MU-NLPC/Calc-aqua_rat huggingface dataset:
In an examination, 300 students appeared. Out of these students; 29 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.	Choose the correct choice from the following answers
A) 51
B) 37
C) 54
D) 99
E) 01

Solution: The number of students with first division = 29 % of 300 = 29/100 × 300 = 8700/100= 
8700/100 = 87
87   51nd, the number of students with second division= 54 % of 300   = 54/100 × 300   =16200/100= 
16200/100 = 162
162   Therefore, the number of students who just passed= 300 – (87 + 162) = 51   51nswer:51
Answer: A
1,245
1,254
1,425
.....
....
+5,421
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,4,5 exactly once in each integer. What is the sum of these 24 integers?	Choose the correct choice from the following choices
A) 74,446 B) 79,992 C) 83,338 D) 86,662 E) 91,114

Solution: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.   Then the sum equals 6(1111)+6(2222)+6(4444)+6(5555) = 79,992   The answer is 79,992.
Answer: B
A man spends 15% of his income in house rent, 25% of the rest on his children’s education, 20% of the rest miscellaneous causes. If he now posses Rs. 2988 then his income is? Choices: A) A)Rs.3625 B) B)Rs.4625 C) C)Rs.4585 D) D)Rs.5655 E) E)Rs.6225

Solution: X * (85/100) * (75/100) * (80/100) = 2988   X * 0.85 * 0.75 * 0.8=2988   X = 2988/0.48= 
2988/0.48 = 6_225
6225   ANSWRs.6225R:Rs.6225
Answer: E
How many times do the hands of a clock coincide in a day?
Choose the correct choice from the following answers:
A) 29  B) 28  C) 22  D) 88  E) 27

Solution: Explanation:   The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they   coincide only once, i.e., at 12 o'clock).   The hands overlap about every 65 minutes, not every 60 minutes.   The hands coincide 22 times in a day.   Answer: 22) 22
Answer: C
A bat is bought for Rs.410 and sold at a gain of 20% find its selling price Options:
A) s.430/-  B) s.492/-  C) s.400/-  D) s.580/-  E) s.600/-

Solution: 100 % ------> 410   120 % ------> 120*410/100   Selling price = Rs.492/-   s.492/-
Answer: B
The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Choose the correct choice from the following options.
A) 79 kmph  B) 85 kmph  C) 35 kmph  D) 23 kmph  E) 14 kmph

Solution: S = (10 + 60)/2= 
(10 + 60)/2 = 35
35 kmph   Answer:35 kmph
Answer: C
If 0.10 of a number is equal to 0.070 of another number, the ratio of the numbers is : Select:
A) 2 :3  B) 3 :4  C) 7:10  D) 20 : 3  E) 30:7

Solution: 0.10A = 0.070B   -> A/B = 0.07/0.10 = 7/10   :. A : B = 7 : 10   ANSWER:7:10
Answer: C
Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :
Select the correct option
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 49.5 greater than the correct number.   Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)   Then the incorrect number was cba.   100c + 10b + a - (100a + 10b + c) = 495   99c - 99a = 99(c - a) = 495   495 = 99*5 = 99(c - a)   So c - a = 5   Answer (5)
Answer: C
A man is 28 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is	Select the correct option:	A) 20 years	B) 21 years	C) 22 years	D) 24 years	E) 26 years

Solution: Explanation:   Let the son's present age be x years. Then, man's present age = (x + 28) years   => (x + 28) + 2 = 2(x + 2)   => x + 30 = 2x + 4   So, x = 26   Answer: Option 26 years
Answer: E
An uneducated retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?
Choose the correct choice from the following choices:  A) 12.50%  B) 12%  C) 13.50%  D) 13%  E) 11%

Solution: Let C.P =Rs 100.   then ,marked price =Rs100   S.P=75% of Rs 150=Rs112.50   Hence,gain%=12.50%   Option 12.50%
Answer: A
Look at this series: 97, 97, 97, 87, 87, 87, 67, 67, 67 ... What number should come next?  Choices.
A) 47	B) 57	C) 45	D) 48	E) 55

Solution: Explanation:   In this series, each number 20 is subtracted from previous number to arrive at the next number.   Answer: Option 57
Answer: B
Group A has 3 boys and 4 girls, group B has 2 boys and 2 girls and group C has 4 boys and 4 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
Choose the correct option
A) 13/4	B) 19/28	C) 9/15	D) 29/35	E) 77/27

Solution: Group A has 3 boys and 4 girls; 7   Group B has 2 boys and 2 girls; 4   Group C has 4 boys and 4 girls. 8   Selected group should have one girl and two boys.   Girl from A, boy from B, boy from C: 4/7*2/4*4/8 = 1/7;   Boy from A, girl from B, boy from C: 3/7*2/4*4/8 = 3/28;   Boy from A, boy from B, girl from C: 3/7*2/4*4/8 = 3/7.   Sum = 1/7 + 3/28 + 3/7 = 19/28.   Answer: 19/28.
Answer: B
A restaurant meal cost $40 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between  Choose the correct choice from the following answers
A) $43 and $47 B) $39 and $4 1 C) $38 and $40 D) $37 and $39 E) $36 and $37

Solution: Hence it will be between 40 * (1+10/100) and 40 * (1+15/100).   i.e b/w 44 and 46. Hence the answer $43 and $47 (b/w 43 and 47).
Answer: A
The arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?	Choose the correct choice from the following options
A) 10.5  B) 11  C) 11.5  D) 12  E) 12.5

Solution: The value which isexactlytwo SD less than the mean is:mean-2*SD=14.0-2*1.5= 
14.0-2*1.5 = 11
11.   Answer: 11.
Answer: B
Worker A takes 4 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?	Choices
A) 20/9  B) 40/9  C) 40/14  D) 60/9  E) 80/9

Solution: one day work of A = 1/4   one day work of B = 1/10   so one day work of A and B together = 1/4 + 1/10 = 14/40   so total days required = 40/14   ANSWER:40/14
Answer: C
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choose the correct answer
A) 12 sec B) 30 sec C) 27 sec D) 87 sec E) 15 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer:30 sec
Answer: B
We can rent a car for x dollars per day for the first 3 days and then y dollars for each additional day. How much will it cost to rent a car for z days, where z>3?	Choose the correct answer
A) x + zy	B) 3y+(z-3)x	C) 3x + 3zy	D) 3x+(z-3)y	E) 3x + zy

Solution: The first 3 days cost 3x.   The next (z-3) days cost (z-3)y.   The total cost is 3x+(z-3)y.   The answer is 3x+(z-3)y.
Answer: D
The average of 11 numbers is 12.9. If the average of first six is 12.5 and that of the last six is 11.4 the sixth number is? Choose the correct choice:
A) 10.5
B) 11.5
C) 12.5
D) 13.5
E) 14.5

Solution: 1 to 11 = 11 * 12.9= 
11 * 12.9 = 141.9
141.9   1 to 6= 6 * 15.5= 
6 * 15.5 = 93
93   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   93 + 68.4= 
93 + 68.4 = 161.4
161.4 – 149.9= 11.5   6th number = 11.5   ANSWER:11.5
Answer: B
A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?  Select the correct option:
A) 4 km/hr  B) 6 km/hr  C) 7 km/hr  D) 8 km/hr  E) 2 km/hr

Solution: Rate downstream =16/2= 
16/2 = 8
8 kmph.   Rate upstream=16/4= 
16/4 = 4
4 kmph.   Speed in still water=	1/2	(8 + 4) kmph = 6 kmph.   ANSWER:6 km/hr
Answer: B
A sum of Rs. 4500 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest?  Choose the most appropriate option:  A) 37%  B) 25%  C) 35%  D) 6%  E) 20%

Solution: S.I. = (9000 - 4500) = Rs. 4500\   Rate = (100 * 4500) / (4500* 4)= 
(100 * 4500) / (4500* 4) = 25
25%   Answer: 25%
Answer: B
The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 462 the Other is	Choose the correct answer
A) 330  B) 300  C) 270  D) 150  E) 350

Solution: The other number   = L.C.M * H.C.F/given number   = 2310*30/462= 
2310*30/462 = 150
150   Answer is 150.
Answer: D
Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time Q it could take for 10 cars to be complete?
Choose the most appropriate option
A) 111 1/9 minutes	B) 115 2/5 minutes	C) 116 minutes	D) 120 minutes	E) 125 minutes

Solution: A builds 4 cars in 80 min   B builds 4 cars in 100 min   So A builds another car in another 20 min (i.e total 5 cars)   B builds another car in another 25 minutes (i.e, total 5 cars)   However, A can build another car in next 20 min (i.e total 6 cars)   So total time Q= 125 min by B, which is > 120 min by A   B - 4 cars, A - 6 cars   Answer = 120 minutes
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 11 cm.	Choose the correct answer:
A) 335 cm2  B) 209 cm2  C) 285 cm2  D) 825 cm2  E) 725 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (11)   = 209 cm2   Answer: 209 cm2
Answer: B
Three fair coins are labeled with a zero (0) on one side and a one (1) on the other side. Jimmy flips all three coins at once and computes the sum of the numbers displayed. He does this over 1000 times, writing down the sums in a long list. What is the expected standard deviation of the sums on this list?
Choose the correct choice from the following options
A) 1/2  B) 3/4  C) √3/2  D) √5 /2  E) 5/4

Solution: variance of binomial distribution is n*p*(1-p), n = 3, p = 1/2   variance = 3*1/2*(1-1/2)= 3/4   stddev = sqrt(variance) = sqrt(3)/2   After many trials sample standard deviation is close to theoretical standard deviation = sqrt(3)/2.   √3/2 is the answer.
Answer: C
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A do the work if he is assisted by B and C on every third day? Choose the correct choice:
A) 22 days
B) 15 days
C) 77 days
D) 99 days
E) 11 days

Solution: A's 2 day's work = (1/20 * 2) = 1/10   (A + B + C)'s 1 day work = (1/20 + 1/30 + 1/60) = 1/10   Work done in 3 days = (1/10 + 1/10) = 1/5   Now, 1/5 work is done in 3 days.   Whole work will be done in (3 * 5)= 
(3 * 5) = 15
15 days.   Answer: 15 days
Answer: B
How many positive 5-digit integers have the odd sum W of their digits? Select.
A) 9*10^2 B) 9*10^3 C) 10^4 D) 45*10^3 E) 9*10^4

Solution: We are looking at numbers between 10000 and 99999 both inclusive.   There are 90000 numbers.   Now for   10000 : sum of digits is odd;   10001 :sum of digits is even;   10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.   (Exception for the above statement :   When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd   and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)   This means exactly half of the numbers will have odd sum W of their digits. i.e 45000   Answer :45*10^3
Answer: D
A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 13 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Choose the correct choice from the following options:  A) 2,060  B) 1,320  C) 545  D) 315  E) 286

Solution: 13*12*11/3*2*1 = 286   286
Answer: E
A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?  Choose the correct choice from the following answers.
A) 635 B) 700 C) 1404 D) 2620 E) 3510

Solution: 8 Men - 5 Women   Choose 6 ( two cases)   Case 1:2 men, 4 women   No of ways to choose 2 men out of 8 is 8C2 . This includes that one case in which the two men who refuse to serve together are included. So men can be chosen in 8C2 - 1 ways.   No. of ways to choose 4 women out of 5 is 5C4.   Number of ways of choosing 2 men and 4 women = (8C2 - 1)*(5C4) = 27*5= 
27*5 = 135
135   Case 2: 3 men, 3 women   No of ways to choose 3 men out of 8 is 8C3. No of ways to choose those two men together is 6C1 (You choose them and choose one more to make 3). So men can be chosen in 8C3 - 6C1 ways.   No of ways to choose 3 women out of 5 is 5C3.   Number of ways of choosing 3 men and 3 women= (8C3 - 6C1)*(5C3) = 500   Total number of ways = 135 + 500= 
135 + 500 = 635
635   635NSWER:635
Answer: A
John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $70. What is the percent decrease?
Choose the correct option.
A) 20%
B) 30%
C) 40%
D) 50%
E) 60%

Solution: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 70 = 30. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (30/100)*100 = (0.3)*100= 
(0.3)*100 = 30
30%.   30%
Answer: B
There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?  Choose the correct choice
A) 34  B) 39  C) 42  D) 45  E) 49

Solution: Suppose the average join the mess , total expenditure = 35x + 42   Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1   or, 35x + 42 = 42x – 42   or, x = 12   Thus the original expenditure of the mess = 35 x 12 = Rs. 42   42
Answer: C
A man is 46 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options
A) 44 years	B) 18 years	C) 20 years	D) 22 years	E) 16 years

Solution: Let the son's present age be x years. Then, man's present age = (x + 24) years.   (x + 46) + 2 = 2(x + 2)   x + 48 = 2x + 4   x = 44.   answer :44 years
Answer: A
The number of livestock in a farm at the beginning of year 2000 was 100,000. During the year, the number increased by p%. During the next year 2001, there was a famine and the number decreased by q%. A census at the end of year 2001 revealed that the number of livestock in the farm was 100,000. Which of the following expressions is correct?	Choose the correct option:  A) p > q  B) q > p  C) p = q  D) With the exception of 1 instance, p will be equal to q  E) There is no relation between p and q

Solution: Number plugging in will be best strategy for this question.   Let p = 5%,   Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence p > q is the correct answer
Answer: A
A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:	Pick
A) 145	B) 253	C) 370	D) 352	E) 300

Solution: Explanation:   Let the middle digit be x. Then, 2x = 10 or x = 5.   So, the number is either 253 or 352. Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit. Hence, required number = 253.   ANSWER IS 253
Answer: B
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? Choose the most appropriate option:
A) 2 sec B) 6 sec C) 7 sec D) 8 sec E) 4 sec

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6 sec
Answer: B
The owner of an electronic store charges his customer 9% more than the cost price. If a customer paid 1,26440 for an LED T.V., then what was the original price of the T.V.? Choose the correct choice from the following
A) 115000
B) 115500
C) 116000
D) 117000
E) 118000

Solution: Selling Price = 109% of CP;   :. CP = 126440 × 100/109 = 116000   117000)
Answer: D
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer	Choices
A) I only B) II only C) I and II D) I and III E) II and III

Solution: If x is an odd negative integer and y is an even integer, which of the following statements must be true?   I. (3x - 2y) is odd   3x - is always negative and odd   2y - can be 0, when y=0, or always even integer (positive or negative)   odd integer +/- even integer = always odd   I statement is always true   II. xy^2 is an even negative integer   y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true   III. (y^2 - x) is an odd negative integer   y can be 0 => -x will be positive => III statement is not true   basing on above, only I statement will always be true   answer is I only
Answer: A
If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students? Choose the correct choice from the following answers:	A) 53.23	B) 54.68	C) 51.33	D) 50	E) 52

Solution: Explanation:   Average marks of batch 1 = 50   Students in batch 1 = 55   Total marks of batch 1 = 55 × 50   Average marks of batch2 = 55   Students in batch2 = 60   Total marks of batch2 = 60 × 55   Average marks of batch3 = 60   Students in batch3 = 45   Total marks of batch3 = 45 × 60   Total students = 55 + 60 + 45= 
55 + 60 + 45 = 160
160   Average marks of all the students=(55×50)+(60×55)+(45×60)/160   =275+330+270/16   =875/16=54.68   Answer: Option 54.68
Answer: B
A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?
Answers.
A) 33
B) 57
C) 55
D) 99
E) 12

Solution: 2 *3(15 + 4) = 114   114 * 1/2 = Rs.57   Answer: 57
Answer: B
In a camp, there is a meal for 120 men or 200 children. If 170 children have taken the meal, how many men will be catered to with remaining meal?
Choose one.
A) 30	B) 20	C) 18	D) 57	E) 63

Solution: There is a meal for 200 children.   170 children have taken the meal.   Remaining meal is to be catered to 30 children.   Now, 200 children 120 men.   30 children = (120/200)x 30 = 18 men.   18
Answer: C
A family had dinner in a restaurant and paid $30 for food. They also had to pay 9.5% sale tax and 10% for the tip. How much did they pay for the dinner? Choose the correct choice
A) $35.83
B) $35.84
C) $35.85
D) $35.86
E) $35.87

Solution: SOLUTION   They paid for food, sales tax and tip, hence   total paid = $30 + 9.5% * 30 + 10% * 30 = $35.85   Answer $35.85
Answer: C
Two coins are tossed, find the probability that two Tails are obtained  Choose the correct choice from the following choices:
A) 1/3
B) 1/4
C) 1/5
D) 1/7
E) 2/3

Solution: The sample space S is given by.   S = {(H,T),(H,H),(T,H),(T,T)}   Let E be the event "two heads are obtained".   E = {(T,T)}   P(E) = n(E) / n(S) = 1/4   1/4
Answer: B
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 7 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
Pick one:  A) 60  B) 56  C) 84  D) 90  E) 108

Solution: B is the answer....   D = TS where D=distance, T=Time and S=Speed   To travel half distance, (2+2T) = 7T ==> T = 2/5 ==> 24 minutes   To travel double distance, 2(2+2T) = 7T ==> 2 ==>80 minutes   Difference, 56 minutes   56
Answer: B
The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
Choose the correct choice from the following:
A) 31  B) 67  C) 29  D) 97  E) 27

Solution: Total score of the batsman in 20 matches = 800.   Total score of the batsman in the next 10 matches = 130.   Total score of the batsman in the 30 matches = 930.   Average score of the batsman = 930/30= 
930/30 = 31
31.   31nswer: 31
Answer: A
A certain airline's fleet consisted of 110 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
Pick one:  A) 15  B) 16  C) 17  D) 18  E) 19

Solution: Let x be the number of years.   4x > 110 - 3x   7x > 110   x > 15 + 5/7   The answer is 16.
Answer: B
The circumferences of the wheels of a carriage are 6 3/14 dm and 8 1/18 dm. What is the least distance in which both wheels simultaneously complete an integral number of revolutions ? How often will the points of the two wheels which were lowest at the time of starting touch the ground together in 1 kilometre ?	Choose the correct choice.
A) 47	B) 24	C) 45	D) 34	E) 56

Solution: LCM of 6 3/14 dm and 8 1/18 dm =435/2=217 1/2 dm   and the required no. of revolutions = 2*10000/435= 45.9   The required answer =45 times   Answer is 45
Answer: C
A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 10% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices  Choose one.
A) $22.68	B) $23.94	C) $24	D) $25.20	E) $30

Solution: $22.68.
Answer: A
What is the next number in the sequence below?
1 4 9 16 25 36 49 64__ ?
Choose the correct choice from the following answers:	A) 121	B) 100	C) 49	D) 64	E) 81

Solution: as the series of numbers are squares of numbers   1^2=1   2^2=4   3^2=9   and so on   therefore 9^2=81   ANSW81R:81
Answer: E
A rectangular swimming pool is 20 feet by 28 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 884 square feet. What is the width of the deck?  Select
A) 2 feet B) 2.5 feet C) 3 feet D) 4 feet E) 5 feet

Solution: Assume the width of the deck = x   Area of pool and deck = (20 + 2x)*(28 + 2x) =884 {The deck is present at both ends of the length and the breadth, hence we need to add 2x}   (20 + 2x)*(28 + 2x) =884 can be written as   (10 + x)*(14 + x) = 221   140 + 24x + x^2 = 221   x^2 + 24x - 81 = 0   (x + 27)(x - 3) = 0   Hence x = -27 or 3. But a length cannot be negative   Hence width of the deck = x = 3   3 feetorrect option: 3 feet
Answer: C
The probability that B can shoot a target two out of two times is 0.35. What is the probability that the target will be missed by B immediately after such two shots?	Select the correct option.
A) 0.25	B) 0.65	C) 0.75	D) 0.4	E) 0.8

Solution: Suppose there are total 'x' shots.   B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.   therefore, 2/x = 0.25 (given)   the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.   thus, the probabilty of missing just after 2 shots is (x-2)/x.   (x-2)/x = 1 - 2/x   = 1 - 0.35= 
1 - 0.35 = 0.65
0.65   Answer : 0.4
Answer: D