MU-NLPC/Calc-aqua_rat huggingface dataset:
If x, y, and s are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=s and if x is less than y, which of the following could be the value of s?
Answers
A) 10 B) 12 C) 15 D) 18 E) 30

Solution: Answer choice C: s= 15   (10x + 20y)/(x+y) = 15   10x + 20y = 15x + 15y   5y = 5x   y = x   Doesn't work because the problem states that x<y.   We need y to be larger, so let's try answer choice D: s=18   10x + 20y = 18x + 18y   2y = 8x   y/x = 8/2   Success! x<y.   The correct answer is 18.
Answer: D
The sum of the first five terms of a G.P is 363. If the common ratio is 1/3 find the first term.  Select the correct option:
A) 323
B) 243
C) 232
D) 332
E) 432

Solution: Sum of the first n terms of a G.P = a (1 -rn )/1 - r ,   a [ 1 - (1/3) 5 ]/ (1 - 1/3) = 363   a = 363 [ 1-1/3 ] /1- (1/3) 5 = ( 363* 2/3) / ( 1- 1/242 ) = 242/ ( 242/243 )= 
242/ ( 242/243 ) = 243
243   ANSWER:243
Answer: B
It takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate. If 5 workers start to build the machine at 11:00 AM, and one extra worker per hour is added beginning at 1:00 PM, at what time will the machine be complete?  Choose the correct choice from the following options:  A) 4:30  B) 4:45  C) 5:00  D) 5:15  E) 5:30

Solution: 3 workers build 1/15 of a machine in one hour.   1 worker builds 1/45 of a machine in one hour.   In the first 2 hours, 5 workers build 5*(1/45)*2=10/45 of a machine.   From 1:00 to 2:00, 6 workers build another 6/45. The total is 16/45.   From 2:00 to 3:00, 7 workers build another 7/45. The total is 23/45.   From 3:00 to 4:00, 8 workers build another 8/45. The total is 31/45.   From 4:00 to 5:00, 9 workers build another 9/45. The total is 40/45.   To build another 5/45, 10 workers need (5/10)*60 minutes which is 30 minutes.   The machine is complete at 5:30.   The answer is 5:30.
Answer: E
If an object travels 200 feet in 4 seconds, what is the object's approximate speed in miles per hour? (Note: 1 mile = 5280 feet)	Options.
A) 36	B) 34	C) 356	D) 12	E) 45

Solution: 1 mile = 5280 feet   => 1 feet = 1/5280 miles   If the object travels 200 feet in 4 sec   then it travels 200/4 * 60 * 60 feet in 1 hour (1 hr = 60 min * 60 sec)   = 3600 * 50 feet in 1 hour   = 180000 feet in 1 hr   = 180000/5280 miles in 1 hour   = 18000/528 miles/hr ~ 34 miles/hr   Answer - 34
Answer: B
In a certain country 1/7 of 8 = 5. Assuming the same proportion, what would be the value of 1/5 of 40 ?	Answers: A) 54 B) 25 C) 45 D) 35 E) 52

Solution: 35   35
Answer: D
A scuba diver descends at a rate of 80 feet per minute. a diver dive from a ship to search for a lost ship at the depth of 4000feet below the sea level..how long will he take to reach the ship?  Options.
A) 70 minutes	B) 72 minutes	C) 50 minutes	D) 66 minutes	E) 67 minutes

Solution: Time taken to reach = 4000/80= 
4000/80 = 50
50 minutes   ANSWER:50 minutes
Answer: C
A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
Choose the correct choice from the following answers
A) 10.8 km/hr  B) 12.8 km/hr  C) 11.8 km/hr  D) 16.8 km/hr  E) 17.8 km/hr

Solution: A   10.8 km/hr   Total distance traveled = 10 + 12= 
10 + 12 = 22
22 km /hr.   Total time taken= 10/12 + 12/10 = 61/30 hrs.   10.8 km/hrverage speed = 22 * 30/61 = 10.8 km/hr.
Answer: A
If one root of the equation 2x^2 + 3x – k = 0 is 5, what is the value of k? Choose one:
A) 65
B) 79
C) 68
D) 87
E) 90

Solution: We just enter this root into the equation in order to recieve an equation to find the answer!   2*5^2+3*5-k=0   k=50+15= 
50+15 = 65
65   The answer is 65
Answer: A
For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?  Select the correct option:	A) 1 : 3	B) 3 : 4	C) 1 : 6	D) 2 : 7	E) 3 : 8

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120 + 480 = 8 1 + 4 = 1 ....(i)   x y x y 15   And, 200 + 400 = 25 1 + 2 = 1 ....(ii)   x y 3 x y 24   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4   3 : 4
Answer: B
Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 34 square meters. What is the area that is covered with three layers of wallpaper?
Choices.
A) 43 Square Meters	B) 36 Square Meters	C) 42 Square Meters	D) 83.3 Square Meters	E) 120 Square Meters

Solution: 300 - 180= 
300 - 180 = 120
120 sq m of the wallpaper overlaps (in either two layers or three layers)   If 36 sq m has two layers, 120 - 34= 86 sq m of the wallpaper overlaps in three layers. 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m.   43 Square Metersnswer (43 Square Meters).
Answer: A
One hour after Sid started walking the 60 miles from X to Y, James started walking from X to Y as well. Sid walks 3 miles per hour and James walks 1 mile per hour faster than Sid . How far from X will James be when he catches up to Sid ?	Choose the correct answer
A) 8 miles  B) 9 miles  C) 12 miles  D) 11 miles  E) 13 miles

Solution: First, determine how far Sid has walked in the one hour. he has walked three miles which means he is three miles ahead of James when he sets off. James walks at four miles/hour which means that every hour, james will get one mile closer to Sid . If he gets one mile closer every hour, it will take him three hours to catch up to him which means he travels 3hours * 4 miles/hour = 12 miles and he travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.   A slightly different way to solve...   We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,   r*t (james) = r*t (Sid )   r*(t) = r*(t+1)   4t = 3t+3   t=3   d=r*t   d=4*3= 
4*3 = 12
12   12 miles) 12 miles
Answer: C
The price of 2 sarees and 4 shirts is $1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? Choose the correct choice from the following options.
A) 3800  B) 3300  C) 2400  D) 4200  E) 1400

Solution: C   $2400   Let the price of a saree and a shirt be $x and $y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   2400ost of 12 shirts = $(12 x 200) = $2400.
Answer: C
If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is	Select:
A) 2 B) 3 C) 4 D) 6 E) 7

Solution: Solution   Let the number be x.	= Then, 2x+20 = 8x–4   = 6x = 24   ‹=›x = 4.   Answer 4
Answer: C
The diameter of the wheel of a car is 120m. How many revolution/min must the wheel makein order to keep a speed of 60 km/hour approximately?	Select the correct option.
A) 210  B) 245  C) 230  D) 254  E) 265

Solution: Distance to be covered in 1 min. = (60 X 1000)/(60) m = 1000 m.   Circumference of the wheel = (2 x (22/7) x 0.60) m = 3.77 m.   Number of revolutions per min. =(1000/3.77) = 265   265
Answer: E
Indu gave Bindu Rs.6500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? Choose the correct option:
A) 12.8
B) 20
C) 10.4
D) 11.6
E) 15

Solution: 6500 = D(100/4)2   D = 10.4   Answer: 10.4
Answer: C
Anand and Deepak started a business investing Rs. 27,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?	Select the correct option:  A) 7728  B) 2888  C) 8400  D) 2882  E) 2781

Solution: Ratio of their shares = 27500 : 35000 = 11:14   Deepak's share = 13800 * 14/25 = Rs. 7728.   7728nswer: 7728
Answer: A
A math teacher has 27 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.  Choose the correct answer:
A) 9	B) 10	C) 11	D) 12	E) 13

Solution: a square is a special kind of rhombus (sides are perpendicular)   a square is a special kind of rectangles (sides with same length)   Among the 27 cards with have:   15 rectangles   10 rhombus   8 squares   Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.   Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.   We have 8 squares.   So the minimum different cards that represent a square, a rhombus or a rectangle is   2 + 7 + 8= 
  2 + 7 + 8 = 17
17   Which means that the maximum number of circles that you could have is  27 - 17= 
 27 - 17 = 10
10   Answer (10)
Answer: B
Dexter was born between October 6th and 10th (6th and 10th excluding). His year of birth is also known. What is the probability of Dexter being born on a Saturday?
Pick one:
A) 0 or 1/3
B) 1/7 or 3/7
C) 1/3 or 1/7
D) 1/3 or 1/4
E) cannot be determined.

Solution: Explanation :   Since the year of birth is known, the birthday being on Saturday can have a zero probability.   Also since between 6th and 10th, there are three days i.e. 7th,8th and 9th.   Therefore, probability of birthday falling on Saturday can be 1/3.   0 or 1/3nswer : 0 or 1/3
Answer: A
3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is:	Choose the correct choice from the following choices.
A) 2/9	B) 1/9	C) 8/9	D) 7/9	E) 1/4

Solution: let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house   there will be 1 case when x,y,z will buy house a   another when they buy house b   and another when they buy house c   so the prob that they buy same house is 3*1/27=1/9   ANSWER:1/9
Answer: B
A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? Pick one:  A) 177  B) 199  C) 800  D) 171  E) 128

Solution: 25 = E/(1000 - E) * 100   1000 - E = 4E   1000 = 5E => E = 200   1000 - 200= 
1000 - 200 = 800
800   Answer: 800
Answer: C
From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 72 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
Choose the most appropriate option:
A) 20	B) 10	C) 30	D) 55	E) 40

Solution: Assume the number of boys at present = x   Then, the number of girls at present = 5x   Before the boys left, the number of boys were (x+72) and number of girls were 5x   Hence, 2(5x) = x + 72   => 10x = x + 72   => x = 8   Number of girls in the beginning = (5x + 15) = (5×8 + 15) = 55   Answer is 55.
Answer: D
When positive integer N is divided by positive integer J, the remainder is 27. If N/J = 204.09, what is value of J? Answers.
A) 300
B) 320
C) 360
D) 410
E) 420

Solution: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder   So, Dividend/Divisor = Quotient + Remainder/Divisor   Given that N/J = 204.09   Here 204 is the quotient.   Given that Remainder = 27   So, 204.09= 204 + 27/J   So, J = 300   300nswer: 300
Answer: A
The length of a train and that of a platform are equal. If with a speed of 180 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Pick.
A) 1500
B) 266
C) 299
D) 750
E) 261

Solution: Speed = [180 * 5/18] m/sec = 50 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 50 => x = 50 * 60 / 2= 
50 * 60 / 2 = 1_500
1500   1500nswer: 1500
Answer: A
If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.	Answers:
A) 8r  B) 4r  C) 9r  D) 7r  E) 10r

Solution: Hint: (1-cos(t))0.5 = 20.5×sin(t/2)   The answer is 8r.   Imagine the circle resting on coordinate (0,0) and moving east.   Also magine the point on the circle to start at (0,0).   Let t be the angle between the point on the circle and the center of the circle.   The position of the point on the circle, relative to t, is:   x = rt - r×sin(t)   y = r - r×cos(t)   Taking the derivatives:   dx/dt = r - r×cos(t)   dy/dt = r×sin(t)   The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.   So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.   After a few steps this integral becomes:   r×21/2 × (1-cos(t))1/2.   Using the hint:   r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi   = 2×r × (-2×cos(t/w) from 2×pi to 0)   = 8r   correct answer 8r
Answer: A
Seven 6 faced dice are thrown together. The probability that all the three show the same number on them is? Choose the most appropriate option:
A) 1/32
B) 1/46656
C) 1/33
D) 1/38
E) 1/34

Solution: The three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6= 
6 * 6 * 6 * 6 * 6 * 6 * 6 = 279_936
279936 ways.   Hence the probability is 6/279936= 1/46656   Answer: 1/46656
Answer: B
In a hostel there were 100 students. 20 students left the hostel,the average budget is increased by rupees 10. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?  Pick one:
A) 2200  B) 1660  C) 5400  D) 2400  E) 1800

Solution: Let average is x   100x + 400 = 80(x+10)   x = 20   100 * 20 + 400= 
100 * 20 + 400 = 2_400
2400   Answer:2400
Answer: D
man can row upstream at 30 kmph and downstream at 40 kmph, and then find the speed of the man in still water?
Choose the correct choice from the following options.
A) 30  B) 35  C) 40  D) 70  E) 45

Solution: US = 30   DS = 40   M = (30 + 40)/2= 
(30 + 40)/2 = 35
35   Answer:35
Answer: B
Find the odd man out
6, 13, 29, 61, 125, 253, 509  Choose the correct option:	A) 6	B) 13	C) 29	D) 125	E) 509

Solution: 1*2+3= 
1*2+3 = 5
5   5*2+3= 
5*2+3 = 13
13   13*2+3= 
13*2+3 = 29
29   29*2+3= 
29*2+3 = 61
61   61*2+3= 
61*2+3 = 125
125   125*2+3= 
125*2+3 = 253
253   253*2+3= 
253*2+3 = 509
509   6NSWER:6
Answer: A
The equation of line a is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line a?  Choose the correct choice from the following options:
A) 48
B) 50
C) 60
D) 75
E) 100

Solution: This can be solve in two steps and without any complex calculation.   Given : equation of line a as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).   This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)   So a perpendicular from the (0,0) to hypotenuse will be the answer.   Area of triangle= 0.5*100*75=0.5*125* x   => x=60;   SO answer is 60=60
Answer: C
A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 6, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?  Select the correct option:  A) 27  B) 22  C) 24  D) 26  E) 30

Solution: Total # of codes possible is 3*3*3= 
3*3*3 = 27
27. Oit of those 27 codes   27nswer: 27
Answer: A
Insert the missing number.
8, 7, 11, 12, 14, 17, (....)  Pick one:
A) 27  B) 20  C) 22  D) 17  E) 26

Solution: There are two series (8, 11, 14, 17) and (7, 12, 17) increasing by 3 and 5 respectively.   answer : 17
Answer: D
From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 63 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning Choose the correct choice from the following options
A) 20  B) 10  C) 30  D) 50  E) 40

Solution: Assume the number of boys at present = x   Then, the number of girls at present = 5x   Before the boys left, the number of boys were (x+63) and number of girls were 5x   Hence, 2(5x) = x + 63   => 10x = x + 63   => x = 7   Number of girls in the beginning = (5x + 15) = (5×7 + 15) = 50   Answer is 50.
Answer: D
Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements R are possible? Choose the correct option.
A) 30  B) 60  C) 90  D) 180  E) 540

Solution: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.   But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.   I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements R INCLUDING the order of tasks.   could you explain the highlighted step... i'm getting 90 = 15 * 3!   suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z   one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways   X--	Y--	Z   12--	34--	56   12--	56--	34   34--	12--	56   34--	56--	12   56--	12--	34   56--	34--	12   so the answer should be 15*6= 
15*6 = 90
90   But now you can fruther decide which task you want to perform first X Y or Z..90
Answer: C
How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5? Pick one
A) 10  B) 20  C) 40  D) 35  E) 45

Solution: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.   The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.   The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.   Required number of numbers = (1 x 5 x 4) = 20   20
Answer: B
Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?  Choose the correct choice from the following answers:
A) 375  B) 400  C) 450  D) 350  E) 250

Solution: 375+B+C = 1500   375 = 1/3(B+C); B = 2/3(375+C)   375/(B+C) = 1/3   375 = 1/4 * 1500= 
1/4 * 1500 = 375
> 375   375NSWER 375
Answer: A
If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Pick
A) 288	B) 162	C) 878	D) 168	E) 122

Solution: 12 m/s = 12 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 12 * 18/5 * 15/4= 
12 * 18/5 * 15/4 = 162
162 km.   Answer: 162
Answer: B
If 10 crates have 96 apples each and how many apples more is required in order to make 100 apples in each crate?
Pick one:
A) 5 B) 10 C) 40 D) 20 E) 0

Solution: Each crate requires 4 apples and totally there are 10 crates so required apples = 10 * 4= 
10 * 4 = 40
40   Answer: 40
Answer: C
85% of a number is added to 24, the result is the same number. Find the number?
Choose the correct answer:
A) 277 B) 267 C) 222 D) 160 E) 123

Solution: (85/100) * X + 24 = X   3X = 480   X = 160   Answer:160
Answer: D
If the sides of a rectangle are increased by 35%, what is the percentage increase in the area?	Choose the correct choice from the following answers
A) 38.25%	B) 40.25%	C) 82.25%	D) 50%	E) 65%

Solution: If sides are a and b, after increase sides would be 1.35a and 1.35 b.   Percentage increase in area = (1.35a*1.35b - ab) *100/ab = 82.25   Answer : 82.25%
Answer: C
The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?	Choose the correct choice:
A) 100 kg B) 102.5 kg C) 85 kg D) Data inadequate E) None of these

Solution: Explanation:   Total weight increased = (10 x 3.5) kg = 35 kg.   Weight of new person = (65 + 35)= 
(65 + 35) = 100
100 kg.   100 kgnswer: 100 kg
Answer: A
Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?  Choose the correct option:
A) 1/7
B) 2/7
C) 1/3
D) 7/12
E) 2/3

Solution: Same amount of water made bigger jar 1/6 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/6+1/6=2/6= 1/3 full.   Answer: 1/3.
Answer: C
The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?
Select.
A) 60  B) 80  C) 40  D) 120  E) 160

Solution: Explanatory Answer   Let the original number be x.   Let A be the value obtained when x is increased by 12.5%.   Therefore, A = x + 12.5% of x   Let B be the value obtained when x is decreased by 25%.   Therefore, 80 = x - 25% of x   The question states that A - 80 = 30   i.e., x + 12.5% of x - (x - 25% of x) = 30   x + 12.5% of x - x + 25% of x = 30   37.5% of x = 30   x = 30/37.5*100= 
30/37.5*100 = 80
80   The correct choice is (80)
Answer: B
A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction?
Pick one
A) 8%  B) 10%  C) 2%  D) 5%  E) 6%

Solution: Actual price = 100+10= 
100+10 = 110
$110   Saving= 10/110 * 100 = 100/11 =10% approximately   Answer is 10%
Answer: B
If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire? Options
A) 2 meters
B) 6 meters
C) 5 meters
D) 3 meters
E) 7 meters

Solution: 400 rev / minute = 400 * 60 rev / 60 minutes   = 24,000 rev / hour   24,000 * C = 72,000 m : C is the circumference   C = 3 meters   correct answer 3 meters
Answer: D
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?  Choose the correct choice from the following:
A) 159  B) 194  C) 205  D) 209  E) None of these

Solution: We may have 1 boy and 3 girls or 2 boys and 2 girls or 3 boys and 1 girl or 4 boys   Required number of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + 6C4   = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + 6C2   = (6 x 4) +[(6x5)/(2x1) x (4x3)/(2x1)] + [(6x5x4)/(3x2x1)) x 4] +[(6x5)/(2x1)]   = 24 + 90 + 80 + 15= 
24 + 90 + 80 + 15 = 209
209   Answer 209.
Answer: D
A man sold two chairs at Rs. 1,200 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is:
Choose the correct choice from the following answers: A) 1% loss B) 2% loss C) 4% loss D) 15 gain E) NOne

Solution: Solution: In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut:   Loss on total deal,   = (Common loss or gain percentage /10)2 = (20/10)2   = 4%   Alternatively, It can be also calculated through Graphic Change Method: This can be given by,   100==20% gain ==>120==20% loss==>96.   Loss = 4% (As 100 became 96).   Answer: Option 4% loss
Answer: C
If - 5 < x < 7 and y < - 9, then the lowest possible value for (-xy) is  Choose the correct choice from the following: A) between 60 and 70 B) between 0 and 60 C) 0 D) between 0 and -70 E) none of these

Solution: If - 5 < x < 7 and y < - 9,   Say y = -100 (y<-9)   x = 6   So -xy =600 which is more than 70.   Answer is none of these.
Answer: E