MU-NLPC/Calc-aqua_rat huggingface dataset:
In a meeting of 3 representatives from each of 7 different companies, each person shook hands with every person not from his or her own company. If the representatives did not shake hands with people from their own company, how many handshakes took place?	Select the correct option:  A) 189  B) 179  C) 159  D) 169  E) 180

Solution: In fact, all 21 people will shake hands with 18 others.   So, it SEEMS like the TOTAL number of handshakes = (21)(18)   HOWEVER, we need to keep in mind that we have counted each handshake TWICE.   To account for this DUPLICATION, we must divide (21)(18) by 2.   So, the TOT189L # of handshakes = (21)(18)/2 = 189   189nswer : 189
Answer: A
What is the unit digit in 12^100?
Answers:	A) 0	B) 1	C) 2	D) 4	E) 6

Solution: Unit digit in 12^100 = unit digit in [(12^4)^25 ]But unit digit in 12^4=6unit digit 12^100= 6Answer is 6
Answer: E
A fellow borrowed a certain sum of money at 3% per annum at simple interest and in 3 years the interest amounted to Rs.1820 less than the sum lent. What was the sum lent?	Choose the correct choice from the following choices.
A) 1050  B) 1220  C) 1250  D) 2000  E) 1110

Solution: P - 1820 = (P*3*3)/100   P = 2000   Answer: 2000
Answer: D
If R = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in R than the median of the numbers in R?	Choose one: A) 1.0 B) 1.5 C) 2.0 D) 2.5 E) 3.0

Solution: This is a good question to understand the difference between mean and median.   Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)   Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median   Coming to this question,   Mean = (1 + 7 + 18 + 20 + 29 + 33)/6= 
(1 + 7 + 18 + 20 + 29 + 33)/6 = 18
18   Median= (18 + 20)/2= 
(18 + 20)/2 = 19
19   Difference= 1   Option 1.0
Answer: A
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
Choose the correct choice from the following.
A) 30%	B) 32%	C) 40%	D) 44%	E) 48%

Solution: Let original length = x metres and original breadth = y metres.   Original area = (xy) m2.   New length = 120	x	m	= 6	x	m.   100	5   New breadth = 120	y	m	= 6	y	m.   100	5   New Area = 6	x x	6	y	m2	= 36	xy	m2.   5	5	25   The difference between the original area = xy and new-area 36/25 xy is   = (36/25)xy - xy   = xy(36/25 - 1)   = xy(11/25) or (11/25)xy   Increase % = 11	xy x	1	x 100	%	= 44%.   25	xy   44%
Answer: D
Equal weights of two alloys containing tin, copper and lead in the ratio 3:2:7 and 4:11:3 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?	Choose the correct choice from the following answers.
A) 41:81:37 B) 33:91:81 C) 17:28:27 D) 51:86:89 E) None of these

Solution: Exp. Let the weight of the two alloys be w each   Required ratio =   (3w/12 +4w/18): ( 2w/12 +11w/18 ): (7w/12+3w/18)   = 17w/36 : 28w/36 : 27w/36   = 17:28: 27   Answer: 17:28:27
Answer: C
The cost of fuming the engine of an army tank is proportional to the square of the speed and Rs 64 per hour for a speed of 16km/hr. Other costs amount to Rs 400 per hour. The tank has to make a journey of 400km at a constant speed.The most economical speed for this journey is :	Choose the correct choice from the following answers.
A) 20 km/hr  B) 30 km/hr  C) 35 km/hr  D) 40 km/hr  E) None of these

Solution: Explanation :   Cost = k2×speed2[ Where k is constant], And   =>64 = k×16×16   =>k=1/4.   =>cost=speed2 /4.   Total cost=[(speed2/4)+400]×400/speed   using options, putting different values of speed, we find speed = 40km/hr to be most economical.   Answer : 40 km/hr
Answer: D
Two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 125 metres, in what time (in seconds) will they cross each other travelling in opposite direction?  Choose the correct choice from the following choices.
A) 6  B) 14  C) 16  D) 20  E) 18

Solution: Sol.   Speed of the first train = [150 / 10] m/sec = 15 m/sec.   Speed of the second train = [150 / 15] m/sec = 10 m/sec.   Relative speed = (15 + 10) = m/sec = 25 m/sec.   ∴ Required time = (125 + 125) / 25 secc = 6 sec.   6nswer 6
Answer: A
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?  Select the correct option:
A) 45 B) 37 C) 29 D) 26 E) 12

Solution: A:B:C = (10×7):(12×5):(15×3)   = 70 :60 :45   = 14 :12 :9   C's rent = Rs.(175×9/35)   =Rs. 45.   45nswer: 45
Answer: A
A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?	Options.
A) 1,250 meters / minute	B) 1,350 meters / minute	C) 1,450 meters / minute	D) 1,550 meters / minute	E) 1,650 meters / minute

Solution: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify   75 kilometers per hour = 75 km/hr   = (75 * 1000 meters) / (60 minutes) = 1,250 meters / minute   correct answer 1,250 meters / minute
Answer: A
Antony can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows Antony has in his herd?	Choose the correct answer:
A) 155
B) 120
C) 456
D) 180
E) 336

Solution: On first look B,C,E are not divisible either by 5 or 6 - ruled out.   D,B divisible by both 5,6, but 180 is divisible by 9.   Answer : 120
Answer: B
What is the product of all the prime factors of 12?	Options.
A) 108	B) 18	C) 9	D) 6	E) 12

Solution: 12 , factors are 2,3,4,6,1. Now again prime Numbers are Only Two i.e 2 and 3 , this time we would have  2*2*3= 
 2*2*3 = 12
12   Answer : 12
Answer: E
If 325/999=0.125, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction? Choose the correct option.
A) 3  B) 3.5  C) 4  D) 4.5  E) 5

Solution: 0.[u]325[/u = 0.325325325.....   Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.   Answer 5
Answer: E
Thomas has age that is twice of Matt now, two years from now Thomas's age would be 1.5 times that of Matt. How old is the Matt now?	Select the correct option: A) 2 B) 6 C) 8 D) 12 E) 4

Solution: Lets assume the age of Matt be x, so that makes Thomas's age y.   From 2 years from now (y+2)=1.5(x+2)   and y is 2x, so substituting we get (2x+2)=1.5x+3   .5x=1 and it makes x=2.   Matt's current is 2   2nswer:2
Answer: A
The difference between a number and its three-fifth is 50. What is the number?  Choose the correct option:
A) 75
B) 100
C) 125
D) 150
E) 175

Solution: Let the number be x. Then,   x - 3/5 x = 50 => 2/5 x = 50   x = (50 * 5)/2= 
(50 * 5)/2 = 125
125.   ANSWER:125
Answer: C
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is? Select:
A) 5/18
B) 5/12
C) 5/17
D) 5/11
E) 5/10

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9)   = 5/12   Answer:5/12
Answer: B
If after 100 grams of water were added to the 20%-solution of alcohol, the strength of the solution decreased by one-fourth, how much of the 20%-solution was used?
Select:
A) 300
B) 250
C) 150
D) 200
E) 210

Solution: The 20% alcohol solution decreases by 1/4 once the 100 grams of water is added so  100/.05= 
 100/.05 = 2_000
2000*.15% (3/4 of 20%) is 300 grams.   answer is 300
Answer: A
Cindy paddles her kayak upstream at b kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?  Pick one
A) bnp	B) bn/p	C) (b + n)/p	D) bnp/(b + n)	E) pm/n- pn/m

Solution: let t1 and t2 be the time taken to row upstream and downstream respectively   now,   t1=distance/speed=d/b   similarly,   t2=d/n (as same distance has to be rowed)   also,   t1+t2=p   therefore,   p=(d/b)+(d/n)   =d(b+n)/bn   d=pbn/(b+n)=bnp/(b + n)
Answer: D
Which of the following points is symmetric with y=x at (-3,-4)?  Choose the correct choice from the following.
A) (-2,-1) B) (-4,-3) C) (2,1) D) (-1,-2) E) (-1,2)

Solution: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.   (-3,-4) would become (-4,-3).   Answer ((-4,-3)).
Answer: B
Narendra started a business, investing 40000. Six months later, Chandan joined him with 20000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?
Choose the correct option:
A) A)Rs.7000	B) B)Rs.8000	C) C)Rs.8500	D) D)Rs.8600	E) E)Rs.8700

Solution: The ratio of their investments = 40000 × 12 : 20000 × 6 = 4 : 1.   :. Narendra’s share on profit of Rs.10000 = 10000 × 4/5 = Rs.8000.   Rs.8000)
Answer: B
If the average cost of a house was $40,000 in 1965 and was x in 2005, what was the average increase in home prices per year over this period? Choose the correct choice from the following options:
A) A)(x+50,000)/40  B) B)(x-40,000)/40  C) C)(50,000/40)+x  D) D)(50,000-x)/40  E) E)x/40

Solution: Average house price in 2005: x   Average house price in 1965: 40,000   2005-1965= 
2005-1965 = 40
40   Average increase per year: (x-40,000)/40   Answer is (x-40,000)/40
Answer: B
In a right isosceles triangle, the lengths of the two nonhypotenuse sides are designated a. What is the area of the triangle in terms of a?	Choose the correct option.
A) 1/3*a^2
B) √2/3∗a^2
C) 1/2*a^2
D) √3/2∗a^2
E) √2^a2

Solution: Since it is right angled isosceles triangle then other two sides will be equal let's say a and a and third side be c   Area of triangle is 1/2*b*h = 1/2*a*a .   option 1/2*a^2 is correct answer.
Answer: C
If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 9 people to do 9 times of that particular work?  Choose the most appropriate option:
A) 1
B) 2
C) 3
D) 9
E) 12

Solution: 3 people can do the work one time in one day.   1 person can do 1/3 of the work in one day.   9 people can do 9/3 of the work in one day.   9 people can do 9 times the work in 3 days.   The answer is 3.
Answer: C
If cost of sugar increases by 50%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed? Choose the correct choice from the following choices
A) 33%
B) 50%
C) 20%
D) 90%
E) 60%

Solution: 100   150   -----   150 ----- 50   100 ------ ? => 33%   33%nswer: 33%
Answer: A
The set X = {7,8,9,10}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer?
Choose the correct answer:
A) 7/16  B) 5/16  C) 3/16  D) 7/8  E) 5/8

Solution: The total number of x and y pairs is 4*4= 
4*4 = 16
16.   There are five pairs such that x / y is an integer.   The probability that x / y is an integer is 5/16.   The answer is 5/16.
Answer: B
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II.18.16
III. 17.18
Choices: A) I only B) II only C) III only D) I and III only E) I and II only

Solution: Problem statement was difficult to parse. but some how I managed to understand what we can do.   1) x/y = 15 + 0.15   2) x/y = 18 + 0.16   3) x/y = 17 + 0.18   w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)   therefore :   1) y*0.15=60 -- we can get y an integer.   2) y*0.16=60 -- we can get y an integer.   3) y*0.18=60 -- we can't get y an integer.   Therefore 1 and 2 are possible answers.   Ans I and II only
Answer: E
It takes one machine to paint 1000 sq.m. surface in 24 minutes.Another machine does the same job in 40 seconds.How much time will it take if both machines are put on the same work? Choose the most appropriate option:  A) 10.0 seconds  B) 20.0 seconds  C) 38.9 seconds  D) 40.0 seconds  E) 52.0 seconds

Solution: By guess it is clear that the time taken will be less than 40 seconds and very near to it. Therefore, answer 38.9 seconds will be correct. Answer-38.9 seconds
Answer: C
Over a three-week period, the price of an ounce of gold increased by 10% in the first week, decreased by 20% in the following week, and increased by 30% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks?	Choose the most appropriate option: A) 1.124G B) 1.144G C) 1.164G D) 1.184G E) 1.204G

Solution: After 3 weeks, the price was 1.3*0.8*1.1*G=1.144G   The answer is 1.144G.
Answer: B
If x=kc and y=kt,then 2y-x =?  Pick.
A) k(t-c)  B) k(c-t)  C) c(k-t)  D) t(k-c)  E) k(2t-c)

Solution: Just put in the given values of y and x   2y - x = 2kt - kc   Now take k common   2y - x = k(2t - c)   You get (k(2t-c)) as your answer.
Answer: E
The pilot of a small aircraft with a 60-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 10 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?  Choose the correct choice from the following answers.
A) 5 B) 12 C) 2 D) 4 E) 6

Solution: Actual miles/gallon is = 480/60= 
480/60 = 8
8 miles/gallon.   Current engine miles/gallon is 10 miles/gallon.   Additional 2 miles/gallon is required to match the actual mileage.   ANSWER:2
Answer: C
a^2*b^2+a^2+b^2=259
b^2*c^2+b^2+c^2=1299
c^2*a^2+c^2+a^2=499
then find a+b+c=?
Pick one: A) 13 B) 14 C) 15 D) 16 E) 17

Solution: a^2*b^2+a^2+b^2+1= (a^2+1)(b^2+1)   by using above one we can write   a^2*b^2+a^2+b^2+1=260..(1)   b^2*c^2+b^2+c^2+1=1300..(2)   c^2*a^2+c^2+a^2+1=500..(3)   by doing (1)/(2) we will get a^2+1/c^2+1 = 1/5..(4)   by doing (4)*(3) we will get (a^2+1)^2=10,   by solving a=3, b=5,c=7   so a+b+c=15   ANSWER:15
Answer: C
There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairy tales, novels and plays.
Answers
A) 17200 B) 17250 C) 17280 D) 17300 E) 17400

Solution: There are 4 books on fairy tales and they have to be put together.   They can be arranged in 4! ways.   Similarly, there are 5 novels.   They can be arranged in 5! ways.   And there are 3 plays.   They can be arranged in 3! ways.   So, by the counting principle all of them together can be arranged in 4!×5!×3!=4!×5!×3!= 17280 ways   Option is 17280
Answer: C
One side of a rectangular field is 15 m and one of its diagonal is 17 m. Find the area of the field.  Answers:	A) 100	B) 120	C) 150	D) 180	E) None

Solution: Solution   Other side = √(17)2 - (15)2   = √289 - 225= 
289 - 225 = 64
√64= 8 m.   ∴ Area = (15 x 8)m2 = 120 m2.   Answer 120
Answer: B
The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
Choose the correct choice from the following answers:
A) 5/11
B) 4/11
C) 3/11
D) 6/45
E) 7/44

Solution: The denominator be P, the numerator will be (P - 8).   The fraction will be (P - 8)/P.   Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.   (P - 5)/(P - 3) = 3/4   P = 20 - 9 => P = 11.   The fraction is: 3/11.   Answer: 3/11
Answer: C
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?	Choose the correct answer
A) 3377 B) 2899 C) 2500 D) 2778 E) 1991

Solution: A:B:2500 = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 200   B capital = 15000*1/6= 
15000*1/6 = 2_500
2500   Answer: 2500
Answer: C
A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is
Choices:
A) 1  B) 3  C) 5  D) 7  E) 9

Solution: Solution   (1000 + N) > (1000N)   Clearly, N=1.   1nswer 1
Answer: A
If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to  Choose the correct choice from the following choices: A) 143 B) 150 C) 123.75 D) 140.55 E) None

Solution: Solution   y = 125 + 10% of 125   = 125 + 12.50 = 137.50.   x = 137.50 - 10% of 137.50   = 137.50 - 13.75   = 123.75.   Answer 123.75
Answer: C
Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 75 percent carbonated water, what percent of the volume of the mixture is P?
Choose the correct choice.
A) 40% B) 50% C) 60% D) 80% E) 90%

Solution: 75% is 5%-points below 80% and 20%-points above 55%.   So the ratio of solution P to solution Q is 4:1.   Mixture P is 4/5 = 80% of the volume of mixture PQ.   The answer is 80%.
Answer: D
Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is	Answers:	A) 10 cm	B) 12 cm	C) 16 cm	D) 18 cm	E) None

Solution: Sol.   Volume of the new cube   = (63 + 83 + 103) cm3   = 1728cm3.   Let the edge of the new cube be a cm.   ∴ a3 = 1728   ⇒ a = 12.   Answer 12 cm
Answer: B
which of the following options is the correct value of r, given the equation 6^r +1^(-r) = 217?  Choose the correct choice from the following choices:
A) 5
B) 7
C) 3
D) 2
E) 0

Solution: Plugging in the various option into the equation to find out which is correct:   6^r +1^(-r) = 217   6^3 +1^(-3) = 217 Ans. 3
Answer: C
Which of the following is equal to 2^k*3^(k-1)?
Choose the most appropriate option
A) 2*6^(k-1)	B) 3*6^(k-1)	C) 6^k	D) 2*6^k	E) 6^(2k-1)

Solution: 2^k*3^(k-1) = 2*2^(k-1)*3^(k-1) = 2*6^(k-1)   The answer is 2*6^(k-1).
Answer: A
A does half as much work as B in three- fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?  Choose the most appropriate option:
A) 30 days
B) 35 days
C) 40 days
D) 45 days
E) 50 days

Solution: Explanation:   Let ‘x’ be the number of days taken by B alone to finish the whole work   Then, A alone will finish the whole work in 3x/4 × 2 days = 3x/2 days.   Then, working together,   3x/2 × x/3x/2 + x = 18 days   3x × x/5x = 18   3x/5 = 18   Therefore, the number of days taken by B = x = 18 × 5/3 = 30 days.   30 daysnswer: Option 30 days
Answer: A
A number a is squared and then multiplied by negative 1. The result of this operation is equal to 2 times the sum of 4 times a and 8. What is one possible value of a ?	Pick.
A) 1 B) 2 C) 4 D) 8 E) 5

Solution: -1*a^2=2(4a+8)   a= -4 or -4   a=-4=B   ANSWER:4
Answer: C
2 persons allotted to one work. John can do piece of work in 30 days while Bruce alone can do it in 40 days. In how many days can John and Bruce working together to do it? Choose the correct choice from the following choices
A) 17 2/7days  B) 17 1/7days  C) 17 3/5days  D) 18 1/7days  E) 17 1/4days

Solution: Therefore John′s one day’s work = 130   17 1/7daysruce′   s one day’s work = 140   (A+17 1/7days)′   s one day’s work = 130+140   4+3120=7120   Number of days required for John   and 17 1/7daysruce to finish the work = 17/120=17 1/7days   17 1/7days
Answer: B
A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?  Select:
A) 2/4
B) 3/4
C) 4/5
D) 5/6
E) 6/7

Solution: consider A,3/4,C events and AA,3/43/4,CC not solving the problems   now P(1)=1/2, P(3/4)=2/3 and P(C)=1/4   Not solving events =1/2*2/3*3/4   ==>1-1/4= 3/4   ANSWER 3/4
Answer: B
A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?
Answers: A) 24 years B) 14 years C) 65 years D) 17 years E) 15 years

Solution: Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.   R = (100 * 3x)/(x * 8)   = 300/8 %   If the sum becomes ten times itself, then interest is 9x.   The required time period   = (100 * 9x)/(x * 300/8)   = (100 * 9x * 8)/(x * 300)   = 24 years.   Answer:15 years
Answer: E
If in a race of 100m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
Choose the correct choice from the following choices.
A) 20m  B) 16m  C) 11m  D) 10m  E) 15m

Solution: Explanation:   The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.   The distance covered by B in 5 seconds = (100 * 5) / 25= 
(100 * 5) / 25 = 20
20m   Hence, A beats B by 20m.   20mNSWER 20m
Answer: A
The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 30 terms of this sequence?  Choices:
A) 1/30-1/32  B) 1 - (1/30 + 1/30)  C) (1+1/2) – (1/31 +1/ 32)  D) 1 - 1/32  E) 1/32-1/30

Solution: The answer would most certainly be[C]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.   The sequence is :   a1 = 1-1/3   a2 = 1/2 - 1/4   a3 = 1/3 - 1/5....   We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/32 and -1/31 from a30 and a29 term which could not be cancelled.   Hence the sum = (1+1/2) – (1/31 +1/ 32)   Answer : (1+1/2) – (1/31 +1/ 32)
Answer: C
Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?
Select the correct option:
A) 2 kg
B) 2.4 kg
C) 2.5 kg
D) 10 kg
E) none of these

Solution: The weight of non-water in 20 kg of fresh grapes (which is 100-90= 
100-90 = 10
10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20= 
100-20 = 80
80% of whole weight), so 20∗0.1=x∗0.8--> x=2.5   Answer: 2.5 kg.
Answer: C
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?  Options.
A) 802	B) 800	C) 829	D) 389	E) 245

Solution: Area of the square = s * s = 5(125 * 64)   => s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   Answer: 800
Answer: B
In a group of 250 readers who read science fiction or literacy works or both, 180 read science fiction and 88 read literacy works. How many read both science fiction and literacy works?	Choose the correct option.
A) 268 B) 180 C) 150 D) 18 E) 88

Solution: Consider total number of reader n(S U L) = 250   People who read science fiction n(S) = 180   People who read literacy works n(L) = 88   both science fiction and literacy n(S âˆ© L) = ?   n(S U L) = n(S)+ n(L) - n(S âˆ© L)   250 = 180 + 88 - n(S âˆ© L)   n(S âˆ© L) = 268 - 250   n(S âˆ© L) = 18   SO People read both science fiction and literacy works are 18   ANSWER:18
Answer: D
At Veridux Corporation, there are 180 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?	Choices.
A) 95	B) 20	C) 85	D) 75	E) 35

Solution: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 180 â€“ 90 = 90 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 180 â€“ 40 = 140 must be associates.   Now, in the â€œassociateâ€ row, 135 + E = 140, which means E = 5 â€” the other 5 associates must be female.   Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B +5 = 90, which means B = 85. There are fifteen female managers in this company. Thus, the answer = (85).
Answer: C