MU-NLPC/Calc-aqua_rat huggingface dataset:
The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 5 months. At this time, the construction was behind schedule by how many projects?
Choose the correct choice from the following answers:
A) 34
B) 62
C) 198
D) 204
E) 504

Solution: Project/month :   612/18= 
  612/18 = 34
34   Project in 6 month to be completed= 34*5= 
34*5 = 170
170   Lag :  170-108= 
  170-108 = 62
62   62 is the answer
Answer: B
The average (arithmetic man) of three integers a, b, and c is exactly once the median. If a < b < c and a = 0, what is the value of c/b?  Select
A) 2	B) 3	C) 4	D) 5	E) Cannot be determined from the information given.

Solution: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=b --> since a=0, then (0+b+c)/3=b --> c=2b --> c/b=2.   2nswer: 2.
Answer: A
Rahul went to a shop and bought things worth Rs. 25, out of which 30 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) 21.1  D) 21.7  E) 23

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   Option '19.7'
Answer: B
A circle in the coordinate plane passes through points (-3, -2) and (2, 4). What is the smallest possible area of that circle?  Pick:
A) 13π
B) 15.25π
C) 262√π
D) 52π
E) 64π

Solution: The distance between the two points is sqrt(61).   radius = sqrt(61)/2   Area= pi*(sqrt(61)/2)^2   B. 15.25π
Answer: B
Suganya and Suriya are partners in a business. Suganya invests Rs. 15,000 for 8 months and Suriya invests Rs.42,000 for 10 months. Out of a profit of Rs.31,570. Suganya's share is  Pick
A) Rs.9471  B) Rs.12,628  C) Rs.18,040  D) Rs.7015.56  E) None

Solution: Solution   Ratio of their shares	=(15000Ã—8):(42000Ã—10)   = 2 : 7.   Suganya's share	= Rs.(31570 Ã—2/9)   = Rs.7015.56   Answer Rs.7015.56
Answer: D
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 73°, what fraction of the wheel’s area is represented by the smallest sector?	Select the correct option:	A) 7/60	B) 9/80	C) 11/120	D) 13/240	E) 17/360

Solution: The largest angle is 73.   Let d be the difference between any two angles in the progression.   The sum of all the angles will be:   73 + (73-d) + (73-2d) + ... + (73-7d) = 584 - 28d   The sum of all the central angles in a circle = 360   584 - 28d = 360   d = 224/28= 
224/28 = 8
8   The smallest sector is (73-7d)= 73-7*8= 
73-7*8 = 17
17   The fraction of the area covered is 17/360.   The answer is 17/360.
Answer: E
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3? Select:
A) 39 B) 42 C) 45 D) 47 E) 48

Solution: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).   In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.   i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0   or −27+36+21+12=k−27+36+21+12=k   or k=k= 42   42
Answer: B
A person starts walking at a speed of 5km/hr through half the distance, rest of the distance he
covers with aspeed 4km/hr. Total time of travel is 9 hours. What is the maximum distance he
can cover? Choices:	A) 20km	B) 40km	C) 60km	D) 80km	E) 90km

Solution: t=d/s, so   9=x/2*1/5+x/2*1/4(because half distance with 5 km/ph, and remaining half with 4km/hr)   9=x(18/80)   x=40km   ANSWER:40km
Answer: B
If y is not equal to zero, and y+1/y = 2, then what is the value of y^4 + (1/y)^4?	Options
A) 2  B) 4  C) 5  D) 8  E) 0

Solution: y + 1/y=2   we square both sides so we have y^2 + 1/y^2 +2 = 4   or y^2 + 1/y^2= 2   squaring again we have y^4 + 1/y^4 + 2 = 4   or y^4 + 1/y^4 = 2   answer =2 (2)
Answer: A
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 10 years?
Choose one:
A) 3 : 2
B) 1 : 3
C) 2 : 3
D) 1 : 5
E) 2 : 1

Solution: Explanation :   Simple Interest = PRT/100   Here Principal(P) and Rate of Interest (R) are constants   Hence, Simple Interest ∝ T   Required Ratio = Simple Interest for 2 years/Simple Interest for 10 years   =T1/T2   =2/10   =1/5   =1:5   Answer : Option 1 : 5
Answer: D
A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B	Choose the correct choice from the following choices
A) s. 3400
B) s. 2700
C) s. 1720
D) Rs. 7200
E) s. 8200

Solution: Explanation:   Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y   Then, savings of A = 5x-3y = 1800—?(1)   Savings of B = 6x-4y = 1600 —?(2)   By solving equations (1) and (2)   y = 1400   Monthly income of B = Expenses of B + savings of B   = 4y+1600 = 4(1400) + 1600 = Rs. 7200   Answer: Rs. 7200
Answer: D
A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many S apples did each person get before 45 people joined the feast?	Pick.
A) 20.
B) 21.
C) 22.
D) 23.
E) 24.

Solution: Before solving it algebraically, let us prime factorize 1430 = 2*5*11*13.   Since number of apples per person * total persons S= 1430, the answer should be a factor of 1430. Only C is. And that's your answer.22.
Answer: C
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is	Choose the correct choice: A) 0° B) 5° C) 10° D) 20° E) None

Solution: Solution   Angle traced by hour hand in13/3 hrs	= (360/12 x 13/3)°   =130°   Angle traced by min. hand in 20 min	= (360/60x20)°   = 120°   Required angle	= (130 - 120)= 
(130 - 120) = 10
10°.   Answer 10°
Answer: C
36 men can complete a piece of work in 18 days. In how many days will 9 men complete the same work ?
Options: A) 24 B) 77 C) 88 D) 72 E) 21

Solution: Explanation:   Less Men, means more 72ays {Indirect Proportion}   Let the number of days be x   then,   9 : 36 :: 18 : x   x = 72   Answer: 72) 72 days
Answer: D
Two airplanes fly the same exact route from Atlanta to Chicago. Plane A flies 200 mph while plane B flies 300 mph (assume that simple model versus actual acceleration/deceleration near the airports). If plane A took off exactly 40 minutes before plane B, after how many minutes will plane B overtake plane A? Pick
A) 65  B) 80  C) 90  D) 115  E) 120

Solution: We can use some form of the equation D=RT [distance = rate * time]   rate of plane A: 200 mph   rate of plane 80: 300 mph   Plane A will be in the sky 40 minutes longer than plane 80 (2/3 of an hour)   time of plane A when 80 overtakes it: T+(2/3) use 2/3 of an hour since the rate is in hours   time of plane 80 when 80 overtakes A: T   At the time that 80 overtakes A, they will have travelled the same distance so RT is equal for each plane:   200*(T+2/3) = 300*T   200T + 400/3 = 300T   400/3 = 100T   4/3 = T   this is 1 and a third hour, so 60 minutes + 20 minutes = 80 minutes   80
Answer: B
If the average (arithmetic mean) of 5 positive temperatures is m degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
Options.
A) 6m	B) 4m	C) 5m/3	D) 3m/2	E) 3m/5

Solution: The sum of three greatest should be more than sum of two lowest.   The total sum is; 5m   A. 6m; 6m is more than 5m. Not possible.   B. 4m; 5m-4m=m(Possible)   C. 5m/3; 10m/3; 10m/3 > 5m/3. Not possible   D. 3m/2; 7m/2; 7m/2 > 3m/2. Not possible   E. 3m/5; 22m/5; 22m/5 > 3m/5. Not possible.   Ans:4m
Answer: B
A number consists of 3 digits 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) 253	B) 366	C) 298	D) 266	E) 992

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.   253nswer: 253) 253
Answer: A
Solve below question 2x + 1 = -21 Answers:	A) -11	B) -9	C) 9	D) 8	E) -7

Solution: 2x + 1 = -21   x = -11   -11
Answer: A
A certain sum amount to $1400 in 2 yrs and $2000 in five years on certain fixed simple interest. In how many yrs would the amount be $1750 had it been put at the rate of interest compounded annually?
Pick.
A) 4.5
B) 3.5
C) 3
D) 2
E) 1.5

Solution: We can form equations as following:   Initial amount = P, Total amount after interest = T, Interest per year = I   T = P+I   Given T1 = P+2I = 1400T2 = P+ 5I = 2000   From this we get, P = 1000I = 200 $   Now we know that simple interest is<Compound interest ( CI = SI only after 1st year if CI is compounded annually)   consider simple interest - after 1st yer it is 200$ , after 2nd years it is 400$ and after 3rd year it is 600$.   To get a 350 $ compound interest the duration have to be > 1 year and < 2 years.   Only option fitting : Option 1.5.
Answer: E
If z is a positive integer, which of the following could NOT be the square of z?
Choose the correct choice from the following choices.
A) 4932  B) 9126  C) 4566  D) 6815  E) 3355

Solution: A number ending in 2 cannot be a perfect square.   4932 ends in a number 2, making that the correct answer   (4932) 4932
Answer: A
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Choose the correct choice from the following answers.
A) 14, 2  B) 14, 9  C) 14, 5  D) 14, 4  E) 14, 1

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x = 14, y = 4.   Answer: 14, 4
Answer: D
Six consecutive traffic signals each show either red or green. How many different arrangements of the six signals are possible? Choose the correct choice from the following options.
A) 90 B) 79 C) 64 D) 57 E) 36

Solution: Since the answer choices to the question are so small (relatively speaking), you can get to the correct answer without having to do any fancy calculations. With a drawing and a bit of 'brute force', you can answer this question relatively quickly.   We're told that 6 consecutive traffic signals each show either red or green. We're asked how many different arrangements of the 6 signals are possible.   Total Options: 64   Final Answer:   64
Answer: C
John makes $60 a week from his job. He earns a raise and now makes $110 a week. What is the % increase?  Choose the correct choice from the following answers: A) 16% B) 83.33% C) 17% D) 17.61% E) 17.56%

Solution: Increase = (50/60)*100 = (5/6)*100 = 83.33%.   83.33%
Answer: B
Find the greatest number which on dividing 1255 and 1490, leaves a reminder of 8 and 11 respectively Choose the correct choice from the following answers: A) 27 B) 29 C) 33 D) 39 E) 41

Solution: Explanation:   In this type of question, its obvious we need to calculate the HCF, trick is   HCF of (1255 - 8) and (1490 -11)   = HCF (1247, 1479) = 29   Option 29
Answer: B
In how many ways can 8 people from a group of 9 people be seated around a circular table
Choose the correct choice from the following choices:
A) 56  B) 80  C) 45002  D) 34000  E) 45360

Solution: 9C8 * (8-1)! (Select 8 out of 9 and arrange them in circular manner)   = 9 * 7!   = 9 * 5040= 
9 * 5040 = 45_360
45360   Answer - 45360
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 3 seconds. What is the length of the train?
Answers
A) 20 metres B) 50 metres C) 32 metres D) 70 metres E) 80 metres

Solution: Speed= 60 x	5/18	m/sec	= 50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train = 50/3	x 3 m = 50 m.   Option 50 metres
Answer: B
In how many no. between 10 and 50 exactly Two of the digits is 5?  Select the correct option: A) 47 B) 65 C) 1 D) 35 E) 65

Solution: It's simple can be solved by elimination of answer choices.   Option B and D are too large, not possible. Even AE are large to have correct choice.   Ans : 1
Answer: C
The cash difference between the selling prices of an book at a profit of 5% and 10% is $3. The ratio of the two selling prices is:	Choose the correct answer:
A) 21:22 B) 52:33 C) 52:53 D) 45:53 E) 51:34

Solution: Let C.P. of the book be $x.   Then, required ratio = 105% of x / 110% of x   = 105/110 = 21/22 = 21:22   21:22
Answer: A
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Choose the correct choice from the following answers
A) 1078 B) 1276 C) 1000 D) 1021 E) 1029

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   Answer:1000
Answer: C
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, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 44 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?  Pick: A) 35 B) 36 C) 37 D) 38 E) 42

Solution: Amount earned by James = 40*x + 4*2x = 48x   Therefore, Amount earned by James = 48x   But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x   [[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 48x]]   So x*(1.5y -45 +30) = 48x   Or x*(1.5y - 15) = 48x   So 1.5y - 15 = 48   So 1.5y = 63   So y = 42   Answer is 42
Answer: E
A right circular cylinder has a height of 21 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid? Choose the correct choice from the following choices
A) 500(π – 3) B) 500(π – 2.5) C) 510(π – 1.5) D) 500(π – 2) E) 500(π – 1)

Solution: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?   The square base has sides of sqrt(50) due to the 45-45-90 triangle   21*25*pi - 15*sqrt(50)^2   =510(π – 1.5)   C. 510(π – 1.5)
Answer: C
A single discount equivalent to the discount series of 20%, 10% and 5% is? Choose the correct option
A) 31.7
B) 31.3
C) 31.6
D) 31.9
E) 31.2

Solution: 100*(80/100)*(90/100)*(95/100)= 
100*(80/100)*(90/100)*(95/100) = 342/5 = around 68.4
68.4   100 - 68.4= 
100 - 68.4 = 31.6
31.6   Answer: 31.6
Answer: C
The mean of 50 observations was 36. It was found later that an observation 29 was wrongly taken as 23. The corrected new mean is :  Options:
A) 36.1 B) 36.5 C) 36.22 D) 36.12 E) 36.18

Solution: Explanation:   Correct Sum = (36 * 50 + 29 - 23)= 
(36 * 50 + 29 - 23) = 1_806
1806.   Correct mean= = 1806/50= 
1806/50 = 903/25 = around 36.12
36.12   Answer: 36.12) 36.12
Answer: D
2 dice are tossed. What is the probability that the total score is a prime no. is? Answers.
A) 2/11	B) 5/12	C) 6/13	D) 7/15	E) 8/17

Solution: 5/12   5/12
Answer: B
The difference between a number and its two-fifth is 510. What is 5% of that number?	Choose the correct choice from the following choices
A) 425
B) 300
C) 255
D) 300
E) 400

Solution: Let the number be x. Then,   x - 2/5 x = 510   x = (510 * 5)/3= 
(510 * 5)/3 = 850
850   5% of 850= 425.   425nswer:425
Answer: A
Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of b crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of b?	Choose the correct choice from the following choices:
A) b/2
B) b
C) 3b/2
D) 2b
E) 3b

Solution: Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Amy carries 3 crumbs per trip. Also let Arthur make 2 trips and so Amy makes 4 trips.   Thus total crumbs carried by Arthur (b) = 2 x 2 = 4, total crumbs carried by Amy = 3 x 4 = 12. 12 is 3 times 4, so 3b
Answer: E
Raffle tickets numbered consecutively from 101 through 250 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ? Choose the correct answer:
A) 51/250 B) 2/7 C) 33/83 D) 99/250 E) 100/249

Solution: SOLUTION   The number of integers from 101 to 250, inclusive is 250, out of which 100 (from 200 to 250) will have a hundreds digit of 2. Thus the probability is 51/250.   51/250nswer: 51/250.
Answer: A
A train covers a distance of 12 km in 10 min. If it takes 15 sec to pass a telegraph post, then the length of the train is?
Choose the correct option.
A) 300 m
B) 168 m
C) 120 m
D) 168 m
E) 178 m

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec   = 20 m/sec.   Length of the train = 20 * 15   = 120 m.   300 mnswer: 300 m
Answer: A
It takes 10 days for digging a trench of 100 m long, 50 m broad and 10 m deep. What length of trench,
25 m broad and 15 m deep can be dug in 30 days ?  Choose the correct choice from the following answers:	A) 400 m	B) 200 m	C) 100 m	D) 89m	E) 56m

Solution: Expl : More days, more length (Direct)   Less breadth, more length (Indirect)   More depth, less length (Indirect   Days 10 : 30;   Breadth 25 : 50; : : 100 : x   Depth 15 : 10;   :. 10 * 25* 15 * x = 30 *50 * 10 *100   x= (30*50*10*100)/10*25*15 = 400   So the required length = 400m   400 mnswer: 400 m
Answer: A
Machine P and Machine Q are each used to manufacture 330 sprockets. It takes Machine P 10 hours longer to produce 330 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
Choose the correct choice from the following options
A) 5  B) 15  C) 3  D) 95  E) 125

Solution: P makes x sprockets per hour.   Then Q makes 1.1x sprockets per hour.   330/x = 330/1.1x + 10   1.1(330) = 330 + 11x   11x = 33   x = 3   The answer is 3.
Answer: C
A certain number of men can do a work in 40 days . If there were 5 men less it could be finished in 10 days more . How many men are there?  Choose the correct choice from the following answers
A) 15 men
B) 25 men
C) 18 men
D) 12 men
E) 14 men

Solution: Explanation:   x*40 =(x-5)*50   5x-4x =25   X=25 men   Answer: Option 25 men
Answer: B
The sum of two numbers is 40 and their difference is 20. Find their product. Pick one:
A) 300  B) 108  C) 114  D) 325  E) None

Solution: Sol.   Let the numbers be x and y.   Then, x + y = 40 and   x - y = 20.   2x = 60 => x = 30 So y = 10   xy = 30 * 10= 
30 * 10 = 300
300   300nswer : 300
Answer: A
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Choices:
A) 8
B) 10
C) 11
D) 12
E) 13

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer: Option 10
Answer: B
If xy = 3 and x^2 + y^2 = 12, then x/y + y/x = Choose the correct answer:
A) 4	B) 3 1/7	C) 5 1/3	D) 7	E) 60

Solution: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:   x^2 + y^2 = 12   xy = 3   we can calculate the answer 12/3 -> 4 so answer is 4
Answer: A
The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor? Select the correct option
A) 10	B) 13	C) 18	D) 19	E) 12

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.   Answer: Option 18
Answer: C
A certain restaurant offers 7 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?  Choose the most appropriate option:
A) 120  B) 240  C) 480  D) 600  E) 1200

Solution: MAGOOSHOFFICIAL SOLUTION:   To count the number of meals, we have to count the possibilities for the three components, and then, according to theFundamental Counting Principle, we multiply. For more on the FCP, seethis blog.   For salads, there are 8 possibilities. Done.   For main courses, there are 5 different possibilities. Done.   For desserts, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can usethe shortcut, nC2 = (n*(n-1))/2.   6C2 = (6*5)/2= 
(6*5)/2 = 15
15   So, there are 15 combinations of two different desserts.   For the number of meals, we multiply 7*5*15. We know 8*5= 525   Answer = (600)
Answer: D
Each of the integers from 1 to 18 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even Choose the correct option
A) 19	B) 12	C) 11	D) 10	E) 3

Solution: Out of the 18 integers: 9 are odd and 9 are even.   If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:   1. we will end up picking odd numbers one by one, so we will pick all 9 odd numbers first   2. 10th number will be the first even number   So we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even.   So, answer will be 10. (10)
Answer: D
A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party T. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
Choose the correct choice from the following answers.
A) 15	B) 20	C) 30	D) 35	E) 45

Solution: S=100   not( T and B ) =35   only T=20   (T and B)/B=1/2   let ( T and B ) =x   only B =2x   so now, 20+35+x+2x=100   x= 15   15 ans
Answer: A
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Choose the correct choice from the following options:
A) 40	B) 88	C) 26	D) 18	E) 11

Solution: Explanation:   The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150   Profit(%) = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%   40nswer:40
Answer: A