MU-NLPC/Calc-aqua_rat huggingface dataset:
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30% while buying and by 10% while selling. What is his percentage profit? Choose the correct choice from the following choices:  A) 10.22%  B) 20.22%  C) 21.22%  D) 30%  E) Can't be calculated

Solution: The owner buys 100kg but actually gets 130kg;   The owner sells 100kg but actually gives 90kg;   Profit: (130-90)/90*100=30%   Answer: 30%.
Answer: D
Tina has 5 socks and 3 pair of shoes. How many combinations does Barbara have, if she doesn’t wear 2 specific socks with 1 specific pair of shoes?  Select the correct option
A) 4  B) 7  C) 10  D) 11  E) 13

Solution: Total no of combinations available is= 5 Socks X 3 pair of shoes = 15   13liminate the 2 socks X 1 pair of shoes combo = 2 which gives.......>> 15-2= 
15-2 = 13
13   ANSW13R: 13
Answer: E
Find the common ratio of three numbers in G.P whose product is 216 and the sum of the products taken in pairs is 114.	Choose the correct choice from the following answers
A) 2 or ½	B) 2/3 or 3/2	C) ¾ or 4/3	D) 4 or ¼	E) 5 or 1/5

Solution: Let the terms be a/r, a , ar   a/r *a * ar = a 3 =216, a =6   (a/r*a )+ (a*ar) + (ar*a/r ) =114, a 2/r + a 2 r + a 2 =114   a 2 ( 1/r + r +1 ) = 114, 36[( 1+ r 2 +r )/r] =114   6 [( 1 +r 2+ r )/r ]= 19, 6 r 2 -13 r + 6 = 0,   On solving, r = 2/3 or 3/2   ANSWER:2/3 or 3/2
Answer: B
Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 5 more than the average expenditure of all the nine. The total money spent by all of them was	Choose the correct choice from the following choices
A) 26	B) 40	C) 29.25	D) 32.625	E) None of the above

Solution: Let the average expenditure of all the ninte be x   Then, 3 × 8 + x + 5 = 9x   ⇒ x = 3.625   ∴ Total money spent = 9x = 9 × 3.625 = 32.625   Answer 32.625
Answer: D
The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 21 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken in 10 minutes ?  Choose the correct choice:
A) 13  B) 14  C) 15  D) 16  E) 21

Solution: a must be an integer as it is the number shoots at a rate of 21sec/shoot   3*60 + 21a = 10*60   21a = 420   a = 20   The total number of shoots -->1 +20 = 21 and   22th shoot will be taken at 621 seconds which is above 10 minutes   ANSW21R: 21-- 1 +20= 
-- 1 +20 = 21
21 and   22th shoot will be taken at 621 seconds which is above 10 minutes   ANSW21R: 21
Answer: E
What will come in place of the x in the following Number series? 25, 100, x, 1600, 6400	Choose the correct choice from the following answers:  A) 6400  B) 6900  C) 7340  D) 7500  E) 7900

Solution: (6400)   25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Answer: A
A group of 10 representatives is to be selected out of 13 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?  Choices.
A) 13C₅ * 10 B) 13C₇ * 10 C) 13C8 * ¹⁰C₅ D) 12 * ¹⁰C₅ E) None of these

Solution: Here, five seniors out of 13 seniors can be selected in 13C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 1313C8 * ¹⁰C₅₅ * ¹⁰13C8 * ¹⁰C₅₅ = 1313C8 * ¹⁰C₅8 * ¹⁰13C8 * ¹⁰C₅₅   since 1313C8 * ¹⁰C₅₅ = 1313C8 * ¹⁰C₅8   ANSWER:13C8 * ¹⁰C₅
Answer: C
From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 5 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
Choices
A) 38	B) 39	C) 40	D) 41	E) 43

Solution: Soln:-   5x=45 --> 21/20*x=45 --> x=45*20/21=300/7=~43.   Answer: 43.
Answer: E
A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?  Choose the correct choice from the following choices: A) 7 sec B) 6 sec C) 8 sec D) 4 sec E) 2 sec

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6 sec
Answer: B
What will be the fraction of 25%  Pick
A) 1/4
B) 1/5
C) 1/10
D) 1/8
E) None of above

Solution: Explanation:   It will 25*1/100 = 1/4   1/4nswer: Option 1/4
Answer: A
At a summer camp with 1,500 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 1,500 campers will the 8- to 12-year-olds represent?  Choose the correct option.
A) 33 1/3%	B) 50%	C) 55%	D) 60%	E) 66 2/3%

Solution: Total - 1,500 participants   campers are aged 8 to 12 = (1/2)*1500= 
(1/2)*1500 = 750
750   Next year, campers are aged 8 to 12= (4/3)*750= 
(4/3)*750 = 1_000
1000   Percentage= (1000/1500)*100 = 66 2/3%   Answer: Option 66 2/3%
Answer: E
A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 4:3 and B:C = 4:5. If the total runs scored by all of them are 75, the runs scored by B are? Select the correct option.
A) 20.23	B) 20.13	C) 30.93	D) 20.93	E) 10.93

Solution: A:B = 4:3   B:C = 4:5   A:B:C = 16:12:15   12/43 * 75 = 20.93   ANSWER:20.93
Answer: D
A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should A pay?  Choose one.
A) 240	B) 270	C) 276	D) 271	E) 272

Solution: 12*8 :16*9 = 18*6   8: 12: 9   8/29 * 870= 
8/29 * 870 = 240
240   240nswer: 240
Answer: A
A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/4 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?	Choose one.
A) 2.5% B) 17.67% C) 28.3% D) 45.2% E) 32.5%

Solution: Fiction Novels = 5,508   Transferred to another location = 6,120   Transferred fiction novels = 1,530   Non Transferred Fiction Novels = 3,978   Percent of the remaining collection was fiction novels = 3978/(18360 - 6120 ) * 100= 
3978/(18360 - 6120 ) * 100 = 65/2 = around 32.5
> 32.5%   Hence answer will be (32.5%)
Answer: E
In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 40, what is the least possible difference between n and m. Choose the most appropriate option:
A) a.1
B) b.3
C) c.5
D) d.7
E) e.9

Solution: 2n+5m=40   try with n=5 and m=6 the equation will be satisfied   2(5)+5(6)=40   so difference between M and N is 1,   a.1nswer a.1
Answer: A
What is the ratio between perimeters of two squares one having 7 times the diagonal then the other?
Answers
A) 3: 7 B) 3: 5 C) 3: 8 D) 7: 1 E) 3: 5

Solution: d = 7d d = d   a√2 = 7d a√2 = d   a = 7d/√2 a = d/√2 => 7: 1   Answer: 7: 1
Answer: D
In a certain country 1/3 of 4 = 6. Assuming the same proportion, what would be the value of 1/6 of 20 ?  Choices
A) 14	B) 15	C) 20	D) 22	E) 25

Solution: 15   15
Answer: B
In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?	Choose the most appropriate option.
A) 1:7  B) 2:3  C) 1:8  D) 2:3  E) 1:3

Solution: Number of men in the colony = 4/7 * 70= 
4/7 * 70 = 40
40.   Number of women in the colony= 3/7 * 70 = 40.   Number educated women in the colony = 1/5 * 30= 
1/5 * 30 = 6
6.   Number of uneducated women in the colony= 4/5 * 50 = 24.   Number of educated persons in the colony = 8 /35 * 70= 
8 /35 * 70 = 16
16.   As 6 females are educated, remaining 10 educated persons must be men.   Number of uneducated men in the colony= 40 - 10= 
40 - 10 = 30
30.   Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1 : 3.   Answer:1:3
Answer: E
A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?  Select the correct option:
A) 227  B) 400  C) 230  D) 288  E) 271

Solution: Speed = [300 / 18] m/sec = 50/3 m/sec.   Let the length of the platform be x meters.   Then, x + 300 / 42 = 50/3   3(x + 300) = 2100 è x = 400m.   Answer: 400
Answer: B
If the compound interest on a sum of Rs.7000 for 2 years is Rs.1470 then the rate of interest is (interest compounded yearly) Choices:
A) 10 % p.a. B) 12 % p.a. C) 11 % p.a. D) 9 % p.a. E) None

Solution: Given CI=1470   P=7000   Thus 10 % p.a.=CI+P=8470   Now 10 % p.a.=p(1+R/100)^n   So,8470=7000(1+R/100)^2   (11/10)^2=(1+R/100)^2   11/10=1+R/100   Thus R=10%   10 % p.a.NSWER:10 % p.a.
Answer: A
A straight line in the xy- plane has slope 2 . On this line the x-coordinate of the point is 300 and y-coordinate is 900 then what is the y intercept of the plane?
Choose the most appropriate option:
A) 200  B) 250  C) 100  D) 300  E) 220

Solution: Eq of line = Y = MX +C   M= 2   X=300   Y=300*2+ C,   Substitute Y by 900 as given in question.   900=600+C , C =200   correct option is 200
Answer: A
A person can swim in still water at 8 km/h. If the speed of water 4 km/h, how many hours will the man take to swim back against the current for 8km?  Choose one:
A) 2
B) 4
C) 5
D) 6
E) 7

Solution: M = 8   S = 4   US = 8 - 4= 
8 - 4 = 4
4   D= 4   T = 8/4= 
8/4 = 2
2 2nswer:2
Answer: A
There are some students in a school.The 1/2 of number of students is a whole number. The 1/6 of number of students is a whole number. The 1/5 of number of students is a whole number. The 1/7 of number of students is a whole number.Find the number of students. Options.
A) 200
B) 210
C) 220
D) 230
E) 240

Solution: 210   ANSWER:210
Answer: B
When N is divided by T, the quotient is S and the remainder is C. Which of the following expressions is equal to N?  Choose the correct choice.
A) ST
B) S + V
C) ST + C
D) T(S+V)
E) T(S – V)

Solution: Using the rule dividend = Quotient * divisor + remainder =>ST + ST + C ST + C is correct
Answer: C
A certain team consists of 3 professors and 4 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)  Choose the correct choice from the following options.
A) 25 B) 28 C) 31 D) 34 E) 37

Solution: The total number of ways to form a group of 3 from 7 people is 7C3 = 35   The number of ways to form a group without a professor is 4C3 = 4   The total number of ways to form a valid group is   35 - 4= 
  35 - 4 = 31
31.   The answer is 31.
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?  Choose the correct choice from the following answers
A) 120 metres
B) 180 metres
C) 100 metres
D) 228 metres
E) 150 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 6 m = 100 m.   Option 100 metres
Answer: C
A certain team has 6 members, including Joey. A three-member relay team will be selected as follows: one of the 6 members is to be chosen at random to run first, one of the remaining 5 members is to be chosen at random to run second, and one of the remaining 4 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?  Select: A) 1/2 B) 2/3 C) 1/3 D) 1/6 E) 2/5

Solution: Each member has an equal probability to run second (1/6) or third (1/6).   The probability that Joey runs second or third is 1/6 + 1/6 = 1/3   The answer is 1/3.
Answer: C
What is the smallest integer q greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10? Choose the correct option
A) q=21
B) q=41
C) q=121
D) q=241
E) q=481

Solution: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder q as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.q=121
Answer: C
Find the value of x from the below equation? : 3x^2-5x+2 = 0  Pick one:
A) 2/3  B) -1  C) 0  D) -2/3  E) 2

Solution: a = 3, b = -5, c = 2   x1,2 = (5 Â± âˆš((-5)^2 - 4Ã—3Ã—2)) / (2Ã—3) = (5 Â± âˆš(25-24)) / 6 = (5 Â± 1) / 6   x1 = (5 + 1)/6 = 6/6= 
6/6 = 1
1   x2= (5 - 1)/6 = 4/6 = 2/3   2/3
Answer: A
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.15000. A's share is? Choose the correct choice from the following.
A) 2999	B) 2778	C) 6000	D) 5000	E) 6612

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 15000= 
1/3 * 15000 = 5_000
5000   Answer:5000
Answer: D
An investment yielded an interest payment of $350 each month when the annual interest rate was 9%, what is the amount of the investment that should be invested with an annual interest rate of 8% if We want to gain 15% more each month?  Select:
A) $60,375 B) $50,400 C) $41,300 D) $32,500 E) $25,100

Solution: An investment yielded an interest payment of $350 each month when the annual interest rate was 9%, what is the amount of the investment that should be invested with an annual interest rate of 8% if We want to gain 15% more each month?   Based on first statement the total interest earned = 350 * 12 = Principal * interest rate(9/100)   No need to solve for principal here, just continue....   So find the new principal for revised interest rate and 10% more interest, so 350 * 12 * 1.15 = Principal * interest rate (8/100)   solving for Principal = 60,375   $60,375nswer is $60,375 : 60,375
Answer: A
The average age of 7 men increases by 3 years when two women are included in place of two men of ages 18 and 22 years. Find the average age of the women?	Choose the correct choice from the following answers:
A) 30.5  B) 26  C) 30  D) 18  E) 11

Solution: Explanation:   18 + 22 + 7 * 3= 
18 + 22 + 7 * 3 = 61
61/2= 
61/2 = 61/2 = around 30.5
30.5   30.5nswer: 30.5
Answer: A
The length of the longest rod that can fit in a cubical room of 4 m side is?	Choose the correct option:
A) 6.978 m	B) 6.928 m	C) 6.829 m	D) 6.248 m	E) 6.982 m

Solution: The length of the longest rod=4 sq.root of 3=6.928 m   Answer: 6.928 m
Answer: B
Gabriela’s grade was in the 90th percentile out of 100 grades in her class. In another class of 100 students there were 80 grades lower than Gabriela’s. If nobody had Gabriela’s grade, then Gabriela was what percentile of the two classes combined?  Select
A) 90	B) 85	C) 80	D) 75	E) 70

Solution: Being in 90% percentile out of 100 grades means was 91st (from the least grade) in the class (as long as nobody had Gabriela 's grades), she outscored 90.   In another class her grade would rank her 61 (from the least grade out of 101, 100+ Gabriela), 60 had the grades lower than Gabriela.   So in combined classes she outscored  90+60= 
 90+60 = 150
150. There are 200 students  150/200= 
 150/200 = 3/4 = around 0.75
0.75   Answer: D (75%)   Generally being in x% means that x% has the grades less than you.   Gabriela in 90% --> she outscored 90% of of 100=90 (Gabriela is 91st).   Of the 100 grades from another class, 60 were lower than Gabriela, hence Gabriela outscored 60.   So out of total  100+100= 
 100+100 = 200
200, Gabriela outscored   90+60= 
  90+60 = 150
150. Hence she is in 150/200=75%.   Answer:75
Answer: D
At present the age of the father is five times that of the age of the son. Three years hence the father's age would be 4 times that of his son. Find the present age of the father?
Choose one: A) 9years B) 25years C) 45years D) 30years E) 50years

Solution: Age of the son = (4-1)*3 / (5-4)= 
(4-1)*3 / (5-4) = 9
9 years   Age of the father= 9*5= 
9*5 = 45
45 years   Answer is 45years
Answer: C
The security gate at a storage facility requires a five-digit lock code. If the lock code
must consist only of digits from 1 through 7, inclusive, with no repeated digits, and
the first and last digits of the code must be odd, how many lock codes are possible?  Select the correct option.
A) 120 B) 240 C) 360 D) 720 E) 1440

Solution: X-X-X-X-X --> there are 4 odd digits from 1 to 7, inclusive thus options for the first and the last X's are: 4-X-X-X-3. Other X's can take following values: 4-5-4-3-3 --> 4*5*4*3*3=720.   Answer: 720.
Answer: D
A van takes 6 hours to cover a distance of 288 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Choose the correct choice from the following choices.
A) 50 Kmph B) 60 Kmph C) 32 Kmph D) 80 Kmph E) 90 Kmph

Solution: Time = 6   Distence = 288   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 288/9= 
288/9 = 32
32 Kmph   32 Kmph
Answer: C
It is decided to construct a 2 metre broad pathway around a rectangular plot on the inside. If the area of the plots is 96 sq.m. and the rate of construction is Rs. 50 per square metre., what will be the total cost of the construction? Choose one.
A) Rs.3500 B) Rs. 4200 C) Insufficient Data D) Rs. 4400 E) None of these

Solution: Explanation : Let length and width of the rectangular plot be l and b respectively   Total area of the rectangular plot = 96 sq.m.   => lb = 96   Width of the pathway = 2 m   Length of the remaining area in the plot = (l - 4)   breadth of the remaining area in the plot = (b - 4)   Area of the remaining area in the plot = (l - 4)(b - 4)   Area of the pathway   = Total area of the rectangular plot - remaining area in the plot   = 96 - [(l - 4)(b - 4)] = 96 - [lb - 4l - 4b + 16] = 96 - [96 - 4l - 4b + 16] = 96 - 96 + 4l + 4b - 16   = 4l + 4b - 16   = 4(l + b) - 16   We do not know the values of l and b and hence area of the pathway cannot be found out. So we cannot determine total cost of the construction. Answer : Option Insufficient Data
Answer: C
If n is the product of all the integers from 5 to 20, inclusive, what is the greatest integer k for which 2^k is a factor of n ?
Choose the correct choice from the following:
A) 11
B) 12
C) 13
D) 14
E) 15

Solution: 20/2= 
20/2 = 10
10   10/2= 
10/2 = 5
5   Ans: 10+5= 
 10+5 = 15
15   ANSW15R:15
Answer: E
The true discount on a bill of Rs.540 is Rs.90.The banker's discount is  Options:
A) Rs.60
B) Rs.108
C) Rs.110
D) Rs.112
E) None of these

Solution: Solution   P.W	= Rs.(540 - 90)   = Rs. 450   S.I on Rs. 540	=Rs.(90/450 x 540)   = Rs. 108.   Answer Rs.108
Answer: B
A train running at 25 km/hr takes 50 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform. Select:
A) a) 200/3m175/3m
B) b) 36m178m
C) c) 50m45m
D) d) 100/3 m200/3
E) e) none of these

Solution: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m   lets solve it   To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.   The man covered the distance during 12sec is  5*5/50*12= 
 5*5/50*12 = 6
6m so the train covered a distance in 12 sec= 25*5/50*12= 
25*5/50*12 = 30
30   so the length of the train(Lt) is  6+30= 
 6+30 = 36
36m   Now crossing the platform means length of train+length of platform(Lt+p)= 50*25*5/50= 
50*25*5/50 = 125
125m Now the length of platform (Lp) is= 125-36= 
125-36 = 89
89m   So answer is 36m and 89m Must beb) 36m178meven though its mentioned 36m and 178m thinking so typo mistake...........
Answer: B
If two projectiles are launched at the same moment from 2520 km apart and travel directly towards each other at 432 km per hour and 576 km per hour respectively, how many minutes will it take for them to meet? Choose the correct choice from the following choices
A) 130
B) 135
C) 140
D) 145
E) 150

Solution: The projectiles travel a total of 1008 km per hour.   The time to meet is   2520/1008= 
  2520/1008 = 5/2 = around 2.5
2.5 hours= 150 minutes   The answer is 150.
Answer: E
A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 130 pounds?	Choose the correct choice from the following answers: A) 8 B) 14 C) 12 D) 9 E) none of the above

Solution: Ans is 14:   39 pounds --> 6 days   130 pounds --> x days   x = 130*6/39= 
130*6/39 = 20
20   the animal has already consumed food in 6 days so the the number of days   for it's total consumption be 130 pounds is   20-6= 
  20-6 = 14
14
Answer: B
The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 41 what is the value of a1 ?	Pick one
A) 1  B) 6  C) 21  D) 16  E) 21

Solution: Here, each value of an is the previous value plus 5   Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1   a5 = 41   a4 = 36   a3 = 31   a2 = 26   a1 = 21 <<<< Ans 21
Answer: C
If two positive numbers are in the ratio 1/7 : 1/4, then by what percent is the second number more than the first? Choose the correct choice from the following choices
A) 67%. B) 70%. C) 75%. D) 68%. E) 80%.

Solution: Given ratio = 1/7 : 1/4 = 4 : 7   Let first number be 4x and the second number be 7x.   The second number is more than first number by 3x.   Required percentage = 3x/4x * 100 = 75%.   Answer: 75%.3 /4  * 100= 
3 /4  * 100 = 75
75%.   Answer: 75%.
Answer: C
Two goods trains each 375 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?	Choose the correct choice from the following:
A) 40 B) 45 C) 48 D) 51 E) 36

Solution: Relative speed = 45 + 30= 
45 + 30 = 75
75 km/hr.   75 * 5/18= 125/6 m/sec.   Distance covered = 375 + 375= 
375 + 375 = 750
750 m.   Required time= 750 * 6/125= 
750 * 6/125 = 36
36 sec.   Answer: Option 36
Answer: E
There are 4 baskets. The first basket has 3 apples and 4 oranges, the second one has 4 apples and 5 mangoes, the third one has 6 Mangoes and 2 bananas and the last one has 7 bananas and 2 apples. If a fruit is randomly chosen from any basket and it comes out to be an apple, then what is the probability that it was taken out from the second basket?	Choose the correct choice from the following choices:
A) 27/69  B) 28/69  C) 29/69  D) 25/69  E) 28/64

Solution: P(A|1)=3/7   P(A|2)=4/9   P(A|3)=0/8   P(A|4)=2/9   Hence event 1,2,3,4 are the partitions of the sample space.   The probability of choosing an apple, by the law of total probability   P(A)=P(A|1)P(1)+P(A|2)P(2)+P(A|3)P(3)+P(A|4)P(4)   =3/7*1/4+4/9*1/4+0/8*1/4+2/9*1/4   =23/84   28/69y 28/69aye's theorem,   P(2|A)=P(A|2)*P(2)/P(A)   =4/9*(1/4)/(23/84)   =28/69   ANSWER:28/69
Answer: B
Convert the following unit:
2.3 hectares in ares	Pick
A) 200 ares.	B) 210 ares.	C) 220 ares.	D) 230 ares.	E) 240 ares.

Solution: 2.3 hectares in ares   1 hectare = 100 ares   Therefore, 2.3 hectares = 2.3 × 100 ares   = 230 ares.   ANSWER : OPTION 230 ares.
Answer: D
The area of a triangle will be when a = 2m, b = 4m, c = 6m, a, b, c being lengths of respective sides?	Choose the correct choice from the following answers:
A) 3 B) 7 C) 5 D) 6 E) 4

Solution: S = (2 + 4 + 6)/2= 
(2 + 4 + 6)/2 = 6
6   Answer: 6
Answer: D
If it is true that x > -3 and x < 7, which of the following must be true?
Select the correct option.
A) x > 3	B) x > -7	C) x < 3	D) -7 < x < 3	E) none of the above.

Solution: the range is -3 < x < 7   A. x > 3 - no because x can be between -3 < x < 3   B. x > -7 -- the answer is true, because the values of x are always >-7   C. x < 3 - no because x can be between 3 < x < 7   D. -7 < x < 3 - no because x can be between 3 < x < 7   E. none of the above.   Answer: x > -7
Answer: B