 3/2  D) 3/4  E) None of these

Solution: Explanation:   Total 4 cases = [HH, TT, TH, HT]   Favourable cases = [HH, TH, HT]   Please note we need atmost one tail, not atleast one tail.   So probability = 3/4   Option 3/4
Answer: D
Sara and Alan start a company with Rs.100000 and Rs.50000 respectively. how should they share their profits at the end of one year?	Pick one: A) 1:2 B) 3:4 C) 3:8 D) 3:1 E) 3:2

Solution: The ratio of the investments made by 1:2 and B =   100000: 50000=> 2:1.1:2nswer: 1:2
Answer: A
The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time F will it take to fill the tank now?  Pick:  A) 50% less time  B) 50% more time  C) 75% less time  D) 75% more time  E) 100% more time

Solution: (VC)Volume of the cylinderical vessal is directly proportional to R^2.   So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)   Now if with velocity V tank can be filled in T1 time of volume VC   So now Velocity is 50% less i..e V/2   So time taken to fill the capacity VC/4 by V/2 velocity is T2.   VT1 = VC   V/2*T2 = VC/4   So T1/T2 = 1/2   So Tank will be filled in less time. that is F=50 % less.50% less time
Answer: A
Dawson sold an item for Rs.3600/- and incurred a loss of 10%. At what price should he have sold the item to have gained a profit of 10%? Choose the correct choice from the following options:
A) 4000 B) 4100 C) 4200 D) 4300 E) 4400

Solution: Explanation:   10% loss means SP = 90% of CP   :. CP = Rs.3600x100/90 = Rs.4000.   The SP for a gain of 10% = 4000+10% of 4000 = 4000+400= 
4000+400 = 4_400
Rs4400.   Answer: Option 4400
Answer: E
There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability Y that at least one will be orange?  Choose the correct choice from the following answers
A) Y=7/10
B) Y=3/5
C) Y=2/5
D) 3/10
E) 1/10

Solution: Method 1   Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10   Method 2   Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10   Method 3   Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue   = 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)   = 1 - 3C2/5C2   = 1-(3/10) = 7/10   Y=7/10nswer :Y=7/10
Answer: A
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Choices:  A) 7m  B) 8m  C) 4m  D) 3m  E) 2m

Solution: Let the sides of the rectangle be l and b respectively.   From the given data,   (√l2 + b2) = (1 + 108 1/3 %)lb   => l2 + b2 = (1 + 325/3 * 1/100)lb   = (1 + 13/12)lb   = 25/12 lb   => (l2 + b2)/lb = 25/12   12(l2 + b2) = 25lb   Adding 24lb on both sides   12l2 + 12b2 + 24lb = 49lb   12(l2 + b2 + 2lb) = 49lb   but 2(l + b) = 28 => l + b = 14   12(l + b)2 = 49lb   => 12(14)2 = 49lb   => lb = 48   Since l + b = 14, l = 8 and b = 6   l - b = 8 - 6= 
8 - 6 = 2
2m.   Answer:2m
Answer: E
How many numbers between 10 - 99 yield a reminder of 8 when divided by 10 and also yield a remainder of 2 when divided by 8?  Choose the correct option:
A) One
B) Three
C) Two
D) Five
E) Four

Solution: Answer = Three) Three   Numbers between 10 - 99 giving remainder 8 when divided by 10 = 18, 28, 38, 48, 58, 68, 78, 88, 98   The above Numbers giving remainder 2 when divided by 8 = 18, 58, 98 = 3
Answer: B
In how much time will a train of length 100 m, moving at 54 kmph cross an electric pole?  Select:
A) sec B) sec C) sec D) sec E) sec

Solution: Convert kmph to mps. 54 kmph = 54 * 5/18= 
54 * 5/18 = 15
15 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/15= 6.7 sec.   Answer:sec
Answer: D
There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback? Choices.
A) 75
B) 120
C) 210
D) 246
E) 252

Solution: Paperbacks - 4, hardbacks - 6   5 books in total and at least 1 from each.   Total combinations for 5 books = (1pb, 4 hb) + (4pb, 1hb) + (3pb, 2hb) + (2pb, 3hb)   1pb, 4hb = 4c1*6c4 = 60   4pb,1hb = 4c4*6c1 = 6   3pb,2hb = 4c3*6c2 = 60   2pb,3hb = 4c2*6c3 = 120   Total combinations of 5 books = 60+6+60+120= 
60+6+60+120 = 246
>246   Ans 246.
Answer: D
If an integer n is to be chosen at random from the integers 1 to 84, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?	Choose the correct choice:  A) 9/14  B) 3/8  C) 1/2  D) 5/8  E) 3/4

Solution: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.   Thus when n is even, this whole expression will be divisible by 8.   from 1 to 84, there are 42 even integers.   Now when (n+1) is multiple by 8, we have 12 such values for (n+1)   probability that n(n+1)(n+2) will be divisible by 8   = (42 + 12)/84   = 54/84   = 9/14   9/14ns is 9/14
Answer: A
What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?  Choose the correct choice from the following options:
A) 90	B) 95	C) 100	D) 105	E) 110

Solution: 10 and 190 inclusive would mean there are 19 terms.   No need to add up all the terms and further divide by 19 since the terms are evenly spaced in ascending order from 10, 20, 30........190   The middle term is the average which is the tenth term = 100   100 is the answer.
Answer: C
82*83*84*..89 what is the digit in units place?
Options
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: In the product   82*83*84 *85*86......*89   last( unit) digit will be zero as 82 * 85 will give zero as last (unit ) digit and further multiplication with any number will also give zero at unit place.   0NSWER:0
Answer: A
A certain company’s profit in 1996 was 25 percent greater than its profit in 1995, and its profit in 1997 was 30 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?	Select:  A) 5%  B) 62.5%  C) 33%  D) 35%  E) 38%

Solution: Profit in 1995 - 100   Profit in 1996 - 125   %increae Profit in 1997 in comparison to 1995 = 25 + 125*30%= 62.5   Correct Option : 62.5%
Answer: B
Average age of students of an adult school is 40 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.  Choose the correct choice from the following options:
A) 1200
B) 120
C) 360
D) 240
E) None of these

Solution: Explanation :   Let the original no. of students be x.   According to situation, 40x + 120*32 = (x + 120)36 ⇒ x = 120   So, Required no. of students after joining the new students   = x + 120 = 240.   Answer : 240
Answer: D
A sum of money is sufficient to pay A's wages for 20 days and B's wages for 30 days. The same money is sufficient to pay the wages of both for?	Select:
A) 12days	B) 15days	C) 20days	D) 18days	E) 22days

Solution: Let the total money be $x   12days's 1day work = $ x/20   B's 1day work = $ x/30   12days+B 1day work = $ x/12   Money is sufficient to pay the wages of both for 12days   12daysnswer is 12days
Answer: A
On a sum of money, the simple interest for 2 years is Rs. 326, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is  Pick:
A) 15%  B) 14.25%  C) 8.58%  D) 10.5%  E) 11.5%

Solution: Explanation:   The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum   = (R Ã— SI)/(2 Ã— 100)   Difference between the compound interest and simple interest = 340 - 326= 
340 - 326 = 14
14   (R Ã— SI)/(2 Ã— 100)= 14   (R Ã— 326)/(2 Ã— 100) = 14   R = 8.58%   Answer: Option 8.58%
Answer: C
There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
Choose the correct answer
A) 71 ways B) 83 ways C) 85 ways D) 91 ways E) 98 ways

Solution: We first count the number of committee in which   (i). Mr. Y is a member   (ii). the ones in which he is not   case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.   Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).   We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.   case (ii): If Mr. Y is not a member then we left with (6+4-1) people.   we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.   Thus, total number of ways is  7+84= 
 7+84 = 91
91 ways.   91 ways
Answer: D