MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the area of trapezium whose parallel sides are 24 cm and 14 cm long, and the distance between them is 18 cm?	Pick one.
A) 288 cm2
B) 277 cm2
C) 345 cm2
D) 276 cm2
E) 342 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (24 + 14) * (18)   = 342 cm2   Answer: 342 cm2
Answer: E
The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven c = md + b
The cost is $4600 for 10 000 km and $9100 for 25 000 km.
(a) Determine the values of m and b.
(b) Write c as a function of d. Choose the correct choice from the following options.
A) m = 0.3 and b = 1500	B) m = 0.3 and b = 1600	C) m = 0.3 and b = 1700	D) m = 0.3 and b = 1800	E) None

Solution: Solution:   (a)   c = md + b   The cost is $ 4600 for 10 000 km   4600 = m (10 000) + b   10 000 m + b = 4600   b = -10 000 m + 4600 ------- (i)   The cost is $ 9100 for 25 000 km   9100 = m (25 000) + b   9100 = 25 000 m + b   25 000 m + b = 9100   b = -25 000 m + 9100 --------- (ii)   From equation (i) and (ii) we get;   -10 000 m + 4600 = -25 000 m + 9100   -10 000 m + 25 000 m = 9100 – 4600   15 000 m = 4500   m = 4500/15 000   m = 3/10= 
3/10 = 3/10 = around 0.3
0.3   Now, put the value of m= 0.3 in equation (i) we get;   b = -10 000 (0.3) + 4600   b = -3000 + 4600= 
-3000 + 4600 = 1_600
1600   Answer: m= 0.3 and b = 1600   (b) c = md + b   m = 0.3   b = 1600   c = 0.3d + 1600   Answer: c = 0.3d + 1600   Answer m = 0.3 and b = 1600
Answer: B
A person incurs loss for by selling a watch for Rs1140.at what price should the watch be sold to earn a 5% profit ?
Choose the correct choice from the following:  A) 4560  B) 2301  C) 4512  D) 3260  E) 1260

Solution: let the new sp be Rsx.then   (100-loss%) : (1st sp)=(100+gain%) (2nd sp)   {(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95= 
(105*1140)/95 = 1_260
1260.   Ans: 1260
Answer: E
The breath of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the length is 10 units?  Choose the correct choice from the following.
A) 370 sq.units
B) 270 sq.units
C) 170 sq.units
D) 470 sq.units
E) 570 sq.units

Solution: Given that the area of the square = 2025sq.units   => Side of square = √2025 = 45 units   The radius of the circle = side of the square = 45 units breath of the rectangle = 3/5 * 45= 
3/5 * 45 = 27
27units   Given that length= 10 units   Area of the rectangle = lb = 27* 10= 
27* 10 = 270
270 sq.units   Answer:270 sq.units
Answer: B
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?`
Select:  A) 10/21  B) 11/21  C) 2/7  D) 5/7  E) 3/7

Solution: Total number of balls = (2 + 3 + 2)= 
(2 + 3 + 2) = 7
7.   Let S be the sample space.   Then, n(S)= Number of ways of drawing 2 balls out of 7   = 7C2 `   =	(7 x 6)/(2 x 1)   = 21.   Let E = Event of drawing 2 balls, none of which is blue.   n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.   = 5C2   =	(5 x 4)/(2 x 1)   = 10.   P(E) =	n(E)/n(S)	=	10/21.   10/21nswer:10/21
Answer: A
A departmental store has 2 managers and 10 associates. The 2 managers have an average salary of $5000. The 10 associates have an average salary of $20000. What is the average salary for the departmental store?
Select the correct option:
A) $15500  B) $16500  C) $17500  D) $14500  E) $19500

Solution: Number of managers is 2   Their average salary is $5000   Number of associates is 10   Their average salary is $20,000   Total salary of managers is  2*5000= 
 2*5000 = 10_000
$10000   Total salary of associates is 10*20,000=$200,000   Total salary for the departmental store is 200,000+10000=210000   Average salary for the departmental store is 210000/10+2=17500   Answer is $17500
Answer: C
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 35 min, then the slower pipe alone will be able to fill the tank in? Choose the correct answer:
A) 229  B) 787  C) 144  D) 128  E) 140

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/35   4/x = 1/35 => x = 140 min.   Answer: 140
Answer: E
A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 180 m long? Choose the correct option.
A) 38 sec  B) 35 sec  C) 43.2 sec  D) 40 sec  E) none of these

Solution: Speed = 45 km/hr = 45 Ã— (5/18) m/s   = 150/12 = 50/4 = 25/2 m/s   Total distance = length of the train + length of the platform   = 360 + 180= 
360 + 180 = 540
540 meter   Time taken to cross the platform= 540/(25/2) = 540 Ã— 2/25 = 43.2 seconds   ANSWER:43.2 sec
Answer: C
A man buys s cycle for $100 and sells it at a loss of 20%. What is the selling price of the cycle? Choose the correct option
A) $50
B) $60
C) $70
D) $80
E) $90

Solution: S.P. = 80% of the $100 = 80/100 * 100= 
80/100 * 100 = 80
$80   Answer is $80
Answer: D
One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 3,50,000 as total savings, how much has he saved in Public Provident Fund ?	Select.
A) Rs. 130,000	B) Rs. 150,000	C) Rs. 160,000	D) Rs. 140,000	E) None

Solution: EXPLANATION   Let savings in N.S.C and P.P.F. be Rs. x and Rs. (350000 – x) respectively. Then,   1/3x=1/2(350000-x)   => x/3 + x/2 = 175000   => 5x/6 = 175000   => x= 175000 x 6 /5= 210000   Savings in Public Provident Fund = Rs. (350000 – 210000) = Rs. 140000   Answer Rs. 140,000
Answer: D
In how many ways can a cricketer can score 200 runs with fours and sixes only?
Choose the correct choice from the following options:
A) 13  B) 17  C) 19  D) 16  E) 15

Solution: 200 runs can be scored by scoring only fours or through a combination of fours and sixes.   Possibilities are 50 x 4, 47 x 4 + 2 x 6, 44 x 4 + 4 x 6 ... A total of 17 ways   ANSWER:17
Answer: B
What is the Mode of the following data set A- {1,2,4,6,4,9,4,10} Pick one: A) 1 B) 10 C) 6 D) 4 E) 9

Solution: Mode of a set is the data point that is repeated the most number of times. In the set given, 4 is repeated.   Answer : 4
Answer: D
If a man lost 7% by selling oranges at the rate of 21 a rupee at how many a rupee must he sell them to gain 42%?  Choose the correct choice from the following options
A) 12.75	B) 11.75	C) 8.75	D) 15.75	E) 13.75

Solution: 93% ---- 21   142% ---- ?   93/142 * 21 = 13.75   Answer: 13.75
Answer: E
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 7 inches wide on each side, the total area would have been (M + 264) square inches. What is the perimeter of the photograph, in inches? Choose the correct option.
A) 8
B) 12
C) 16
D) 20
E) 24

Solution: Let x and y be the width and length of the photograph.   (x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M   (x+14)(y+14)=M and so (2) xy + 14x + 14y + 196 = M+264   Let's subtract equation (1) from equation (2).   12x + 12y + 192 = 264   2x + 2y = 12, which is the perimeter of the photograph.   The answer is 12.
Answer: B
Find the area of right angled triangle whose hypotenuse is 15 cm and one of the sides is 12 cm.  Select:
A) 34 cm²  B) 38 cm²  C) 54 cm²  D) 56 cm²  E) 64 cm²

Solution: AB² = A54 cm²² - B54 cm²²   = 15² - 12²   = 225 - 144= 
225 - 144 = 81
81   Therefore, AB= 9   Therefore, area of the triangle = ¹/₂ × base × height   = ¹/₂ × 12 × 9   = 54 cm²   ANSWER : 54 cm²
Answer: C
Six unbiased coin are tossed. What is the probability of getting atmost
one head? Select:
A) 61/2  B) 61/4  C) 63/64  D) 63/5  E) 61/6

Solution: Here n(S)= 2^6   Let E=event of getting atmost one head =   n(E)= 63   P(E)=n(E)/n(S)=63/64   Answer option 63/64)
Answer: C
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Answers.
A) 7	B) 6	C) 5	D) 4	E) 3

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec.   Answer:6
Answer: B
The center of a circle is (5, -3). (5, 7) is outside the circle, and (1, -3) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?  Select.
A) 3
B) 5
C) 11
D) 12
E) 13

Solution: r must be greater than 4 and smaller than 10, hence r=5,6,7,8 or 9.   Answer 5
Answer: B
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 salary?
Options
A) Rs. 38,00  B) Rs. 38,000  C) Rs. 40,000  D) Rs. 57,000  E) Rs. 20,000

Solution: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.   Then, 2x + 4000/3x + 4000 = 40/57   57(2x + 4000) = 40(3x + 4000)   6x = 68,000   3x = 34,000   Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.   Answer is Rs. 38,000.
Answer: B
Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
A. 425 B. 476 C. 450 D. 350	Choose the correct choice from the following answers:
A) 425
B) 476
C) 450
D) 350
E) 250

Solution: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x = 476   ANSWER:476
Answer: B
In a certain state, the ratio of registered Republicans to registered Democrats is 3 to 2, and every registered voter is either a Republican or a Democrat. If 90 percent of the Republicans and 15 percent of the Democrats are expected to vote for Candidate X, and everyone else is expected to vote for Candidate Y, by what percent is Candidate X expected to win the election?	Choose the correct choice:
A) 2%
B) 5%
C) 8%
D) 10%
E) 20%

Solution: Since we were expected to find a percentage figure - It thought that it might be easier to pick a 'smart number' to represent the total number of voters (republicans and democrats). Therefore, I picked 100 (as the total number of voters) and thus 30:20 represents the number ratio of Republicans:Democrats. If 90% of Republicans (which is (60*0.9)= 
(60*0.9) = 54
54) and 15% of Democrats (40*0.15= 6) voted for candidate X, means that out of total of 100 voters; 60 (54 + 6) voters voted for candidate X and 40 voted for candidate Y. Thus we can infer that candidate X is expected to win the election by 20 (60-40) votes. Therefore candidate X is expected to win the election by (20/100) votes which is equivalent to 20%.   I think the answer is 20%.
Answer: E
Find the smallest number that must be added to 1780 to make it a perfect
square.
Choose the correct choice from the following options:	A) 17	B) 42	C) 69	D) 47	E) 52

Solution: 4 1780 (42   16   82	180   164   16   Number to be added = (43)2 - 1780 = 1849 - 1780= 
1849 - 1780 = 69
69.   ANSWER 69 69
Answer: C
In a certain football league, the only way to score is to kick a eld goal
for 3 points or score a touchdown for 7 points. Thus the scores 1, 4
and 8 are not possible. How many positive scores are not possible?
Choose the correct choice from the following answers:
A) 5
B) 6
C) 9
D) 11
E) infinitely many

Solution: One checks directly that the following list of scores up to 14 is the complete list   of obtainable scores up to that point: 3, 6, 7, 9, 10, 12, 13, 14. Now, we have 3 consecutive   scores, namely 12, 13, and 14, which are obtainable, and this implies every score > 14 is   obtainable. To see this, observe that if n is an obtainable score, then so is n + 3 (simply   add another eld goal to whatever it took to get n points); hence, 15 = 12+3, 16 = 13+3,   and 17 = 14+3 are all obtainable and so are 18 = 15+3, 19 = 16+3, 20 = 17+3, and so   on. Therefore, the positive integral scores which are not obtainable are 1, 2, 4, 5, 8, and   11. Thus, the answer is 6   correct answer 6
Answer: B
There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station? Choose one
A) 200	B) 190	C) 95	D) 100	E) 380

Solution: The total number of stations = 20   From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.   ²⁰P₂ = 20 * 19= 
20 * 19 = 380
380.   ANSW380R:380
Answer: E
There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 12,000 after 3 years at the same rate?	Answers
A) 2345	B) 3546	C) 4556	D) 6343	E) 3972

Solution: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.   R = 100 x 60 = 10% p.a.   100 x 6   Now, P = Rs. 12000. T = 3 years and R = 10% p.a.   C.I.   = Rs. 12000 x 1 + 10 3 - 1   100   = Rs. 12000 x 331   1000   = 3972.   3972
Answer: E
How many three digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?	Options:
A) 360
B) 297
C) 288
D) 179
E) 120

Solution: The given digits are six.   The number of four digit numbers that can be formed using six digits is   6P3 = 6 * 5 * 4= 
6 * 5 * 4 = 120
120.   Answer: 120
Answer: E
Father's age is three years more than three times the son's age. After three years, father's age will be ten years more than twice the son's age. What is the father's present age?	Pick
A) 339  B) 33  C) 27  D) 28  E) 19

Solution: Let the son's present age be x years.then father's present age will be 3x + 3 years.   After 3 years,3x + 3 + 3 = 2 (x + 3) + 10   Solving we get, x = 10.   Substituting x =10 in 3x + 3,   Hence father's present age will be x = 33 years.   Answer:33
Answer: B
A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 6 hours. Harvesting machine K harvested how many acres of wheat per hour?
Choose the correct option
A) 4
B) 8
C) 12
D) 13
E) 15

Solution: Rate of H = 6 acres/hr   Remaining land to be harvested = 100 - 40= 
100 - 40 = 60
60   Rate of H and K= 60/6= 
60/6 = 10
10 acres/hr   Rate of K= 10 - 6= 
10 - 6 = 4
4   4nswer: 4
Answer: A
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? Choose the most appropriate option:
A) 5/8  B) 5/9  C) 5/5  D) 5/2  E) 5/1

Solution: Two balls can be picked from nine balls in ⁹C₂ ways.   We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.   The required probability = (5 * 4)/⁹C₂ = 20/36   = 5/9   Answer: 5/9
Answer: B
In a stream running at 3 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 57 minutes. Find the speed of motor boat in still water?	Choose the correct choice from the following.
A) 18 kmph	B) 22 kmph	C) 16 kmph	D) 20 kmph	E) None of these

Solution: Explanation:   Let the speed of motor boat instill water be X kmph   Then, speed in downstream = (X + 3) km   and. speed in upstream = (X - 3) kmph   Time taken to row 10km & back = (10/X+3,10/X-3)   10/X+3 + 10/X-3 = 57/60   11X2 - 240X - 44 = 0   (X - 22)(11x + 2) = 0   X = 22 or X = -2/11   Then X = 22 kmph   Answer: Option 22 kmph
Answer: B
Gio, the circus Elephant, is currently three times older than Lee, the circus Lion. In ten years from now, Lee the circus Lion will be exactly half as old as Gio, the circus Elephant. How old is Gio today?
Choices:
A) 20 B) 23 C) 30 D) 28 E) 29

Solution: Gio, the circus Elephant, is currently three times older than Lee, the circus Lion.   Gio = 3*Lee   Usually, ages are integers so there is a good possibility that the age of Gio is 30 (the only option that is a multiple of 3).   Then age of Lee would be 10. In 10 yrs, Gio would be 40 and Lee would be 20 - so Lee would be half as old as Gio.   Answer (30)
Answer: C
The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Choose one.
A) 279
B) 283
C) 308
D) 318
E) 328

Solution: Other number =	(11 x 7700)/275	= 308.   ANSWER :308
Answer: C
Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 16 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.	Choose the correct choice from the following options:	A) 80 days	B) 100/3 days	C) 120 days	D) 110 days	E) 90 days

Solution: Rate of both = 1/20   Together they do = 1/20*16 = 4/5   Left work = 1 - 4/5 = 1/5   Adam completes 1/5 work in 10 day   so he took 10*5= 
10*5 = 50
50 days to complete the left work alone.   Thus the rate of adam is 1/50   Rate of Micheal= 1/20 - 1/50 = 1/(100/3)   Thus micheal takes 100/3 days to complete the whole work.   ans. 100/3 days.
Answer: B
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 90 km/hr. What is the length of the platform?
Choose the correct option
A) 400 B) 488 C) 477 D) 426 E) 422

Solution: Speed = 90* 5/18= 
90* 5/18 = 25
25 m/sec.   Length of the train= 25 * 20= 
25 * 20 = 500
500 m.   Let the length of the platform be x m . Then,   (x + 500)/36= 25 => x =400 m.   400nswer: 400
Answer: A
In how many V ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password? Choose the correct choice from the following choices:
A) 720
B) 864
C) 900
D) 936
E) 1,296

Solution: Total number of four letter passwords = 6*6*6*6= 
6*6*6*6 = 1_296
1296 ------(1)   Total number of passwords in which no letter repeats= 6C4*4!= 15*24= 
15*24 = 360
360------(2)   therefore required value V= (1)-(2)= 1296-360=936.936
Answer: D
The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months .Find the age of the teacher. Pick
A) 22	B) 25	C) 8	D) 27	E) 19

Solution: Sum of the ages of the students = 39×15 = 585   New average = 15 years 3 months = 15 + 1414 year   Sum of the ages of students and teacher = 40×15141514 = 40×614614 = 610   Teacher age = 610 – 585 = 25 years.   Answer:25
Answer: B
24 oz of juice P and 25 oz of juice Q are mixed to make smothies X and Y . The ratio of p to Q in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X? Pick one:  A) 5  B) 10  C) 15  D) 20  E) 25

Solution: Easy way to solve this question is start from the answer and then conform the information provided in the question.   we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to Q ratio is 4:1   this gives us that quantity of juice P in X = 20 therefore quantity of Juice V will be 5 ... hence ratio = 4:1   This will lead to quantity of juice P in X = 4 and quantity of Juice V = 20 ... hence ratio 1:5   if we calculate total Juice P = 24 and total of juice Q = 25   it fits because totals are same as what mentioned in the question ...   thus ans is 20
Answer: D
The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?	Choose the correct choice:	A) 7%	B) 5%	C) 9%	D) 1%	E) 3%

Solution: (30 * 30)/100= 
(30 * 30)/100 = 9
9% decrease   Answer:9%
Answer: C
Dhoni bought 5 toys with the average cost of $10. If David also buys the sixth toy with the price of $ 16, what is the average (arithmetic mean) price of those 6 toys?  Choose the correct choice from the following answers
A) $10	B) $7	C) $8.5	D) $9	E) $11

Solution: 5 toys -> Total cost = 5 * Avg cost = 5*10= 
5*10 = 50
50   Sixth toy cost= 16   Total cost for 6 toys= 50+16= 
50+16 = 66
66   AM= 66/6= 
66/6 = 11
11   Hence $11
Answer: E
An amount of Rs. 75000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was? Choose the correct choice from the following choices.
A) s. 46875; Rs. 28125	B) s. 62500; Rs. 37500	C) s. 72500; Rs. 27500	D) s. 82500; Rs. 17500	E) s. 72500; Rs. 17500

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (75000 - x). Then,   (x * 9 * 1)/100 + [(75000 - x) * 11 * 1]/100 = (75000 * 39/4 * 1/100)   (9x + 825000 - 11x)/100 = 39000/4 = 14625/2   x = 46875   Sum invested at 9% = Rs. 46875   Sum invested at 11% = Rs. (75000 - 46875) = Rs. 28125.   s. 46875; Rs. 28125NSWER:s. 46875; Rs. 28125
Answer: A
A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in.  Select: A) 17 days B) 97 days C) 19 days D) 60 days E) 15 days

Solution: A = 140 days   B = 105 days   1/140 + 1/105 = 7/420 = 1/60   =>60 days   Answer: 60 days
Answer: D
A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?  Choose the most appropriate option.
A) 399 B) 788 C) 350 D) 888 E) 21

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 39 = 50/3   3(x + 300) = 1950 è x = 350m. Answer: 350
Answer: C
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 50. What is the value of x?
Select:
A) 50
B) 100
C) 200
D) 140
E) 2,000

Solution: y = 50% of 50% 0f x   = x/4   and   y/100 of x = 50   y /100 *4y =50   y = 35   and x= 140   Answer - 140
Answer: D
Which of the following values of A satisfies the inequality?
A(A – 2) = 5A – 10
Options:
A) A > 5 or A < 2
B) 2 < A < 5
C) 2 < A = 5
D) A = 5, A = -2
E) None of these

Solution: Explanation:   A ( A – 2) = 5 A – 10   A( A – 2) = 5 ( A – 2)   A = 5 if A – 2 > 0   A = 5, A > 2   i.e. 2 < A = 5   ANSWER: 2 < A = 5
Answer: C
In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 25 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars? Choose the correct option
A) 9x/80  B) 13x/20  C) 80/9x  D) 16x  E) 80x/9

Solution: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;   Sales of Japanese tools = 25% of the sales of imported tools = 0.25*{total}/4 = 1/4*{total}/4 = 1*{total}/16.   Since the sales of of Japanese tools was x, then 1*{total}/16 = x --> {total} = 16x.   Answer: 16x.
Answer: D
The average age of an adult class is 40years. 18 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class? Choose one.
A) 8  B) 12  C) 15  D) 17  E) 18

Solution: Let original strength = y   Then , 40y + 18 x 32 = ( y + 18) x 36   â‡’ 40y +576 = 36y + 648   â‡’ 4y = 72   âˆ´ y = 18   18
Answer: E
Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/3 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?	Choose the correct answer
A) 20	B) 60	C) 108	D) 144	E) 180

Solution: The number of ornaments = a   Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6   1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12   1/3 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/3   => 5 + a/12 = a/3 => a = 200   20ns: 20
Answer: A