MU-NLPC/Calc-aqua_rat huggingface dataset:
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank? Choose the correct choice from the following answers.
A) 12 minutes B) 17 minutes C) 27 minutes D) 97 minutes E) 26 minutes

Solution: Part filled by A in 1 min. = 1/20   Part filled by B in 1 min. = 1/30   part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.   Both the pipes can fill the tank in 12 minutes.   12 minutesnswer: 12 minutes
Answer: A
A three-person committee must be chosen from a group of 7 professors and 12 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?  Choose the correct choice from the following choices.
A) A)70  B) B)743  C) C)749  D) D)1,260  E) E)1,980

Solution: Total number of ways to select at least one professor = Number of ways to select 3 people from 12 students and 7 professors - Number of ways to select 3 people from 12 student (i.e. without including any professor)   = 197493 - 127493 = 969 - 220= 
969 - 220 = 749
749   ANSWER:749
Answer: C
In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be  Choose the correct option.
A) 3:2	B) 1:1	C) 1:2	D) 3:4	E) 3:8

Solution: Lots of little places to make a mistake or panic here. =)   R = 3G   B = R/2   G/R = 1/3 ----> Doubled G/R = 2/3   R/B = 2 ----> Doubled R/B = 4   B/G = (B/R)*(R/G) = (1/4)*(3/2) = 3/8   ANSW3:8R:3:8
Answer: E
Find the value of m 82519 x 9999 = m? Choose one:  A) 724533811  B) 353654655  C) 825107481  D) 725117481  E) 477899932

Solution: 82519 x 9999 = 82519 x (10000 - 1)   = 82519 x 10000 - 82519 x 1   = 825190000 - 82519= 
825190000 - 82519 = 825_107_481
825107481   825107481
Answer: C
In a group of 100 cars, 47 cars do not have air conditioning. If at least 55 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
Select.
A) 45	B) 47	C) 49	D) 51	E) 53

Solution: Lets assume AC=53(includesonly AC carsandcars with AC and racing stripes)   lets assume RS(racing stripes)>=55(includescars with AC and racing stripesandonly racing stripes).   Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=55.. we have to assign atleast 8 tocars with AC and racing stripes.   Hence AC=53-8= 
53-8 = 45
45.   The answer is 45
Answer: A
In a club there are no more than 20 persons. What is the smallest number of fruits that must be brought to the club so that each person receives the same number of fruits?	Select the correct option:
A) 26  B) 75  C) 80  D) 45  E) 33

Solution: The number of persons is not specified. We are just given that there are no more than 20 persons.   If we assume that number of persons is 15 then answer will be B.   If we assume that number of persons is 20 then answer will be 80 because only 80 is divisible by 20.
Answer: C
The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils? Choose the correct option:
A) 87  B) 91  C) 100  D) 96  E) 101

Solution: number of pens = 1001   number of pencils = 910   Required number of students = H.C.F. of 1001 and 910 = 91   Answer is 91
Answer: B
The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.	Pick one:	A) B=900;H=300	B) B=900;H=302	C) B=900;H=338	D) B=900;H=329	E) B=900;H=122

Solution: Explanation:   Area of the field = Total cost/rate = (333.18/25.6) = 13.5 hectares   Let altitude = x metres and base = 3x metres.   Then,   Base = 900 m and B=900;H=300ltitude = 300 m.]   B=900;H=300nswer: B=900;H=300)
Answer: A
A florist has 2 azaleas, 3 buttercups, and 5 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?  Choose the correct choice from the following answers
A) 31/45
B) 23/45
C) 14/45
D) 11/15
E) 8/15

Solution: The probability that two of the same flowers were chosen:   P(31/4531/45) = 2/10 * 1/9 = 2/90   P(BB) = 3/10 * 2/9 = 6/90   P(PP) = 5/10 * 4/9 = 20/90   The sum of these probabilities is 14/45   P(two flowers are different) = 1 - 14/45 = 31/45   The answer is 31/45.
Answer: A
Find the least number with which 16200 should be multiplied, to make it a perfect cube.  Choose one:
A) 23  B) 28  C) 45  D) 20  E) 11

Solution: Explanation:   16200 = 23 * 34 * 52   A perfect cube has a property of having the indices of all its prime factors divisible by 3.   Required number = 32 * 5 = 45   Answer:45
Answer: C
In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 440, how many purple chips were selected?	Choose the correct choice from the following options.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 440 = 1*5*8*11   The factor of 8 must come from the purple point value, so there is 1 purple chip.   The answer is 1.
Answer: A
Three numbers are in the ratio 3:5:7. The largest number is 49. What is the difference between smallest and largest number?
Choose the correct answer:
A) 16
B) 20
C) 24
D) 28
E) 32

Solution: The three numbers are 3x, 5x, and 7x.   The largest number is 49 = 7*7, so x = 7.   The smallest number is   3*7= 
  3*7 = 21
21.   49 - 21= 
49 - 21 = 28
28   The answer is 28.
Answer: D
A girl has 8 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?  Select: A) A)96 B) B)102 C) C)108 D) D)110 E) E)112

Solution: The girl can select one jeans in 8 ways.   The girl can select one shirt in 12 ways.   The number of ways in which he can select one jeans and one shirt is 8 * 12= 
8 * 12 = 96
96 ways.   96
Answer: A
What is the sum of the different positive prime factors of 1020?	Choose the correct choice from the following options:
A) 13
B) 17
C) 20
D) 25
E) 27

Solution: I think answer is 27: 27   1020 = 2*2*3*5*17   Sum of theDIFF27R27NTpositive prime factors = 2 + 3 + 5 + 17= 
2 + 3 + 5 + 17 = 27
27
Answer: E
The distance between two stars is 1.8 × 10^4 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)	Choices: A) 8.8 x 10^2 B) 6.6 x 10^2 C) 2.2 x 10^3 D) 5.5 x 10^3 E) 8.8 x 10^4

Solution: 1.8 × 10^4 ly / (3.26 ly/parsec) = (1.8/3.26) x 10^4 = 0.55 x 10^4 = 5.5 x 10^3 parsec   The answer is 5.5 x 10^3.
Answer: D
A tradesman by means of his false balance defrauds to the extent of 28%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? Choices:	A) 44%	B) 48%	C) 94%	D) 45%	E) 64%

Solution: g% = 28 + 28 + (28*28)/100   = 64%   Answer: 64%
Answer: E
What is the minimum value of z for which z^2 + z - 3/2 > 0 is not true?	Choose the correct choice from the following answers: A) -5/2 B) -3/2 C) -3 D) 1/4 E) 1/2

Solution: I think -3 -3 is the best ans...
Answer: C
Let Q represent a set of seven distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?  Select the correct option:
A) 1
B) 2
C) 3
D) 5
E) 7

Solution: Q = p1+p2+p3+p4+p5+p6+p7 = even (and all primes are distinct)   if the least prime is 2 then we have sum of Q =even.   Ans. C. 3
Answer: C
John purchased a fridge and a mobile for Rs.5000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
Choose the correct choice from the following answers.
A) Rs. 100 B) Rs. 150 C) Rs. 200 D) Rs. 260 E) Rs. 280

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 4/100) = 15000 - 600   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200   As this is positive, an overall profit of Rs. 200 was made.   Rs. 200
Answer: C
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years. Choose the correct choice from the following:	A) 306.08	B) 306.00	C) 306.04	D) 306.02	E) 306.01

Solution: A = 5000(51/50)3   = 5306.04   5000   -----------   306.04   Answer: 306.04
Answer: C
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?	Pick one.
A) 16 years	B) 18 years	C) 20 years	D) Cannot be determined	E) None of these

Solution: (x-6)/(y-6)=6/5   (x+4)/(y+4)=11/10   after solving we get y=16   16 yearsNSWER:16 years
Answer: A
A man bets on no. 16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14spans and is therefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what are the odds of winning on the bet that he takes? Choose the correct choice from the following choices:
A) 37:2	B) Either ;35:1	C) 39:3	D) 41:31	E) 31:12

Solution: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.   Either ;35:1   Either ;35:1)
Answer: B
There are 7 players in a bowling team with an average weight of 103 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight? Choose the correct choice from the following choices
A) 95 Kg.	B) 99 Kg.	C) 89 Kg.	D) 90 Kg.	E) 92 Kg.

Solution: The New average will be= (103*7+110+60)/9= 
(103*7+110+60)/9 = 99
99 kgs   99 Kg. is the answer
Answer: B
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock?  Pick one:	A) 60 miles	B) 70 miles	C) 90 miles	D) 120 miles	E) 400 miles

Solution: Answer = B. 70 miles   Relational speed = 130 - 100= 
130 - 100 = 30
30 miles per hour   In 3 hours, difference= 30 * 3= 
30 * 3 = 90
90 miles   Fast train trailing 20 miles, so effective difference= 90 - 20= 
90 - 20 = 70
70 miles
Answer: B
Two dice are rolled. What is the probability that the sum on the top face of both the dice will be greater than 9?  Choose one.
A) 3/8	B) 2/3	C) 1/2	D) 1/3	E) 1/6

Solution: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)   Hence, total number of outcomes possible two dice are rolled, n(S) = 6 × 6 = 36   1/6 = Getting a sum greater than 9 when the two dice are rolled = {(4, 6), {5, 5}, {5, 6}, {6, 4}, {6, 5}, (6, 6)}   Hence, n(1/6) = 6   P(1/6) = n(1/6)/n(S)=6/36=1/6
Answer: E
When positive integer N is divided by positive integer J, the remainder is 8. If N/J = 150.25, what is value of J?  Answers.
A) 16	B) 26	C) 32	D) 132	E) 20

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 150.25   Here 150 is the quotient.   Given that Remainder = 8   So, 150.25 = 150 + 8/J   So, J = 32   Answer: 32
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?  Choose the correct choice from the following answers: A) 3/8 B) 3/2 C) 3/5 D) 3/9 E) 3/2

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.   Answer: 3/2
Answer: B
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 45 kg, then the weight of B is:	Pick one:
A) 31 kg B) 32 kg C) 33 kg D) 35 kg E) None of these

Solution: Explanation:   Let A, B, C represent their respective weights. Then, we have:   A + B + C = (45 x 3) = 135 …. (i)   A + B = (40 x 2) = 80 …. (ii)   B + C = (45 x 2) = 90 ….(iii)   Adding (ii) and (iii), we get: A + 2B + C = 170 …. (iv)   Subtracting (i) from (iv), we get : B = 35.   B’s weight = 35 kg.   Answer: 35 kg
Answer: D
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?	Select
A) 0	B) 1	C) 11	D) 9	E) 7

Solution: In this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 ...the remainder which comes now will be the answer.   1271 div by 12==>remainder = 11   1275 div by 12 ==>rema = 3   1285 div by 12 ==> remain = 1   1277 div by 12 ==> rema = 5   now multiply the remainder = 165   165 div by 12 rem = 9   ANSWER:9
Answer: D
Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 100% more than Bert had in savings, and separately, the same price was also 60% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.  Choices:
A) 1:5	B) 2:5	C) 3:5	D) 4:5	E) 1:1

Solution: Suppose bert had 100 so price becomes 200 , this 200 = 1.6 times R's saving .. so R's saving becomes 125   So required ratio is 100:125=4:5   ANSWER:4:5
Answer: D
What is the probability that Terry and Tim will get selected for a job they both applied for in a company, given that their chances of getting selected is 3/8 and 2/7 respectively?  Choose the correct option.
A) 2/21
B) 2/25
C) 3/28
D) 5/28
E) 3/25

Solution: Explanation:   P(Terry) = 3/8   P(Tim) = 2/7   E = {Terry and Tim both get selected}   P(E) = P(Terry)*P(Tim)   = 3/8 * 2/7   = 3/28   ANSWER: 3/28
Answer: C
Find the area of circle whose radius is 14m? Pick one:
A) 288
B) 154
C) 616
D) 168
E) 178

Solution: 22/7 * 14 * 14= 
22/7 * 14 * 14 = 616
616   Answer: 616
Answer: C
There are 12 yes or no questions. How many ways can these be answered? Choose the correct answer
A) 1324	B) 6234	C) 3651	D) 4562	E) 4096

Solution: Each of the questions can be answered in 2 ways (yes or no)   Therefore, no. of ways of answering 12 questions = 212 = 4096 ways.   Ans:4096
Answer: E
The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum E of all the digits of the integers from 0 to 99 inclusive?  Choose the correct choice from the following:	A) 450	B) 810	C) 900	D) 1000	E) 1100

Solution: We want the sum of the digits from 0 to 99, so I approximated:   0-9 ->45-> (9+0)*10/2   40-49 ->85(13+4)*10/2   90-99 ->135(18+9)*10/2   We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just E=900:the answer is 900.
Answer: C
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Choose the correct answer
A) 5 : 6	B) 6 : 5	C) 8 : 3	D) 3 : 8	E) None of these

Solution: Explanation :   Let the rate upstream of the boat = x kmph   and the rate downstream of the boat = y kmph   Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.   Since distance = speed × time, we have   x × (8(4/5)) = y × 4   x × 44/5 = y × 4   x × 11/5 = y --------- (equation 1)   Now consider the formula given below   Hence, speed of the boat = (y+x)/2   speed of the water = (y−x)/2   Required Ratio = left(fracy+x2right):left(fracy−x2right)left(fracy+x2right):left(fracy−x2right)   = (y + x):(y − x)   ∵ (Substituted the value of y from equation 1)   = left(frac11x5+xright):left(frac11x5−xright)left(frac11x5+xright):left(frac11x5−xright)   = (11x + 5x) : (11x − 5x)   = 16x : 6x   = 8 : 3 Answer : Option 8 : 3
Answer: C
A rectangular floor that measures 6 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $15 apiece, what is the total cost for the number of carpet squares needed to cover the floor?  Answers.
A) $200	B) $240	C) $480	D) $225	E) $1,920

Solution: The width of the rectangular floor(6 m) is a multiple of one side of the square(2 m), and the length of the floor(10 m) is also a multiple of the side of the square. So the number of carpets to cover the floor is (6/2)*(10/2)= 
(6/2)*(10/2) = 15
15.   The total cost is 15*15= 
15*15 = 225
$225.   The answer is, therefore, $225.
Answer: D
The successive discounts 20% and 15% are equal to a single discount of?  Choose the correct choice.
A) 26	B) 22	C) 32	D) 82	E) 61

Solution: Explanation:   Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   Clearly, single discount is 32%.   Answer: 32
Answer: C
21 people are there, they are shaking hands together, how many hand shakes possible,if they are in pair of cyclic sequence. Choose the correct choice from the following answers
A) 19  B) 20  C) 21  D) 22  E) 23

Solution: in case of cycle no of handshakes = no of persons   hence ans = 21   ANSWER:21
Answer: C
If A,B,C,D,E,F,G,H,I,J are in an increasing Arithmetic Progression as such. Then Which of the following operations will result in only mean being modified but not the median.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed	Choose the correct choice from the following answers:  A) 1) A and B  B) 2) A and E  C) 3) A,C,E  D) 4) All of them  E) 5) None of them

Solution: There are 10 equidistant numbers on the number line.   Mean and median will be the average of middle two numbers.   If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where mean will change and median will not change.   Answer: 5) None of them
Answer: E
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Pick one
A) 276 sq.cm	B) 268 sq.cm	C) 618 sq.cm	D) 297 sq.cm	E) 600 sq.cm

Solution: 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 = √(625 - 225)= 
(625 - 225) = 400
√400= 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.   Answer:600 sq.cm
Answer: E
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?
Pick:
A) 69.5 km/hr	B) 70 km/hr	C) 79 km/hr	D) 79.2 km/hr	E) 89.2 km/hr

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 km/hr
Answer: D
An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of  Choices.
A) 580 Kmph
B) 550 Kmph
C) 540 Kmph
D) 530 Kmph
E) 520 Kmph

Solution: Speed of aeroplane = 420 Kmph   Distance travelled in 6 hours   = 420 Ã— 6 = 2520 Km   Speed of aeroplane to acver 2520 Km in 14/3   = 2520 Ã— 3/14 = 540 Km   ANSWER IS 540 Kmph
Answer: C
The points A(0, 0), B(0, 4a - 4) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC? Choose the correct option:
A) 88
B) 98
C) 108
D) 78
E) 90

Solution: 1/2bh=1/2(2a+1)(2a+6)   Now 4a-4=2a+6   2a=10 , a=5   Therefore,   88(0,0); B(0,16); C(11,16)   1/2*11*16= 
1/2*11*16 = 88
88   88nswer: 88
Answer: A
A and B start a business with Rs.2000 and Rs.3000 respectively. Hoe should they share their profits at the end of one year?
Choose the most appropriate option:
A) 1:2	B) 3:4	C) 2:5	D) 3:7	E) 2:3

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and B =   2000 : 3000 => 2:3   ANSW2:3R:2:3
Answer: E
In a theater, the first row has 12 seats and each row has 2 more seats than previous row. If the last row has 48 seats, what is the total number of seats in the theater?	Choose the correct option.
A) 550  B) 570  C) 590  D) 610  E) 630

Solution: The number of seats in the theater is   12 + (12+2) + ...+ (12+36)=   19(12) + 2(1+2+...+18)=   19(12) + 2(18)(19)/2=   19(12+18) = 19(30) = 570   The answer is 570.
Answer: B
On selling 15 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is: Choose one:  A) s. 45  B) s. 50  C) s. 55  D) s. 60  E) s. 72

Solution: (C.P. of 15 balls) - (S.P. of 15 balls) = (C.P. of 5 balls)   C.P. of 10 balls = S.P. of 15 balls = Rs.720.   C.P. of 1 ball = Rs.720/10	= Rs. 72.   Answer: Option s. 72
Answer: E
Bid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Bid have meant to type?	Choose the most appropriate option:
A) 10  B) 16  C) 21  D) 24  E) 27

Solution: Should be 21.   Bid intended to type a seven-digit number there are two possibilities for placing 2 3s .   case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.   -5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)   case 2: two 3s are not together, i.e. they have one or more digits between them .   -5-2-1-1-5- , in this arrangement   if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.   if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.   if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.   if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.   if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.   so total 15 ways.   case 2 + case 1 = 6+ 15= 
6+ 15 = 21
21 ways   Answer 21
Answer: C
From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1, 1993, was 60 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?  Choose the correct choice from the following answers:
A) 38
B) 39
C) 40
D) 41
E) 52

Solution: 1.15x=60 --> 23/20*x=60 --> x=60*20/23=1200/23=~52.   Answer: 52.
Answer: E
Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 5 days?
Choose the correct choice from the following choices
A) 6
B) 7
C) 10
D) 12
E) 15

Solution: This is an inverse proportional problem......   5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 5 = 12   So, 12-5 = 7   Answer 7
Answer: B