MU-NLPC/Calc-aqua_rat huggingface dataset:
Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability y that the World Series will consist of fewer than 7 games? Choose the most appropriate option:
A) 12.5%	B) 25%	C) 31.25%	D) 68.75%	E) 75%

Solution: In order to determine the probability y that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.   In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.   Let's analyze one way this could happen for Team 1:   Game 1 Game 2 Game 3 Game 4 Game 5 Game 6   T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses   There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.   Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.   Thus, there are a total of 40 ways for the World Series to last the full 7 games.   The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.   Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.   Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:   Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.   The correct answer is 68.75%. 100  - 31.25= 
 100  - 31.25 = 68.75
68.75%.   The correct answer is 68.75%.
Answer: D
For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence -1, -3, 2,-5, 4, -6,10,-3?  Pick
A) 6	B) 2	C) 3	D) 4	E) 5

Solution: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.   -3*2=-6=negative;   2 * -5 = -10 > negative   -5*(4)=-20=negative.   4 * (-6) = -24 > negative   -6 * 10 = -60 > negative   -3 * 10 = -30 > negative   So there are 6 pairs of consecutive terms.   6nswer: 6.
Answer: A
The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Choose the correct answer.
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35   So 30x + 35 + 31(x + 1) = > x = 4.   4nswer: 4
Answer: A
Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $40 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?	Choose the correct choice from the following.
A) $5	B) $10	C) $14	D) $4	E) $28

Solution: Bill = Fixed Charge + Charge of Calls made   in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $40   in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76   i.e. x+y = 40   and 2x+y = 76   Take the difference if two equations   i.e. (2x+y) - (x+y) = 76 - 40   i.e. x = 36   i.e. Fixed Monthly Charge, y = 4   Answer: Option   $4
Answer: D
On sport’s day, if 12 children were made to stand in each column, 98 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed ? After a certain music being played the plan was that the children have to stand in concentric circles such that the innermost circle will have one student, the next circle will have two students, the third circle will have 3 students and so on. How many circles will be formed in this manner.  Select the correct option:
A) 48
B) 20
C) 50
D) 29
E) 19

Solution: no of students will be 98*12= 
98*12 = 1_176
1176   let us consider n circles then 1+2+3+....+n=1176   n(n+1)/2=1176   n=48 circles   48NSWER:48
Answer: A
How many 5 no. digit no. can be formed with digits 1,2,3,4,5,6 which are divisible by 4 and digits not repeated	Answers
A) 144 B) 168 C) 192 D) 186 E) none

Solution: last 2 digits can be 12,16,24,32,36,52,56,64.   so total possible 5 digit numbers = 8*4*3*2= 
8*4*3*2 = 192
192 numbers   ANSWER:192
Answer: C
If log3N+log9Nlog3N+log9N is whole number, then how many numbers possible for N between 100 to 100?	Options:	A) 1, 9, 81	B) 1, 9, 89	C) 1, 9, 88	D) 1, 9, 22	E) 1, 9, 11

Solution: log3N+log9Nlog3N+log9N = log3N+log32Nlog3N+log32N = log3N+12log3Nlog3N+12log3N =32log3N32log3N   Now this value should be whole number.   Let 32log3N32log3N = w   ⇒log3N=23w⇒log3N=23w   N=3(23w)N=3(23w)   As N is a positive integer, So for w = 0, 3, 6 we get N = 1, 9, 81.   1, 9, 81nswer:1, 9, 81
Answer: A
The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is  Choose the correct answer.
A) 33  B) 278  C) 75  D) 978  E) 27

Solution: Explanation:   The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is  360/12= 
 360/12 = 30
30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.   Answer: 75) 75
Answer: C
6000, 1200, 300, 60...
Pick.
A) 30
B) 15
C) 20
D) 36
E) 46

Solution: 6000/5= 
6000/5 = 1_200
1200   1200/4= 
1200/4 = 300
300   300/5= 
300/5 = 60
60   60/4= 
60/4 = 15
15   ANSWER:15
Answer: B
Which of the following describes all values of x for which 9-x^2 ≥ 0 ?  Pick:  A) x ≥ 1  B) x ≤ -1  C) 0 ≤ x ≤ 1  D) x ≤ -1 or x ≥ 1  E) -3 ≤ x ≤ 3

Solution: 9-x^2 >= 0 ---> x^2-9<=0   --> (x+3)(x-3)<=0   Above equation true for   i) x+3<=0 and x-3>=0 ---> x<= -3 and x>=3 ---> this is not possible ---Strike out this solution   ii) x+3>=0 and x-3<=0 ---> x>=-3 and x<=3 --> -3<=x<=3   Answer -3 ≤ x ≤ 3
Answer: E
A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A. Choose the correct choice from the following.
A) 100	B) 110	C) 120	D) 140	E) None of above

Solution: In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.x/6 = (30+x)/8x = 90. So distance from start after which B will catch A = 90+30= 
90+30 = 120
120km Answer : 120
Answer: C
The surface of a cube is 150sq cm. Find its volume?	Choose the correct choice from the following answers
A) 8cc	B) 9cc	C) 125cc	D) 4cc	E) 6cc

Solution: 6a2 = 150 = 6*25   a = 5 => a3 = 125cc   Answer: 125cc
Answer: C
The sum of four consecutive even numbers is 292. What would be the smallest number?	Choose the correct choice from the following options:
A) 22	B) 27	C) 70	D) 28	E) 11

Solution: Explanation:   Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)   Their sum = 8x - 4 = 292 => x = 37   Smallest number is: 2(x - 2) = 70.   Answer: 70
Answer: C
The present population of a town is 3456. Population increase rate is 20% p.a. Find the population of town before 2 years? Choose the correct answer:
A) 2400
B) 2100
C) 3500
D) 3600
E) 2050

Solution: P = 3456   R = 20%   Required population of town = P/(1 + R/100)^T   = 3456/(1 + 20/100)^2   = 3456/(6/5)^2   = 2400(approximately)   2400nswer is 2400
Answer: A
Average of 10 matches is 32, How many runs one should should score to increase his average by 3 runs. Choose the most appropriate option:
A) A)65	B) B)76	C) C)78	D) D)80	E) E)88

Solution: Explanation:   65verage after 11 innings should be 35   So, Required score = (11 * 35) - (10 * 32)   = 385 - 320= 
385 - 320 = 65
65   65nswer: Option 65
Answer: A
Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?  Choose the correct choice from the following answers:	A) 22	B) 16	C) 27	D) 28	E) 20

Solution: Speed Ratio = 1:4/3 = 3:4   Time Ratio = 4:3   1 -------- 4   4 --------- ? 16 m.Answer:16
Answer: B
The population of a town increases by 12% during first year and decreased by 10% during second year. If the present population is 50,400, what it was 2 years ago?
Options.
A) 40,000	B) 35,000	C) 50,000	D) 60,000	E) none of these

Solution: Here A = 50400, x = 12, y = - 10   Therefore, the population 2 years ago   = A /[( 1 + x/100) ( 1 + y/100)]   = 50400 / [( 1 + 12/100) ( 1 - 10/100)]   = (50400 x 100 x 100) / (112 x 90)   = 50,000.   ANSWER:50,000
Answer: C
A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability Y that all 3 jellybeans removed from the bag are blue?
Select.
A) 9/100 B) 2/19 C) 1/8 D) 3/20 E) 3/10

Solution: Method-1   10 red jellybeans and 10 blue jellybeans   Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140   Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all 2/19lue out of 10 2/19lue = 10C3 = 120   Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3   Probability Y= 120 / 1140 = 2/19   Answer: option 2/19   Method-2   Probability of First jelly bean to be 2/19lue = 10/20 [Total 10 2/19lue out of total 20 jellybeans]   Probability of Second jelly bean to be 2/19lue = 9/19 [Total 9 2/19lue remaining out of total 19 jellybeans remaining]   Probability of Third jelly bean to be 2/19lue = 8/18 [Total 8 2/19lue remaining out of total 18 jellybeans remaining]   Required Probability = (10/20)*(9/19)*(8/18) = 2/19   Answer: option 2/19
Answer: B
Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?  Select:
A) 1500 B) 1300 C) 1200 D) 1000 E) 5000

Solution: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140   X = 1000   ANSWER 1000
Answer: D
An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point? Choose the correct choice from the following options:
A) 6 hrs 21 min  B) 6 hrs 71 min  C) 6 hrs 32 min  D) 6 hrs 27 min  E) 6 hrs 23 min

Solution: Time taken to cover 600 km = 600/100= 
600/100 = 6
6 hrs.   Number of stoppages= 600/75 - 1= 
600/75 - 1 = 7
7   Total time of stoppages= 3 * 7= 
3 * 7 = 21
21 min   Hence, total time taken= 6 hrs 21 min.   6 hrs 21 minnswer:6 hrs 21 min
Answer: A
Bert left the house with N dollars. He spent 1/3 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10.50 left in his pocket. What was the value of N?  Choose the correct choice from the following:
A) $42  B) $44  C) $52  D) $60  E) $68

Solution: started to test answer $42   if he had 42, then he spent 13 2/3 at hardware store   now he was left with 27 1/3$   he spent 7 dollars on cleaning, thus he remained with 20 1/3$   he then spent 1/2 of 20 1/3 or 10.5,   hence,right OPTION is $42.
Answer: A
The average weight of 49 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?	Choices:  A) 51 1⁄3  B) 52 30/49  C) 52 1⁄49  D) 43.42  E) None of these

Solution: Total weight of 49 students   = 49 × 52 = 2548 kg   Total weight of 5 students who leave   = 5 × 48 = 240 kg   Total weight of 5 students who join   = 5 × 54 = 270 kg   Therefore, new total weight of 49 students   = 2548 – 240 + 270 = 2578   ⇒ New average weight = 2578⁄49 = 52 30/49 kg   Answer 52 30/49
Answer: B
Seven children â€” A, B, C, D, E, F, and G â€” are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?
Choose the correct choice from the following answers:	A) 240	B) 480	C) 720	D) 1440	E) 3600

Solution: There are five different â€œthree in a rowâ€ locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B â€” just those two orders. This means the total number of configurations for these three children is 5*2= 
5*2 = 10
10.   Now, consider the non-restricted elements, the other four. Once A & B & G are seated, the remaining four children can be seated in any order among the remaining four seats â€” thatâ€™s a permutation of the 4 items â€”- 4P4= 4! = 24. For any single configuration of A & B & G, there are 24 ways that the other children could be seated in the remaining seats.   Finally, weâ€™ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. Thatâ€™s a total number of configurations of  24*10= 
 24*10 = 240
240. 240nswer= 240
Answer: A
Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number?  Choose the correct option:
A) 6/3	B) 3/8	C) 1/2	D) 5/8	E) 1/8

Solution: There are 4! i.e. 24 ways in which four objects can be arranged in four places. There are a total of 9 instances where the objects are not occupying the place corresponding to the given number. They are as follows:   (2, 1, 4, 3) (2, 3, 4, 1) (2, 4, 1, 3) (3, 1, 4, 2) (3, 4, 1, 2) (3, 4, 2, 1) (4, 1, 2, 3) (4, 3, 1, 2) (4, 3, 2, 1)   Hence, the required probability = 9/24 = 3/8.   ANSWER:3/8
Answer: B
In order to fulfill a local school’s request for x cakes, a parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes to be fulfilled?	Choose the most appropriate option
A) px/a	B) px/(a(a-p))	C) px	D) pxa	E) px(p-a)

Solution: No of cakes each parent has to bake : x/a   No of parents did not bake cake = p   No of cakes that were not baked by p parents = p*x/a   No of parents has to bake additional cakes = a-p   additional number of cakes that each of the other parents had to bake in order for the school’s request for x cakes = px/(a(a - p))   Answer px/(a(a-p))
Answer: B
By selling a watch for Rs.720/-, a man loses 20% what is that watch cost price?  Choose the correct choice from the following choices:
A) s. 600/-	B) s. 700/-	C) s. 800/-	D) s. 850/-	E) s. 900/-

Solution: 80 % ------> 720 (80 * 9= 720)   100 % ------>900 (100 * 9 = 900)   Cost price = Rs. 900/-   s. 900/-)
Answer: E
What is the difference between local value & face value of 6 in the numeral 65793?
Choose one: A) 58453 B) 58956 C) 58994 D) 59894 E) 59994

Solution: (Local value of 6) - (Face value of 6)   = (60000 - 6)= 
(60000 - 6) = 59_994
59994   59994
Answer: E
Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 10 km/hr downstream and 4 km/hr upstream.  Choose the correct option:
A) 7 kmph
B) 8 kmph
C) 9 kmph
D) 7 kmph
E) 6 kmph

Solution: Speed in still water = (10 + 4)1/2 kmph = 7 kmph.   answer :7 kmph
Answer: A
Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-2) = 0, then b + c = Choose the correct answer: A) 18 B) 15 C) -16 D) -21 E) -24

Solution: f(x) = x^2 + bx + c. If f(6) = 0 and f(-2) = 0, then b + c =   f(6) = 0= 36+6b+c--- Taking 36 to the other side   -> 6b+c= -36   f(-2) =0= 4-2b+c --- taking -2b+c to the other side   -> 2b-c=4   When we add these 2 equations, we get 8b= -32---> b= -4   And while substituting b= -4 we get c= -12.   b+c= -16--- Answer -16
Answer: C
If 9^y = 3^16, what is y?	Select the correct option:
A) 2 B) 3 C) 4 D) 6 E) 8

Solution: 9^y = 3^2y = 3^16   2y=16   y = 8   The answer is 8.
Answer: E
A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
Answers:
A) 20 min
B) 30 min
C) 45 min
D) 40 min
E) 70 min

Solution: Sol. 40 ministance between Ramgarh and 40 minevgarh =(50*44)/60=110/3   Average speed of the bus is increased by 5 km/hr then the   speed of the bus = 55 km/hr   Required time = 110/3*60/55= 
110/3*60/55 = 40
40 min   40 min
Answer: D
The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.9.00, Rs.7.00, Rs.4.50 and Rs.5.50 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 20 rupees notes on the counter payment. How many notes did Rahul give?
Pick: A) 8 B) 9 C) 10 D) 9 E) 13

Solution: Explanation :   Let the four cards be a, b ,c and d. 'x' be the number of notes.   Then, according to the question,   => 5a + 5b + 10c + 10d = 20*x.   => a + b + 2(c+d) = 4 * x . -----------------------------(i)   Since, a + b = 9+7= 
9+7 = 16
16   And,=> c + d = 4.50+5.50= 
4.50+5.50 = 10
10 .   Putting these values in (i), we get :-=> 16 + 2 *10 = 4 * x.   => x = 9 .   Answer : 9
Answer: D
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.76 less, he could have gained 25%. What is the cost price?
Choose the correct choice:
A) s.380	B) s.375	C) s.375	D) s.350	E) s.300

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   76 ----- ?=> 380   s.380NSWER:s.380
Answer: A
If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much will he reduce the quantity of petrol purchased?  Pick one:
A) 10% B) 12% C) 8% D) 16% E) None of these

Solution: Explanation :   Let the price of 1 litre of petrol be Rs. x and let Raj initially buys 'y' litres of petrol.   Therefore, he would have spent Rs. xy on petrol.   When the price of petrol increases by 25%, the new price per litre of petrol is 1.25x.   Raj intends to increase the amount he spends on petrol by 15%.   i.e., he is willing to spend xy+15% of xy=1.15xy.   Let, the new quantity of petrol that he can get be 'q'.   Then, 1.25x × q=1.15xy.   =>q=1.15xy/1.25x.   =>0.92y.   As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier i.e a reduction of 8%.   Answer : 8%
Answer: C
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?	Choose the correct option:  A) 210  B) 209  C) 212  D) 211  E) 200

Solution: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.   Hence we have 4 options as given below   We can select 4 boys ...(option 1)   Number of ways to this = 6C4   We can select 3 boys and 1 girl ...(option 2)   Number of ways to this = 6C3 × 4C1   We can select 2 boys and 2 girls ...(option 3)   Number of ways to this = 6C2 × 4C2   We can select 1 boy and 3 girls ...(option 4)   Number of ways to this = 6C1 × 4C3   Total number of ways   = 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3   = 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]   = 15 + 80 + 90 + 24= 
15 + 80 + 90 + 24 = 209
209   209
Answer: B
During one year, the population of town increased by 5% . If the total population is 9975 at the end of the second year , then what was the population size in the beginning of the first year ?	Pick one
A) 12500  B) 7500  C) 5000  D) 20000  E) 10000

Solution: Population in the beginning of the first year   = 9975/[1+(5/100)]*[1-(5/100)] = [9975*(20/21)*(20/19)]9975/ 1+(5/100) * 1-(5/100)= 
9975/ 1+(5/100) * 1-(5/100) = 9_975
[9975*(20/21)*(20/19)= 
9975*(20/21)*(20/19) = 10_000
10000.   Answer is 10000.
Answer: E
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $50,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
Choose the correct answer.
A) $24,000
B) $28,000
C) $32,000
D) $36,000
E) $40,000

Solution: The answer should be -> B. $28,000
Answer: B
In how many ways can a Chief Minister and a Vice Minister be elected from a team of 10 members?
Select the correct option.
A) 80
B) 90
C) 100
D) 110
E) 120

Solution: There are 10 choices for the Chief Minister.   Then there are 9 choices for the Vice Minister.   The total number of ways is  10*9= 
 10*9 = 90
90.   The answer is 90.
Answer: B
Company ABC imported 10,500 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 30 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported? Choose the correct choice from the following answers.
A) 420	B) 840	C) 315	D) 1680	E) 2100

Solution: Answer A.   We are told that 10% of all imported widgets are made of brass and of those, 30% are green and 40% are red. Since we know that there are only three colors, the remaining 30% must be blue. 30% blue of 10% brass widgets leads to 3% blue brass widgets out of the total 10,550 widgets.   10,500 /100 * 3 = 315.   Answer 315.
Answer: C
A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is :
Choose the correct option.
A) 4000 B) 3778 C) 2667 D) 2887 E) 1899

Solution: Explanation:   A : B : C = 500 : 300 : 200 = 5 : 3 : 2.   Let their capitals be 5x, 3x and 2x respectively.   Then, 5x = 10000   => x = 2000.   C's capital = 2x = Rs. 4000.   4000nswer: 4000) 4000
Answer: A
Find out the square of a number which when doubled exceeds its one fifth by 9 ?	Choose the correct choice from the following choices:  A) 16  B) 25  C) 19  D) 26  E) 17

Solution: A   Let the number be p, then the square will be p^2   According to question:   2p = (p/5) + 9   => 10p = p + 45   => p = 5   p^2 = 5^2 = 25.   Answer : 25
Answer: B
If 5 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?  Choose the correct choice from the following answers
A) 8:5:4 B) 8:5:18 C) 8:5:12 D) 8:5:14 E) 8:5:11

Solution: 58:5:4 = 8B = 10 C   8:5:4:B:C = 1/5:1/8:1/10   = 8:5:4   8:5:4nswer: 8:5:4
Answer: A
Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Select: A) Rs. 4500 B) Rs. 4800 C) Rs. 5250 D) Rs. 6150 E) None of these

Solution: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15   = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60   Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.   The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k   It is given that A paid Rs. 1125   45k 45  + 60  + 81  + 60= 
45  + 60  + 81  + 60 = 246
246k   It is given that A paid Rs. 1125   45k= 1125 => k = 25   246k = 246(25) = Rs. 6150   Thus the total rent paid by all the four agencies is Rs. 6150.   ANSWER:Rs. 6150
Answer: D