MU-NLPC/Calc-aqua_rat huggingface dataset:
A train 510 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Choose the correct choice from the following.
A) 52	B) 56	C) 41	D) 42	E) 34

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 550 * 2/25 = 52 sec   52nswer: Option 52
Answer: A
The reflex angle between the hands of a clock at 10.25 is
Choose the correct answer
A) 197 1/2  B) 197 1/9  C) 197 1/2  D) 167 1/3  E) 197 1/6

Solution: Explanation:   197 1/2ngle traced by hour hand in 125/12 hrs = (360/12 * 125/12) =   197 1/2ngle traced by minute hand in 25 min = (360/60 * 25) =   Reflex angle =   197 1/2nswer: 197 1/2) 197 1/2
Answer: A
Three cubes of metal whose edges are 9, 12 and 24 cm respectively, are melted and one new cube is made. Find the edge of the new cube? Choose the correct option.
A) 28 B) 77 C) 66 D) 18 E) 25.3

Solution: 93 + 123 + 243 = a3 => a   = 25.3   Answer: 25.3
Answer: E
If a and b are positive integers, and (2^3)(3^4)(5^7)=(a^3)∗b, how many different possible values of b are there?
Pick.
A) 2
B) 3
C) 4
D) 6
E) 12

Solution: Let's assume 2^3,3^3 and 5^3 as three different entities.   The entity 5^3 is there twice.   Thus, out of these three, we can take none, 1, two or all three. This gives a total of :   3C0+3C1+3C2+3C3 = 1+3+3+1= 
1+3+3+1 = 8
8 ways. Now the other 5^3 will not make a difference when being selected in the mentioned way. It will only make a difference when it is either selected with5^3 only(1 case), or when both of them together are considered with either 2^3(1 case) or 3^3(1 case). Finally, when all the 4 are considered together, we have one final case. Thus a total of   8+3+1= 
  8+3+1 = 12
12 cases.   ANSW12R:12
Answer: E
A house is to be constructed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
Choose the correct choice from the following choices:
A) 76
B) 64
C) 81
D) 120
E) None of these

Solution: Explanation :   Solution: Remaining work = (1-4/7) = 3/7. remaining period =(46-33)= 
(46-33) = 13
13 days.   Let the total men working at it be x.   Less work, less men (Direct proportion)   Less days, more men (Indirect proportion)   More hrs/day, less men (Indirect proportion)   work 4/7 : 3/7   Days 13 : 33 } : : 117 : x   Hrs/Day 9 : 8   .'. 4/7*13*9*x= 3/7*33*8*117 or x = ((3*33*8*117)/4*13*9) = 198.   .'. Additional men to be employed = (198-117)= 
(198-117) = 81
81.   Answer : 81
Answer: C
The length of a rectangle is reduced by 10%. By what % would the width have to be increased to maintain the original area?  Choose the correct choice from the following answers.
A) 10%	B) 11.1%	C) 25%	D) 30%	E) 35%

Solution: Sol. Required change = (10*100)/(100-10)=11.1%   11.1%
Answer: B
Find the amount on Rs.9000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?	Choose the correct choice from the following choices:
A) 5568  B) 9828  C) 5460  D) 5635  E) 6734

Solution: 9000 * 104/100 * 105/100= 
9000 * 104/100 * 105/100 = 9_828
> 9828   Answer:9828
Answer: B
The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Pick
A) 6 2/3%  B) 6 2/7%  C) 6 2/2%  D) 6 3/3%  E) 6 5/3%

Solution: 4/9 P = (P*R*R)/100   R = 20/3 = 6 2/3%   6 2/3%nswer: 6 2/3%
Answer: A
There are three foam generators in the factory, each of the first two can generate 12 liters of foam in one hour and the third can generate 18 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?	Answers.
A) 120. B) 132. C) 141 D) 154. E) 166.

Solution: Let the foam generators capacity be -   A = 12 lit/hr   B = 12 lit/hr   C = 18 lit/hr   Total foam generation in 1 hour will be 42 lit ( 12 + 12 + 18 ) ; since in 1 and 1/2 hr they will generate   42 + 21= 
  42 + 21 = 63
> 63 litres...   Now one of the first generators stops working ( Say A stops working ) , so we have -   B= 12 lit/hr   C = 18 lit/hr   Total foam generation in 2 hour will be 60 litres {2 (12+18)}   The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...   Foam generated by B will be  3/2 * 12= 
 3/2 * 12 = 18
> 18 litres   So, total foam generated will be 141 Litres ( 63 + 60 + 18 ) ; hence answer will be (141)
Answer: C
A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $17000 left with him. find salary..
Choose the correct choice from the following answers
A) $10700	B) $17000	C) $180000	D) $1700	E) $170000

Solution: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount   [1-(1/5 + 1/10 + 3/5)} * total salary= $17000, = [1-9/10] * Total salary = $17000, Total salary = $17000*10 = $180000, correct answer ($170000)
Answer: E
Oranges are bought at 7 for Rs.5. At what rate per hundred must they be sold to gain 33%?
Answers:  A) 57  B) 58  C) 69  D) 84  E) 95

Solution: 7 oranges bought for rs 5   1 orange cost =5/7   therefore for 100 oranges =100*(5/7)   gain =33%    500/7+(33/100)*500/7= 
 500/7+(33/100)*500/7 = 95
rate per hundred he want to sell   ans :95   ANSW95R:95
Answer: E
A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth? Choose one:
A) 22 B) 75 C) 90 D) 78 E) 11

Solution: SP of 1m of cloth = 8925/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 105 - Rs. 15 = Rs. 90.   Answer: 90
Answer: C
If the ratio of apples to bananas is 3 to 2 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers? Pick:	A) 2:3	B) 1:2	C) 3:5	D) 2:5	E) 5:6

Solution: The ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6.   The ratio of apples to bananas to cucumbers is 3 to 2 to 6.   The ratio of apples to cucumbers is 3 to 6 which equals 1:2.   The answer is 1:2.
Answer: B
A rectangular table seats 4 people on each of two sides, with every person directly facing another person across the table. If eight people choose their seats at random, what is probability that any two of them directly face other?	Choose the correct option
A) 1/56
B) 1/8
C) 1/7
D) 15/56
E) 4/7

Solution: A B C D   ------------   | TABLE |   ------------   E F G H   A to H are 8 people.   Prob to select any 1 person = 1   Prob to select the person opposite to the chosen person = 1/7   For ex. If we select A as the person than prob of choosing E is 1/7.   Hence, answer will be 1/7.
Answer: C
Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. In how much time, the tank is full?
Choose the correct answer
A) 43 min  B) 44 min  C) 45 min  D) 46 min  E) 47 min

Solution: part filled in 7 min= 7*(1/36+1/45) =7/20   remaining part= 1-7/20 =13/20   net part filled by pipes A,B,C=(1/36+1/45-1/30) =1/60 (in 1 min.)   13/20 part is filled in = 60*13/20= 
60*13/20 = 39
39 min   total time taken to fill the tank= 39+7= 
39+7 = 46
46 min   ans= 46 min.   ANSWER:46 min
Answer: D
Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?	Choose the correct choice from the following choices:
A) 8 hrs 85 min B) 8 hrs 18 min C) 8 hrs 15 min D) 6 hrs 15 min E) 3 hrs 15 min

Solution: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3   Number of pages typed by Elan in 1 hour = 40/5= 
40/5 = 8
8   Number of pages typed by both in 1 hour= (16/3 + 8) = 40/3   Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min   Answer:8 hrs 15 min
Answer: C
Question:	By selling an mobile for Rs. 3000, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
Options:
A	7%.
B	9%.
C	8%.
D	2%.
E	3%.  Choose the most appropriate option:
A) 9%  B) 2%  C) 3%  D) 7%  E) 8%

Solution: Explanation:   Marked price = Rs. 3000   C.P. = 100/120 * 3000 = Rs. 2500   Sale price = 90% of Rs. 3000 = Rs. 2700   Required gain % = 20/2500 * 100 = 8%.   Answer: 8%
Answer: E
Alex deposited x dollars into a new account that earned 6 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?	Choose the correct choice from the following choices
A) w/(1+1.08) B) w/(1.08+1.16) C) w/(1.16+1.24) D) w/(1.08^2+1.08^2) E) w/(1.06+1.06^2)

Solution: Account at the end of the first year would be 1.06x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.06x+x) dollars. Account at the end of the second year would be (1.06x+x)*1.06=w --> x(1.06^2+1.06)=w --> x=w/(1.06+1.06^2).   Answer: w/(1.06+1.06^2).
Answer: E
Cubes with each side one inch long are glued together to form a larger cube. The larger cube's face is painted with red color and the entire assembly is taken apart. 25 small cubes are found with no paints on them . How many of unit cubes have at least one face that is painted red? Select the correct option.
A) 64  B) 72  C) 86  D) 98  E) 100

Solution: Use the options.   The options which after getting added to 25 shows a cube of a number could be right.   Here    64+25= 
 64+25 = 89
89   72+25= 
72+25 = 97
97   86+25= 
86+25 = 111
111   98+25= 
98+25 = 123
123   100+25= 
100+25 = 125
125 ---(5*5*5)   So we have 100 as the answer!   100
Answer: E
The sum of all possible two digit numbers formed from
three different one digit natural numbers when divided by
the sum of the original three numbers is equal to?	Choose the correct answer:  A) 14  B) 16  C) 18  D) 20  E) 22

Solution: Let the one digit numbers x,y,z   Sum of all possible two digit numbers   =(10x+y)+(10x+z)+(10y+x)+(10y+z)+(10z+x)+(10z+y) = 22(x+y+z)   Therefore sum of all possible two digit numbers when   divided by sum of one digit numbers gives 22.   ANSW22R 22
Answer: E
Which of the following MUST yield a fractional integer when divided by 4?
Pick:
A) The sum of four consecutive positive integers.  B) The square of a prime number.  C) The sum of two odd integers.  D) The product of three consecutive odd numbers.  E) The difference between a multiple of 8 and a multiple of 3.

Solution: Hence A is true. No need to check other answers since there can only be one correct answer.   So, The sum of four consecutive positive integers.ns(The sum of four consecutive positive integers.).
Answer: A
You enter a weight loss challenge game and manage to lose 12% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?	Pick.
A) 10.24%
B) 9.22%
C) 9%
D) 14%
E) 12%

Solution: (100%-12%)*(100%+2%) = 0.88*1.02 = 10.24%   The weigh in records your weight loss at 10.24%!   The 10.24%nswer is 10.24%
Answer: A
A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 30 km in 10 hours. How much time he would have saved if the direction of tide has not changed?	Answers:
A) 2	B) 8	C) 4	D) 6	E) 5

Solution: Explanation:   He covered 5 km in 1 hour , so he might cover 30 km in 6 hours.   But he took 10 hours.   He would have saved 10 â€“ 6 = 4 hours.   Answer: 4
Answer: C
A worker's daily wage is increased by 40% and the new wage is $28 per day. What was the worker's daily wage before the increase?
Choices: A) $18 B) $20 C) $22 D) $24 E) $25

Solution: Let x be the daily wage before the increase.   1.4x = $28   x = $20   The answer is $20.
Answer: B
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is  Select the correct option:
A) 10 years
B) 40 years
C) 30 years
D) 50 years
E) 20 years

Solution: Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.   Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.   Husband's present age = (90 - 50)= 
(90 - 50) = 40
40 years.   Answer: 40 years
Answer: B
The circulation for magazine X in 1981 was 5 times the average (arithmetic mean) yearly circulation for magazine X for the years 1982-1990. What is the ratio of the circulation in 1981 to the total circulation during 1981-1990 for magazine X ? Choose the correct answer:
A) 1/5 B) 1/4 C) 5/14 D) 5/9 E) 5/6

Solution: There are 9 years from 1982-1990, inclusive. Let's say the average circulation every year between 1982-1990 inclusive is x.   So the total circulation is 9x from 1982-1990, inclusive.   In 1981, the circulation is 5x.   So total circulation for 1981-1990 is 5x + 9x = 14x.   Ratio of circulation in 1981 to total circulation during 1981-1990 is 5x to 14x or 5/14.   ANSWER:5/14 5  + 9= 
 5  + 9 = 14
14x.   Ratio of circulation in 1981 to total circulation during 1981-1990 is 5x to 14x or 5/14.   ANSWER:5/14
Answer: C
A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min
48 sec. What is the actual speed of the car?
Pick one
A) 30 km/hr  B) 35 km/hr  C) 25 km/hr  D) 40 km/hr  E) 45 km/hr

Solution: time 1 hr 40 min 48 sec   = 1 hr + 40/60 hr + 48/3600   1 +2/3+1/75=126/75   distance = 42 km   speed = 42 * 75 /126= 
42 * 75 /126 = 25
25 km/hr   that is 5/7 of the actual speed= 25   actual speed = 25 * 7/5= 
25 * 7/5 = 35
35 km/hr   ANSWER 35 km/hr
Answer: B
A fort of 400 soldiers has provisions for 10 days. After 2 days some of them left and the food was now enough for the same period of 10 days as before. How many of them left? Select the correct option
A) 80 B) 90 C) 100 D) 110 E) 120

Solution: 2000 ---- 50   400 ---- 8   x ----- 10   x*10 = 400*8   x=320   400   -------   80   80nswer: 80
Answer: A
A factory produces x widgets per day. The factory's fixed costs are $8420 per day. The price per widget is $80 and the variable costs are $20 per widget. How many widgets need to be produced for profits of $5440 a day? Choices.
A) 42.33 B) 90.33 C) 168 D) 231 E) 400

Solution: profits=5440=60x-8420--> x=231   Answer 231.
Answer: D
In a group of Hens and Goats, the total number of legs are 28 more than twice the number of heads. Find the total number of Goats.	Pick
A) A)16  B) B)12  C) C)14  D) D)8  E) E)6

Solution: Explanation :   Let the number of Hens be d   and number of goats be c   Then, total number of legs = 2d + 4c = 2(d + 2c)   total number of heads = c + d   Given that total number of legs are 28 more than twice the number of heads   => 2(d + 2c) = 28 + 2(c + d)   => d + 2c = 14 + c + d   => 2c = 14 + c   => c = 14   Answer : 14
Answer: C
Sum of the numbers from 1 to 35 is	Options.
A) 630 B) 660 C) 670 D) 450 E) None of these

Solution: Explanation: Sum of first n natural numbers = 1 + 2 + 3 + ..... n = n(n+1)/2   Substitute n = 35.   So S20=35Ã—36/2=630   Correct Option: 630
Answer: A
A basketball coach will select the members of a five-player team from among 12 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter? Choose the most appropriate option:
A) 1/9
B) 1/6
C) 2/9
D) 5/33
E) 1/3

Solution: you can but that will require more cases and will be time consuming.   straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 10c3   total number of ways of selecting 5 players out of 12 = 12c5   probability = 10c3/12c5 = 5/33   5/33
Answer: D
A trader wants 10% profit on the selling price of a product whereas his expenses amount to 15% on sales. What should be his rate of mark up on an article costing 9?  Answers
A) 20%
B) 66 2⁄3%
C) 30%
D) 100⁄3%
E) None of these

Solution: Let the SP of the article be x   Expenses = 15% of x = 0.15x   Profit = 10% of x = 0.10x   CP = 9 (given)   Therefore, 9 + 0.15x + 0.1x = x ⇒ x = 12   ∴ % increase for marked price = 12−9/9×100=100/3%   Answer 100⁄3%
Answer: D
The average age 15 girls of a class is 15 years. Out of these, the average age of 12 girls is 13 years and that of the other 3 girls is 14 years. The age of the 15th girl is?
Choose the correct choice from the following options
A) 35  B) 30  C) 31  D) 28  E) 27

Solution: Age of the 15th girl = 15*15 - (12*13+3*14) = 225-198= 
225-198 = 27
27 years   Answer is 27
Answer: E
If 189*s is a perfect square then s can be which of the following numbers?	Answers:
A) 21
B) 35
C) 54
D) 105
E) 150

Solution: My solution:   For a number to be a perfect square all the prime factors must be in pairs. So,   Prime factors of 945 are 3 *3 *3 * 7   1) 21 = 3 * 7   2) 35 = 5 * 7   3) 54 = 2 * 3 * 3 * 3   4) 105 = 3 * 5 * 7   5) 150 = 2 * 3 * 5 * 5   So only answer choice A completes the pairing of 3, 7. It adds a3, a5, and a7to the prime factors of 945 (3*3*3*7) and makes it a perfect square.21
Answer: A
10 books are placed at random in a shelf. The probability that a pair of books will always be together is -  Choose the correct choice from the following choices: A) 1/5 B) 1/3 C) 1/4 D) 118/2 E) 21/4

Solution: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!   Required probability = 1/5   Answer: 1/4
Answer: C
Which of the following set is equivalent to set A= {a,b,c,d,e}  Choose the most appropriate option:
A) B= {1,2,3,4,5}  B) B= {c,a,b,f}  C) B= {-1,0,2,4}  D) B= {-1,2,4}  E) None of these

Solution: Number of elements of B= {1,2,3,4,5}= Number of elements of B   B= {1,2,3,4,5}NSWER:B= {1,2,3,4,5}
Answer: A
To which of the following shapes the area can't be calculated if the perimeter is given?
Choose the correct choice from the following: A) Circle. B) An isosceles right triangle. C) Rectangle. D) A regular Hexagon E) Square.

Solution: Except for a rectangle all other geometric shapes are dependent on one variable, and thus we can calculate one unique value of the area if we are provided the perimeter.   A. Circle -> Radius   B. An isosceles right triangle -> One side.   C. Rectangle -> Length and breadth.   D. A regular Hexagon -> Side of the hexagon   E. Square -> Side.   ANSWER:Rectangle.
Answer: C
A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 7600 a year. What is his average monthly income?
Select the correct option: A) 2000 B) 2010 C) 2100 D) 2200 E) 2300

Solution: Total expenditure for the first 3 months = 3 × 1600 = 4800   Total expenditure for 4 months = 4 × 1550 = 6200   Total expenditure for 5 months = 5 × 1800 = 9000   Total expenditure and saving (which is income for one year)   = 4800 + 6200 + 9000 + 7600 = Rs. 27600   So, Average monthly income = 27600/12 = Rs. 2300   2300
Answer: E
Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 53 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week? Pick:
A) 48  B) 50  C) 52  D) 54  E) 56

Solution: Annie earned 40x + 13(2x) = 66x   Let H be the number of hours that Harry worked.   Harry earned 30x + 1.5x(H-30) = 66x   (1.5x)(H) = 81x   H = 54 hours   The answer is 54.
Answer: D
Rahul went to a shop and bought things worth Rs. 25, out of which 48 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Choose the correct choice from the following answers:
A) 19	B) 19.7	C) 19.9	D) 16.7	E) 22.8

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 48 Paise is given as tax   => Total tax incurred = 48 Paise = Rs.48/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 48/100   ⇒ 6(25 −0.3 −x) = 48   ⇒ (25 − 0.3 − x) = 8   ⇒ x = 25 − 0.3 − 8 = 16.7   16.7)
Answer: D
In a room filled with 7 people, 2 people have exactly 1 sibling in the room and 5 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings? Pick one:  A) 5/21  B) 3/7  C) 4/7  D) 5/7  E) 16/21

Solution: There are suppose A 3/7 C D E F G members in the room 4 people who have exactly one sibling....A 3/7 C D....(A is 3/7s∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 5 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)   there are now 3 different set of siblings (A and 3/7)   (C and D);(EFG)   Now first selecting 2 people out of 7 is 7C2=21   first sibling pair----(A and 3/7)--selecting 2 people --2C2=1   second sibling pair (C and D)--selecting 2 people--2C2=1   third sibling pair (E F G)--selecting 2 out of 5 --5C2=10   total= 1+1+10= 
1+1+10 = 12
12   but,a/c to formula P(success)-1-p(fail)   here,p(failure)is selecting 2 people who are siblings=12/21(21 is 7C2)   =1-12/21   =9/21   =3/7 ANS 3/7
Answer: B
The price of a certain bicycle this year is $1325, which is 6 percent greater than the cost of the bicycle last year. What was the price of the bicycle last year?
Choose the correct option:	A) $1150	B) $1175	C) $1200	D) $1225	E) $1250

Solution: The price of the bicycle last year was $1325/1.06= 
1325/1.06 = 1_250
$1250   The answer is $1250.
Answer: E
If (x - 1)^2 = 289, which of the following could be the value of x - 3?	Options
A) 18
B) 16
C) 14
D) -17
E) -19

Solution: (x - 1)^2 = 289   (x - 1) = 17 or -17   x = 18 or -16   x - 3 = 15 or -19   The answer is -19.
Answer: E
Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days. They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed. In how many days is the work completed ?  Choose the most appropriate option.
A) 7
B) 6
C) 5
D) 4
E) 3

Solution: (Rajiv +venky+ravi) 2 days work= 2(1/10+1/12+1/15)=1/2   ravi works alone for last 3 days = 3*1/15=1/5   total work 1/2+1/5=7/10   remaining work=1-7/10=3/10   (venky+ravi) 1 days work=1/12+1/15=9/60=3/20   3/10 work will be done by venky and ravi in  3/10*20/3= 
 3/10*20/3 = 2
2 days   total days is the work completed= 2+3+2= 
2+3+2 = 7
7 days   7NSWER:7
Answer: A
If the sides of a triangle are 20 cm, 12 cm and 16 cm, what is its area?
Choose the most appropriate option:
A) 70 B) 79 C) 85 D) 96 E) 92

Solution: The triangle with sides 20 cm, 12 cm and 16 cm is right angled, where the hypotenuse is 20 cm.   Area of the triangle = 1/2 * 12 * 16= 
1/2 * 12 * 16 = 96
96 cm2   Answer: Option 96
Answer: D