MU-NLPC/Calc-aqua_rat huggingface dataset:
0.02 x 0.000197 is equal to: Choose the correct choice from the following options.
A) 6.48 x 10(power -6)  B) 6.84 x 10(power -6)  C) 3.94 x 10(power -6)  D) 5.48 x 10(power -6)  E) None of them

Solution: 2 x 197 = 394. Sum of decimal places = 8   So, 0.02 x 0.000197 = 0.00000394 = 3.94 x 10(power -6)   Answer is 3.94 x 10(power -6)
Answer: C
There are seven leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?  Choose the correct answer.
A) 7 leopard and 3 sheep  B) 4 leopard and 7 sheep  C) 6 leopard and 1 sheep  D) 5 leopard and 1 sheep  E) 2 leopard and 5 sheep

Solution: 6 leopard and 1 sheep   6 leopard and 1 sheep   since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: C
A fruit seller sells mangoes at the rate of Rs.12 per kg and thereby loses 10%. At what price per kg, he should have sold them to make a profit of 15%?
Choose one:
A) Rs.11.81
B) Rs.12
C) Rs.15.33
D) Rs.12.31
E) None

Solution: Solution   90 : 12 = 115 : x   x= (12Ã—115/90)   = Rs.15.33   Hence, S.p per Kg	= Rs.15.33   Answer Rs.15.33
Answer: C
What least number should be added to 1056, so that the sum is completely divisible by 23?  Choose the correct choice from the following
A) 4	B) 3	C) 2	D) 1	E) 0

Solution: Explanation :   1056 ÷ 23 = 45 with remainder = 21   Remainder = 21. 21 + 2 = 23. Hence 2 should be added to 1056 so that the sum will be   divisible by 23. Answer : Option 2
Answer: C
Find the circumference and area of radius 8 cm.
Select
A) 124 cm² B) 201 cm² C) 210 cm² D) 184 cm² E) 194 cm²

Solution: Area of circle = πr²   = 22/7 × 8 × 8 cm²   = 201 cm²   ANSWER:201 cm²
Answer: B
the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century, the population increased by 300 percent. What was the percent increase for the 20th century as a whole?
Choices:
A) 500%	B) 600%	C) 800%	D) 1100%	E) 1200%

Solution: Say initially population was 100.   What is 200% of 100? It is   200/100 * 100= 
  200/100 * 100 = 200
200.   An increase of 200% means the new population became  100 + 200= 
 100 + 200 = 300
300   What is 300% of 300? It is   300/100 * 300= 
  300/100 * 300 = 900
900   An increase of 300% means the new population now is  300 + 900= 
 300 + 900 = 1_200
1200   So from 100, the population increased to 1200 i.e. an increase of 1100.   1100 is what percent of 100?   1100= x/100 * 100   i.e. it is 1100% 1100%
Answer: D
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspapers sales was from Newspaper A and if q percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of q? Choose the correct option:  A) 100p / (125 - p)  B) 150p / (250 - p)  C) 300p / (375 - p)  D) 400q / (500 - q)  E) 500q / (625 - q)

Solution: I have just started with qunats section .. I solved this by making two equations and got the answer ... However it was long way of doing it ...   I got the answer as : 100q /(125 - .25 q)...   Multiply this equation by 4 and you get 400q / (500 - q) as the answer ,...
Answer: D
If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Z/Y?  Choose the correct choice from the following choices:
A) -4.5.
B) -2.
C) -0.5.
D) 3.
E) 2.5.

Solution: X+Y = 2X-2Z   X-Y = 2Z---------- 1   X-2Y = 4Z--------- 2   Subtracting equation 1 from equation 2   2Z = -Y   Z/Y= -0.5   -0.5. is the answer
Answer: C
If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 10 percent, how much would she earn per week?	Answers
A) $374	B) $382	C) $385	D) $392	E) $399

Solution: Soln:-   (406/116)110 =385   In this case long division does not take much time.   (406/116)= 
(406/116) = 7/2 = around 3.5
3.5   35*11= 
35*11 = 385
385(350+35)   ANSWER:$385
Answer: C
A Women can cover a distance in 1 hr 24 min by covering 2/3 of the distance at 4 km/h and the rest at 5 km/h. The total distance is Choose the correct option:
A) 4 km
B) 8 km
C) 2 km
D) 6 km
E) 9 km

Solution: 6 km   6 km   6 kmistance = 2/3S   distance=1-2/3S=1/3S   21/15 hr=2/3 S/4 + 1/3s /5   84=14/3S * 3   S= 6km
Answer: D
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Choose the correct choice from the following choices:
A) 8
B) 4
C) 9
D) 6
E) 1

Solution: M = 45   S = 1.5   DS = 6   US = 3   AS = (2 * 6 * 3) /9= 
(2 * 6 * 3) /9 = 4
4   Answer: 4
Answer: B
If there is exactly one root of the equation x^2 + ax - b, where a and b are positive constants, what is b in terms of a?
Choose the correct choice from the following
A) a/2	B) a	C) -a^2/4	D) a^2/2	E) a^2/4

Solution: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1   Here b = a   c= b   a = 1   substituting these values in 1, we have   a^2 = -4b => b =-a^2/4   Answer is -a^2/4.
Answer: C
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.5 years. The ration of the number of boys to the number of girls in the class is? Pick one:
A) 2:6  B) 2:3  C) 2:5  D) 2:1  E) 1:2

Solution: Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.5 = (k + 1) * 15.8   = (16.4 - 15.8)k = (15.8 - 15.5)   = k = 0.3/0.6 =1/2   Required ratio = 1/2 : 1 = 1:2.   Answer:1:2
Answer: E
If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 1 = ?
Choose the correct choice from the following options:
A) 2
B) 4
C) 8
D) 16
E) 32

Solution: 4 Ø 2 = 2^4/2^2 = 4   4 Ø 1 = 2^4/2 = 8   The answer is 8.
Answer: C
378 × ? = 252	Choose the most appropriate option.
A) 2/3 B) 3/4 C) 1/2 D) 2/8 E) None of these

Solution: Explanation :   378 × ? = 252   ?=252/378=126/189=14/21=2/3   2/3nswer is 2/3
Answer: A
If 1st October is Sunday, then 1st November will be	Choose the correct option:
A) Saturday
B) Thursday
C) Wednesday
D) Tuesday
E) Monday

Solution: Explanation:   Given that 1st October is Sunday   Number of days in October = 31   31 days = 3 odd days   (As we can reduce multiples of 7 from odd days which will not change anything)   Hence 1st November = (Sunday + 3 odd days) = Wednesday   Answer: Option Wednesday
Answer: C
The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 7 years ago ? (RBI Assistant 2015)
Choose the correct answer.
A) 24	B) 18	C) 14	D) 15	E) 13

Solution: Let the present age of Viju be 7x years and that of Aju be 2x years.   Then, 4 years from now   7x + 4 / 2x + 4 = 5 / 2   or 4x = 12   or x = 3   Viju present age = 7 * 3= 
7 * 3 = 21
21 years   Viju age 7 years ago= 21 - 7= 
21 - 7 = 14
14 years   answer :14
Answer: C
Under the Below list which is the smallest prime number:
Choices:
A) 48 B) 41 C) 38 D) 32 E) 30

Solution: 41   41
Answer: B
Two trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 12 sec, then the speed of each train is?
Answers:
A) 22	B) 77	C) 36	D) 108	E) 21

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (360 + 360)/12 => x = 30   Speed of each train = 30 m/sec.   = 30 * 18/5 =- 108 km/hr.   Answer: 108
Answer: D
If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is: Select the correct option:
A) 16 years  B) 16 1/2 years  C) 16 2/3 years  D) 17 years  E) 17 2/3 years

Solution: Total time= (10+6 2/3) = 16 2/3 years   16 2/3 years
Answer: C
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?  Choose the correct choice.
A) 270º
B) 360º
C) 280º
D) 90º
E) 180º

Solution: Angle traced by the hour hand in 6 hours =	(360/12 x 6)º = 180º.   Answer 180º
Answer: E
A work which could be finished in 12 days was finished 3 days earlier after 10 more men joined. The number of men employed was?  Choices
A) 22	B) 20	C) 88	D) 71	E) 10

Solution: x ------- 12   (x + 10) ---- 6   x * 12 = (x + 10)6   x = 10   \Answer: 10
Answer: E
A pump can fill a tank with water in 2 hours. Because of a leak, it took hours to fill the tank. The leak can drain all the water of the tank in: Choices.
A) 33	B) 37	C) 76	D) 14	E) 29

Solution: Explanation:   Work done by the leak in 1 hour ={\color{Black} \left ( \frac{1}{2}-\frac{3}{7} \right )=\frac{1}{14}}   {\color{Black} \therefore } Leak will empty the tank in 14 hrs   Answer: 14) 14 hours
Answer: D
If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?	Answers:
A) 5!4!
B) 5!5!
C) 4!4!
D) 10!
E) 10!/5!

Solution: Let's say that we make a man sits in spot 1. Then, a man must also sit in spots 3, 5, 7, 9. There are 5! ways of arranging the man this way. However, since this is a table (ie: circle), there are 5 ways where the initial man can sit, so we must divide 5! by 5, which equals to 4!.   It follows that a woman must sit in spots 2, 4, 6, 8, 10. There are 5! ways to arrange this.   Therefore, we get 4!5!. So the answer is 5!4!) 5!4!
Answer: A
Which one of the following is the least number of four digits divisible by 71?  Choose the correct choice from the following.
A) 1288
B) 1065
C) 1229
D) 1727
E) 1781

Solution: Explanation:   1000/71 = 14 6/71   1000 + 71 â€“ 6 = 1065   Answer:1065
Answer: B
A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.4 km long? Choose the correct choice from the following answers
A) 2 mins 14 sec B) 2 mins 34 sec C) 2 mins 54 sec D) 4 mins 54 sec E) 2 mins 44 sec

Solution: D = 25 * 60 + 1400= 
25 * 60 + 1400 = 2_900
2900 m   T= 2900/60 * 18/5= 
2900/60 * 18/5 = 174
174 sec= 2 mins 54 sec   ANSWER:2 mins 54 sec
Answer: C
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
Select the correct option:
A) 3:8 B) 3:1 C) 3:4 D) 3:9 E) 3:2

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)   And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)   Solving (i) and (ii), we get x = 60 and y = 80   Ratio of speeds = 60:80 = 3:4   Answer:3:4
Answer: C
Excluding stoppages,the speed of the bus is 72kmph and
including stoppages,it is 54kmph. For how many minutes does the bus stop per hr Choose one:	A) 12 min	B) 11 min	C) 13 min	D) 15 min	E) 17 min

Solution: Due to stoppages,it covers 18km less.   time taken to cover 18 km is [  18/72 *60= 
  18/72 *60 = 15
15min   Answer is 15 min.
Answer: D
.009/?= .01  Answers.
A) .9
B) .09
C) .009
D) .0009
E) None of them

Solution: Let .009/x = .01;   Then x = .009/.01= 
.009/.01 = 0.9
.9/1= 
.9/1 = 0.9
.9   .9nswer is .9
Answer: A
There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 25 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?	Pick:  A) 90.  B) 45.  C) 50.  D) 40.  E) 25.

Solution: STREET-CAT DOMESTIC-Cat   70 130   (25gray+45other) 85gray+45other   Answer:45.
Answer: B
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 4, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist? Choose the correct choice from the following answers.
A) 27	B) 36	C) 72	D) 112	E) 45

Solution: {1}{2}{greater than 6}{divisible by 3}{3x}{x}:   The third digit can take 5 values: 5,6,7, 8, or 9.   The fourth digit can take 3 values: 3, 6, or 9.   The fifth and sixth digits can take 3 values: 31, 62, or 93.   Total = 5*3*3= 
5*3*3 = 45
45.   Answer: 45.
Answer: E
If the price of petrol increases by 25, by how much must a user cut down his consumption so that his expenditure on petrol remains constant? Pick one
A) 25%	B) 20%	C) 16.67%	D) 33.33%	E) None of these

Solution: Explanation :   let us assume before increase the petrol will be Rs. 100.   After increase it will be Rs (100+25) i.e 125.   Now, his consumption should be reduced to :-   =125−100125∗100.   Hence, the consumption should be reduced to 20%.   Answer : 20%
Answer: B
A clock shows the time as 9 a.m. If the minute hand gains 5 minutes every hour, how many minutes will the clock gain by 4 p.m.? Choose the correct option.
A) 30 min	B) 35 min	C) 45 min	D) 50 min	E) 55 min

Solution: there are 7 hours in between 9 a.m. to 4 p.m.   7*5= 
7*5 = 35
35 minutes.   ANSWER:35 min
Answer: B
X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y. Which of the following CANNOT be the difference of X and Y ?  Select the correct option
A) 72 B) 45 C) 27 D) 33 E) 9

Solution: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y:   X = 10a + b   Y = 10a + b   X - Y = (10a + b) - (10a + b) = 9(a - b). As you can see the difference must be a multiple of 9. Only option D is not a multiple of 9.   Answer: 33.
Answer: D
Shobha’s mathematics test had 75 problems i.e.10 arithmetic, 30 algebra and 35 geometry problems. Although she answered 70% of the arithmetic ,40% of the algebra, and 60% of the geometry problems correctly. she did not pass the test because she got less than 60% of the problems right. How many more questions she would have to answer correctly to earn 60% of the passing grade?
Choose the most appropriate option
A) 3
B) 2
C) 6
D) 5
E) 4

Solution: Number of questions attempted correctly   =(70% of 10 + 40% of 30 + 60% 0f 35)   =7 + 12+21= 45   questions to be answered correctly for 60% grade=60% of 75 = 45   therefore required number of questions= (45-40)= 
(45-40) = 5
5   Answer is 5.
Answer: D
Solve the following quadratic equation by factoring.
X2+15X=50
Choose the correct choice from the following choices:
A) 10,4	B) 4,-10	C) 5,10	D) -5,10	E) 6,3

Solution: Now all we need to do is use the zero factor property to get,   X+5 = 0 X=-5 OR   X+10=0, X = -10   ANSWER -5,10
Answer: D
A caterer ordered 125 ice-cream bars and 125 sundaes. If the total price was $275.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?
Choose the correct option:	A) $0.60	B) $0.80	C) $1.00	D) $1.20	E) $1.60

Solution: Let price of a sundae = S   Price of ice cream bar = .6 $   125 * .6 + 125*S = 275   => 125*S =200   => S = 1.6   Answer $1.60
Answer: E
If x and y are prime numbers such that x > y > 1, then x^2 − y^2 must be divisible by which one of the following numbers?
Choose the correct answer.
A) 3	B) 4	C) 5	D) 9	E) 12

Solution: If x=3 and y=2, then x^2-y^2=5 and 5 is divisible only by 5 from the options, thus it must be correct.   Answer: 5.
Answer: C
Set S consists of all prime integers less than 10. If two numbers are chosen form set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen? Select the correct option: A) 1/3 B) 2/3 C) 1/2 D) 7/10 E) 4/5

Solution: S={2, 3, 5, 7}   The simplest way would be to realize that we choose half of the numbers (basically we divide the group of 4 into two smaller groups of 2) and since a tie is not possible then the probability that the product of the numbers in either of subgroup is more than that of in another is 1/2 (the probability doesn't favor any of two subgroups).   Answer: 1/2
Answer: C
Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's present salary? Choose the correct option.
A) Rs.38,0387 B) Rs.38,038 C) Rs.38,036 D) Rs.38,000 E) Rs.38,098

Solution: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.   Then, (2x + 4000)/(3x + 4000) = 40/57   6x = 68000 => 3x = 34000   Sumit's present salary = (3x + 4000) = 34000 + 4000 = Rs.38,000.   Answer: Rs.38,000
Answer: D
How much time will it take for an amount of Rs. 600 to yield Rs. 30 as interest at 2% per annum of simple interest?  Choose the correct choice:
A) 8.1 years B) 4.2 years C) 7 years D) 6 years E) 2.5 years

Solution: Explanation:   Time = (100 x 81)/(450 x 4.5) years   = 2.5 years.   Answer: 2.5 years
Answer: E
If there are 4 peanuts in a box and Mary puts 6 more peanuts inside, how many peanuts are in the box?	Choose the correct choice from the following options:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: 6+4= 
6+4 = 10
10   correct answer is 10)10
Answer: C
Cars C1 and C2 travel to a place at a speed of 30 and 45 km/h respectively. If car C2 takes 21⁄2 hours less time than C1 for the journey, the distance of the place is Choices:
A) 300 km
B) 400 km
C) 350 km
D) 225 km
E) None of these

Solution: Let C1 takes t hrs. Then,   ∴ Distance is same.   ∴ 30t = 45(t - 5⁄2)   ⇒ t = 15⁄2 hrs.   ∴ 225 kmistance = 30 × 15⁄2 = 225 km   Answer 225 km
Answer: D
Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 300 milliliters of solution X to create a solution that is 22 percent alcohol by volume?	Answers:
A) 300	B) 350	C) 400	D) 450	E) 500

Solution: 22% is 12%-points higher than 10% but 8%-points lower than 30%.   Thus there should be 2 parts of solution X for 3 parts of solution Y.   We should add 450 ml of solution Y.   The answer is 450.
Answer: D
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 357, which of the following could be equal to n? Choose the correct choice from the following: A) 38 B) 39 C) 40 D) 41 E) 42

Solution: Since, there is no 51 in the answer choices (357/7 = 51), we know there is at least one 77.   357 - 77= 
357 - 77 = 280
280   280/7= 
280/7 = 40
40   40+1= 
40+1 = 41
41.   If 41 wasn't there, I would have subtracted 77 from 280 and continued in a similar way.   Ans. 41
Answer: D
If a(a - 4) = 21 and b(b - 4) = 21, where a ≠ b, then a + b =	Choose the correct option:
A) −48
B) −2
C) 4
D) 46
E) 48

Solution: a(a - 4) = 21 and b(b - 4) = 21   => a, b must be integers and if a is -3 or 7, b will be 7 and -3 respectively   => a+b = 4   Ans: 4
Answer: C
The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 22,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China? Choose one:
A) 5,476,811 kilometers squared
B) 12,500,148 kilometers squared
C) 9,843,123 kilometers squared
D) 1,878,965 kilometers squared
E) 4,787,900 kilometers squared

Solution: he difference between the areas of Russia and China is given by   22,098,242 - 9,598,094 = 12,500,148 kilometers squared   correct answer 12,500,148 kilometers squared
Answer: B
A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per second does the larger rim makes in terms of x ?  Choose one:  A) 4x/5  B) 75x  C) 48x  D) 24x  E) x/75

Solution: Let's try the explanation. We have two wheels. One with 28pi and the other one with 35pi. They have the same speed. In the smaller wheel it's 28pi*x, which must be equal to the speed of the bigger one (35pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).   Anyway, we have 28pi*x=35pi*a.   (28pi*x)/(35pi). = 4x/5.   4x/5ns :4x/5
Answer: A
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?  Select the correct option:  A) 7.5  B) 7.4  C) 7.9  D) 7.2  E) 8.0

Solution: Net part filled in 1 hour = (1/4 - 1/9) = 1/8   The cistern will be filled in 8/1 hrs i.e., 8 hrs.Answer: 8.0
Answer: E
A train 75 metres long overtook a man who was walking at the rate of 6 km/h and passed him in 18 seconds. Again, the train overtook a second person in 15 seconds. At what rate was the second person travelling ?  Choices
A) 3 km/h
B) 2.5 km/h
C) 4 km/h
D) 1.5 km/h
E) None of these

Solution: Let actual speed of train ST km/h.   Then, ST - 6 = 75⁄18 × 18⁄5 = 15   ⇒ ST = 21 km/h   Now, let speed of second man = Sm   21 - Sm = 75⁄15 × 18⁄5 = 18   ⇒ Sm = 3 km/h   3 km/hnswer 3 km/h
Answer: A
For a three-digit number xyz, where x, y, and z are the digits of the number, f(xyz)=5^x 2^y 3^z . If f(abc)=3*f(def), what is the value of abc-def ?
Choose the correct choice from the following:
A) 1
B) 2
C) 3
D) 9
E) 27

Solution: Since f(abc) = 3*f(def), I would assume that f = c - 1 from the function above.   The answer should be (1)
Answer: A
If 0 < n < 1, what is the median of the values n, n^-1, n^2, n^1/2 and n^3?  Choices
A) n B) n^-1 C) n^2 D) n^1/2 E) n^3

Solution: A. To make the problem less confusing, I picked a number between 0 and 1 such as n = 1/4 and calculate:   n = 1/4   n^-1 = 4   n^2 = 1/16   n^(1/2) = 1/2   n^3 = 1/8.   From this, rearrange the number and the median is 1/4, which is n. nnswer n
Answer: A
Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders.The average expense per boarder is Rs. 700 when there are 25 boarders and Rs 600 when there are 50 boarders.What is the average expense per boarders when there are boarder ? Choose the most appropriate option:
A) 550
B) 580
C) 540
D) 570
E) None of these

Solution: Explanation :   Let x be the fixed cost and y the variable cost   17500 = x + 25y … (i)   30000 = x + 50y … (ii)   Solving the equation (i) and (ii), we get   x = 5000, y = 500   Now if the average expense of 100 boarders be ‘A’.   Then,   => 100 × A = 5000 + 500 × 100 .   ∴ A = 550.   550nswer : 550
Answer: A
A bookstore made 11000 dollars selling 3000 math books and 1000 physics books. A customer bought 1 math book and 1 physics book and paid 7 dollars. What is the price of each book? Choose the most appropriate option
A) 4 and 3	B) 1 and 6	C) 2 and 5	D) None	E) Cannot be determined

Solution: Solution:   Let x be the price of the math book and y be the price of the physics book   x + y = 7   3000 × x + 1000 × y = 11000   Use x + y = 7 to solve for y   x - x + y = 7 - x   y = 7 - x   Substitute 7 - x for y in 3000 × x + 1000 × y = 11000   3000 × x + 1000 × (7 - x) = 11000   3000x + 7000 - 1000x = 11000   2000x = 11000 - 7000   2000x = 4000   x = 2 since 2000 × 2 = 4000   Since 2 + 5= 
2 + 5 = 7
7, y= 5   The price of a math book is 2 dollars and the price of a physics book is 5 dollars.   Answer 2 and 5
Answer: C
Find the value of x: 2x² − 4. Answers.
A) 0,2  B) -2,2  C) -2,1  D) 0,4  E) -1,4

Solution: That quadratic is factored as follows:2x² − 4 = (2x − 2)(x + 2).Now, it is easy to see that the second factor will be 0 when x = −2.As for the value of x that will make2x − 4	=	0,we must solve that equation We have:2x	=	4x = 2The solutions are:x	=	-2 and 2 -2,2
Answer: B