MU-NLPC/Calc-aqua_rat huggingface dataset:
You and your friend are playing Russian Roulette. Of course, the gun is filled with fake pellets. Three bullets are placed inside three consecutive chambers. The cylinder is then spun once. It won't be spun again.
As per the rules, the gun will be passed from one person to other until a pellet is shot. If you want to win this game, would you go first or second ? Choices:
A) 1st
B) 3rd
C) 4th
D) 2nd
E) 5th

Solution: D   2nd   When the cylinder is spun for the first and last time, the following six outcomes are possible:   First:   First chamber is fired first. The first player loses.   Second:   Second chamber is fired first. The first player loses.   Third:   Third chamber is fired first. The first player loses.   Fourth:   Fourth chamber is fired first. The second player loses. (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)   Fifth:   Fifth chamber is fired first. The first player loses. (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)   Sixth:   Sixth chamber is fired first. The second player loses. (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)   Thus, if you analyze, you will find that the second player has a 4/6 chance of winning. Therefore if you want to win the game, going second gives you better shot at it.
Answer: D
If the first half of the English alphabet is reversed and then next portion of English alphabet is reversed so as 'A' takes the portion of 'M' and 'N' takes the portion of 'z' then which letter will be 6th to the left of 17th letter to the right of 7th leter from the left?	Choose the correct answer:
A) Y B) V C) J D) G E) K

Solution: Explanation:   6th to the left of 17th letter to the right of 7th letter from the left = 6th to the left of (17+7 =) 24th letter from the left = (24-6 =) 18th letter from the left.   Thus, we have to count from the left and we have to find out 18th letter from the left that falls into the second section of English alphabet.   Here, both the first half and the second half of the English alphabet have been reversed and we have to count from the left end, then the required letter can be found out using the formula given below. Suppose , the first and the second reversed sections of the English alphabet are and respectively.Then,   The required letter =   Therefore, The required letter = 26 + 13 + 1 - 18= 
26 + 13 + 1 - 18 = 22
22= V   Answer: V
Answer: B
Sum of the numbers from 1 to 45 is  Choose the correct choice from the following answers
A) 1789	B) 1035	C) 1025	D) 1009	E) None of these

Solution: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2   Substitute n = 45.   So S20=45Ã—46/2=1035   Correct Option: 1035
Answer: B
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 60 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?  Answers:  A) 16  B) 36  C) 20  D) 24  E) 30

Solution: Time taken = Total Distance / Relative Speed   Total Distance = 60 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken= 60 / 10= 
60 / 10 = 6
6 hrs   Distance traveled by Brad= Brad's speed * time taken = 6 * 6= 
6 * 6 = 36
36 kms... Answer - 36
Answer: B
Two brother X and Y appeared for an exam. The probability of selection of X is 1/7 and that of B is 2/5. Find the probability that both of them are selected.  Choose the correct choice from the following choices:	A) 2/69	B) 2/60	C) 2/63	D) 2/35	E) 2/38

Solution: Explanation:   Let A be the event that X is selected and B is the event that Y is selected.   P(A) = 1/7, P(B) = 2/5.   Let C be the event that both are selected.   P(C) = P(A) Ã— P(B) as A and B are independent events:   = (1/7) Ã— (2/5) = 2/35   Answer: 2/35) 2/35
Answer: D
In a division, a student took 42 as divisor instead of 36. his answer was 24 . The correct answer is-  Choose the correct choice from the following options
A) 42  B) 32  C) 48  D) 28  E) 38

Solution: X/42 = 24.   X = 24 *42.   So correct answer would be,   (24 *42) /36 = 38.   ANSW38R : 38
Answer: E
An woman swims downstream 81 km and upstream 36 km taking 9 hours each time; what is the speed of the current? Choose the correct choice
A) 0.5  B) 1.5  C) 2.5  D) 3.5  E) 4.5

Solution: 81 --- 9 DS = 9   ? ---- 1   36 ---- 9 US = 4   ? ---- 1 S = ?   S = (9 - 4)/2= 
(9 - 4)/2 = 5/2 = around 2.5
2.5   Answer:2.5
Answer: C
A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is? Choose the correct choice from the following options
A) 50 m
B) 150 m
C) 210 m
D) 300 m
E) None of these

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 140)/25 = x/15 => x = 210 m.   ANSWER:210 m
Answer: C
The average of six number is 3.99. The average of two of them is 3.4, while the average of the other two is 3.85. what is the average of the remaining two number ?  Select:
A) 4.5
B) 4.6
C) 4.72
D) 4.8
E) None of these

Solution: solution:   Sum of the remaining two numbers = (3.99 × 6) - [(3.4 × 2) + (3.85 ×2)]   =23.94 -(6.8 + 7.7) = 23.94 - 14.5 = 9.44.   ∴ Required average =9.44/2= 
9.44/2 = 4.72
4.72 Answer 4.72
Answer: C
50 men can complete a work in 65 days.Five days after started the work, 20 men left the group. In how many days can the remaining work be completed?	Choices:	A) 277	B) 268	C) 260	D) 276	E) 100

Solution: After 5 days, the following situation prevails.   50 men can complete the work in 60 days.   30 men can complete the work in ? days.   M1 D1 = M2 D2   => 50 * 60 = 30 * D2   => D2 = (50 * 60)/30= 
(50 * 60)/30 = 100
100 days.   Answer: 100
Answer: E
In how many ways can an answer key for a quiz be written if the quiz contains 3 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?  Choose the correct choice from the following answers:
A) 164  B) 224  C) 280  D) 384  E) 476

Solution: There are 2^3 = 8 possibilities for the true-false answers.   However we need to remove two cases for TTT and FFF.   There are  4*4*4= 
 4*4*4 = 64
64 possibilities for the multiple choice questions.   The total number of possibilities is  6*64= 
 6*64 = 384
384.   The answer is 384.
Answer: D
How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336 Pick one
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: 132 = 4 x 3 x 11   So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.   264 -> 11,3,4 (/)   396 -> 11,3,4 (/)   462 -> 11,3 (X)   792 -> 11,3,4 (/)   968 -> 11,4 (X)   2178 -> 11,3 (X)   5184 -> 3,4 (X)   6336 -> 11,3,4 (/)   Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.   Required number of number = 4.   4nswer:4
Answer: A
Merry and Mich play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Mich plays first, giving Merry a third of her cards. Merry plays next, and Mich follows. Then the game ends. Merry ended up with 14 more cards than Mich. How many cards did each player have originally? Choose the correct choice from the following:  A) 60  B) 58  C) 56  D) 55  E) 54

Solution: Game Mich Merry   Initially 54 54 assume   After game 1 36 72   After game 2 60 48   After game 3 40 68   Now Merry has 28 cards more than Mich. This option gives us exactly what number of cards they had initially.   So the answer is 54
Answer: E
On dividing 172 by a number, the quotient is 10 and the remainder is 2. Find the divisor.  Choose the correct option:
A) 9 B) 11 C) 13 D) 15 E) 17

Solution: d = (D-R)/Q   = (172 - 2)/10   = 170/10= 
170/10 = 17
17   17
Answer: E
10^190 - 10^9 = Which of the following best approximates the value of the expression above?	Choose the correct choice from the following:  A) 10^170  B) 10^180  C) 10^160  D) 10^181  E) 10^190

Solution: 10^190 - 10^9 =   Which of the following best approximates the value of the expression above?   Yes, answer 10^190 is correct. Note that we need approximate value of the given expression and as 10^(190) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(190)-10^(9)=~10^(190).   Answer : 10^190
Answer: E
If 5 cars park in 5 parking place.there are 3 red colour car,1 blue and 1 green then how many ways we can arrange the cars differently	Choose the correct choice from the following options: A) 10 B) 20 C) 30 D) 40 E) 50

Solution: total car=5   place =5   means cars are place any 5 position means its 5!=120   but 3 cars r red and 1 blue and 1 green   then its arrange 3!,1!,1!   so,   =120/6*1*1= 
120/6*1*1 = 20
20   ANSWER:20
Answer: B
A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes
7 : 9. How many litres of liquid A was contained by the can initially?	Choices
A) 10	B) 20	C) 21	D) 25	E) 26

Solution: Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively   Quantity of A in mixture left   = (7x - 7/12 x 9) litres = (7x - 21/4) litres.   Quantity of B in mixture left   = (5x - 5/12 x 9) litres = (5x - 15/4) litres.   (7x - 21/4) / [(5x - 15/4)+9] = 7/9 = › 28x - 21/20x + 21 = 7/9 =› 252x - 189 = 140x + 147   =› 112x = 336 =’ x = 3.   So, the can contained 21 litres of A.   Answer 21
Answer: C
40 people attend a party. 11 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?	Choose the correct choice from the following answers
A) 5	B) 6	C) 7	D) 11	E) 9

Solution: Total people = number of men + number of women   40 = 7 + number of married men + 22   number of married men = 40- 22-7= 
40- 22-7 = 11
11 men   ANSWER:11
Answer: D
The length of a rectangle is 2 cm more than the width of the rectangle. The perimeter of the rectangle is 20 cm. Find the length and the width of the rectangle.	Answers.
A) l=2,w=9 B) l=5,w=8 C) l=6,w=4 D) l=1,w=7 E) l=2,w=3

Solution: Let length l=x, width w=x−2and perimeter =p   ∴p=2l+2w   =2x+2(x−2)   20=2x+2x−4   4x=24   x=6   l=6 cm and w=l−2=4cm   Answer is l=6,w=4.
Answer: C
If f(x)= 5x^2- 2x+6 and g(y)= 3y-7, then g(f(x))
Choices
A) 82x^2-9x+38
B) 15x^2-6x+11
C) 58x^2-4x+58
D) 87x^2-5x+96
E) 98x^2-7x+94

Solution: g(f(x))=3(5x^2-2x+6)-7   =15x^2-6x+18-7   =15x^2-6x+11   the answer is 15x^2-6x+11
Answer: B
Manoj borrowed Rs.3450 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?  Choose the correct choice from the following options: A) Rs.5625 B) Rs.5355 C) Rs.5365 D) Rs.5345 E) Rs.5395

Solution: Let the sum lent by Manoj to Ramu be Rs.P.   Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100 = Rs.824.85   27P = 62100 = 82485   P = (82485 + 62100)/27 = 3055 + 2300 = Rs.5355   Option Rs.5355
Answer: B
The average age of a group of person going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average becomes 15.5 years. Find the number of persons initially going for picnic.  Choose the correct choice
A) 20
B) 18
C) 22
D) 19
E) None of the above

Solution: Let the number of persons, initially going for Picnic = x   ∴ Sum of their ages = 16x   Also, 16x+15×20/x+20 = 15.5   ⇒ 0.5x = 10 ⇒ x = 20 years.   20nswer 20
Answer: A
I spend 40 hours a week (5 days) at work and like to organize my time so that I spend an equal number of hours on the two tasks I currently have. Currently, I am spending 5 hours a day on Task 1 and 3 on Task 2. How many hours a week less do I need to spend on Task 1 in order to evenly distribute my time?	Choices:
A) 5
B) 3
C) 7
D) 1
E) 6

Solution: 5 x 5 = 25   25 - 5= 
25 - 5 = 20
20   The answer is 5.
Answer: A
The total of the ages of Mahesh, Suresh, Ramesh is 129 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?	Select the correct option.
A) 32years B) 54years C) 42years D) 35years E) 30years

Solution: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x   2x+10 + 3x+10 +4x+10 = 129   x = 11   Ramesh present age = 4*11+10= 
4*11+10 = 54
54 years   Answer is 54years
Answer: B
If the radius of a cylinder is doubled and height 5 times, what is the new volume of the cylinder divided by the old one?  Answers:
A) 8.
B) 2.
C) 6.
D) 20.
E) 10.

Solution: let v and v' be the original and the changed volume   now   v=pir^2h   v'=pi(2r)^2(5h)   v'=20v   20.) 20
Answer: D
The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?	Choose the correct choice from the following answers:	A) 22678	B) 26699	C) 26788	D) 19000	E) 39000

Solution: Money paid in cash = Rs. 1000   Balance payment = (40000 - 1000) = Rs. 39000   Answer: 39000
Answer: E
How many four-digit numbers are there such that all four digits are different and the first digit is not zero? Choose the correct choice:
A) 1504 B) 2648 C) 3720 D) 5832 E) 8105

Solution: All four digits are different and first digit is not zero.   So first digit can be filled in 9 ways.   And, second digit can be filled in 9 ways.   And, third digit can be filled in 9 ways.   And, fourth digit can be filled in 8 ways.   Total ways = 9*9*9*8= 
9*9*9*8 = 5_832
5832   Hence option (5832).
Answer: D
The radius of a wheel is 16.8 cm. What is the distance covered by the wheel in making 300 resolutions?	Choose the correct choice from the following options.
A) 754 m  B) 316.512 m  C) 311.512 m  D) 311.518 m  E) 313.512 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 300 resolutions.   = 300* 2 * 22/7 * 16.8 = 31651.2 cm   = 316.512 m   Answer:316.512 m
Answer: B
A train speeds past a pole in 15 seconds and a platform 120 meters long in 25 seconds. What is the length of the train (in meters)?
Select the correct option.
A) 100 m	B) 140 m	C) 130 m	D) 180 m	E) 170 m

Solution: Let the length of the train be x meters.   The speed of the train is x / 15.   Then, x + 120 = 25*(x / 15)   10x = 1800   x = 180 meters   The answer is 180 m.
Answer: D
A can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?
Answers
A) A-20  B) A-12  C) A-9  D) A-10  E) A-13

Solution: since A is a multiple of 11, we could very well say A = 11K (where K is 1,2...n).   The condition here should now be   11K + 1 = <operation> such that it gives us an integer   11k +1 </operation>= A -20 => A = 11K + 21 Not divisible by 11   11K +1 = A -12 => A = 11K + 31 Not A-10ivisible by 11   11K +1 = A -9 => A = 11K + 10 Not A-10ivisible by 11   11K +1 = A -10 => A = 11K + 11 A-10ivisible by 11   11K +1 = A -13 => A = 11K + 14 Not A-10ivisible by 11   Answer therefore is A -10   ANSWER:A-10
Answer: D
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.40 per glass on the first day, what was the price per glass on the second day?	Choose the most appropriate option
A) $0.15  B) $0.26  C) $0.30  D) $0.40  E) $0.45

Solution: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;   On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;   So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.   We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.   Say the price of the glass of the orangeade on the second day was $x then 2*0.4=3*x --> x=$0.26.   Answer: $0.26.
Answer: B
Here is an ancient problem from Bhaskaracharya's Lilavati:
A beautiful maiden, with beaming eyes, asks me which is the number that. multipied by 3 then increased by thre-fourths of the product. divided by 7 diminished by 52, the square root found,addition of 8, division by 10 gives the number 2?
Well, it sounds complicated, doesn't it? No, not if you know how to go about it.	Choose the correct choice:	A) 16	B) 22	C) 28	D) 29	E) 34

Solution: 28   28   The method of working out this problem is to reverse the whole process--multiplying 2 by 10, deducting 8,squaring the result and so on.
Answer: C
The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 612. What is the banker's discount?
Choose the correct choice from the following choices.
A) 1240 B) 1120 C) 1190 D) 1462 E) None of these

Solution: Explanation :   TD = (BG ×100)/TR = (612×100)/(6×12) = Rs. 850   BG = B1462 – T1462   => 612 = B1462 - 850   => B1462 = 612 + 850= 
612 + 850 = 1_462
1462 Answer : Option 1462
Answer: D
Two employees X and Y are paid a total of Rs. 500 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Choose the correct choice from the following answers:
A) s.227  B) s.287  C) s.297  D) s.300  E) s.380

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 500   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 500   ⇒ y[12/10 + 1] = 500   ⇒ 22y/10 = 500   ⇒ 22y = 5000   ⇒ y = 5000/22 = Rs.227.77   s.227)
Answer: A
800 is increased by 110%. Find the final number.
Choose the correct choice from the following choices.
A) 1200 B) 1210 C) 1180 D) 1190 E) 1680

Solution: 1680xplanationFinal number = Initial number + 110%(original number) = 800+ 110%(800) = 800 + 880= 
800 + 880 = 1_680
1680.Answer 1680
Answer: E
What is the sixth digit to the right of the decimal point, in the decimal expansion of (3/10)^6?	Choose the correct choice from the following choices
A) 7  B) 9  C) 3  D) 6  E) 5

Solution: Step 1 Convert fraction to decimal with two decimal places   3/10= 
  3/10 = 3/10 = around 0.3
0.30 then convert to scientific number= 3*10^-1   Step 2 Multiply 3^6 by 10^-6   Step 3 3 has the sequence 3, 9, 27   Answer is 9
Answer: B
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Choose the most appropriate option.
A) 2288
B) 2778
C) 8297
D) 8112
E) 3241

Solution: A = 7500(26/25)2 = 8112.Answer: 8112
Answer: D
A can do a work in 15 days and B in 20 days. If they work on it together, then the number of days the whole work can be finished is:
Choose one.
A) 7/40
B) 7/60
C) 40/7
D) 60/7
E) 50/7

Solution: A's 1 day's work =1/15   B's 1 day's work =1/20   (A + B)'s 1 day's work =(1/15+1/20)=7/60   the whole work can be finished in 60/7days. Answer: 60/7
Answer: D
P, Q and R have $9000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?	Choose the correct choice from the following choices:
A) 2400
B) 3600
C) 3998
D) 2539
E) 1930

Solution: 3600   3600   Let the amount with R be $ r   r = 2/3 (total amount with P and Q)   r = 2/3(9000 - r) => 3r = 18000 - 2r   => 5r = 18000 => r = 3600.
Answer: B
Ten participants are participating in a competition. In how many ways can the first three prizes be won?
Choose the correct choice from the following answers:
A) 920  B) 680  C) 820  D) 720  E) 620

Solution: Out of 10 participants, the first three prizes can be won in,   10P3 = 10! / (10 - 3)!   = 10 x 9 x 8   = 720 ways   ANSWER:720
Answer: D
Awordis defined as a sequence of three dots arranged in a row. Each dot is colored one of the three colours. How many distinct words can be formed?
Choose the correct option:	A) 23	B) 25	C) 26	D) 28	E) 27

Solution: Each dot can be either one of the three, so 2 options for each dot:   3*3*3= 
  3*3*3 = 27
27.   Answer: 28.
Answer: D
Amy's sells kale at x dollar per pound for the first 20 pounds and .8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 20 for which Amy's becomes an equal or better deal?	Choose the correct option.
A) 26 B) 25 C) 24 D) 27 E) 28

Solution: For 26my's deal to be better, the cost has to be less or equal to Lucia's   26ssuming 'n' is the number of pounds of kale, the equation is   20x + (n-20) (0.8x) <= 14x + (n-14)(0.9x)   Resolve it:   ==> 20x + 0.8nx - 16x <= 14x + 0.9nx - 12.6x   ==> 2.6x <=0.1nx   ==> 26x < =nx   ==> x (n-26) > = 0   as x cannot be 0,   ==> n - 26 >=0   ==> n > = 26   so the minimum value is 26   '26' would be the correct answer
Answer: A
Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?	Choose the correct choice from the following answers
A) $1600	B) $6000	C) $6050	D) $7050	E) $8000

Solution: Let T be the tier price, P be total price = 14000   Per the given conditions:   0.12T + 0.08(P-T) = 1440 ----> T= 8000. $8000 is the correct answer.
Answer: E
A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that p is the ratio of the circumference to the diameter of a circle ( 3.14159265).  Select the correct option:  A) 3.14×(7+43–√3/9)  B) 3.14×(7+43–√3/7)  C) 3.14×(7+43–√3/6)  D) 3.14×(7+43–√3/3)  E) 3.14×(7+43–√3/1)

Solution: By joining centers of 3 unit circles we will get an equilateral triangle of length 2 unit. We have to find the length of the orange line.   And center of the equilateral triangle will be the center of the big circle.   So radius of the big circle will be = (1 + Circum radius of the equilateral triagle)   Formula for Circul radius of the equilateral triangle = 23×(3–√2a)23×(32a) here 3–√2a32a is the height of the triangle. a is the side of the triangle   Circum radius of equilateral triangle = 23×3–√2×2=23–√23×32×2=23   Area of big circle will be =πr2=3.14×(1+23–√)2πr2=3.14×(1+23)2 = 3.14×(1+43–√+43)3.14×(1+43+43)   =3.14×(1+43–√+43)=3.14×(1+43+43) = 3.14×(73+43–√)3.14×(73+43)   =3.14×(7+43–√3/3)   Answer:3.14×(7+43–√3/3)
Answer: D
Assume all CDs are equal in time.
If 21 CDs have X hours of music, how many minutes will Y CDs have?
Choose the correct choice from the following options
A) 21XY/60 B) 7/60XY C) 21/60XY D) 20XY/7 E) 7/20XY

Solution: 21 C20XY/7s have X hours or 60*X minutes   1 C20XY/7 has time = 60*X/21 = 20X/7   Y C20XY/7 time in minutes = Y*20*X/7 = 20XY/7   Hence, the answer is 20XY/7.
Answer: D
a survey of n people in the town of badaville found that 50% of them prefer brand A.another survey of 100 people in the town of Chotaville found that 60% prefer brand A.In total 55% of all the people surveyed prefer brand A.What is the total number of people surveyed?  Choose the correct answer: A) 180 B) 200 C) 220 D) 240 E) 260

Solution: badavilla=50% from 100   chotavilla=60% from 100   total=110 from 200   55% of 200 is also 110   so total number of survey is 200   ANSWER:200
Answer: B