MU-NLPC/Calc-aqua_rat huggingface dataset:
Jennifer had $90 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?	Pick: A) $12 B) $14 C) $5 D) $15 E) $0

Solution: 1/5 x $90 = $15 for sandwich   1/6 x $90 = $45 for museum   1/2 x $90 = $78 for book   $15 + $45 + $18 = $78 spent   $90 - $78 15 +  45 +  18= 
 15 +  45 +  18 = 78
$78 spent   $90 - $78= $12 left over   correct answer $12 90 -  78= 
 90 -  78 = 12
$12 left over   correct answer $12
Answer: A
What will be the vulgar fraction of 0.75 Select the correct option.
A) 3/5  B) 3/4  C) 3/2  D) 3/7  E) 3/8

Solution: Explanation:   0.75 = 75/100 = 3/4   Option 3/4
Answer: B
If five men together completes a job in 5 days then for the same job how many mens are required to complete it in a day.	Choose the correct option
A) 20	B) 10	C) 25	D) 15	E) 24

Solution: work completed in a day by one men = 1/25 = (1/5)*(1/5)   So it takes 25 men to complete this job = 25 * (1/25)= 
25 * (1/25) = 1
1   Answer: 25
Answer: C
A and B enter into partnership. A supplies whole of the capital amounting to Rs. 45000 with the condition that the profits to be equally divided and that B pays A interest on half of the capital at 10% per annum, but receives Rs. 120 per month for carrying on the concern.Find their total yearly profit when B's income is one half of A's income.
Choose the correct choice from the following answers.
A) 2238  B) 9180  C) 2889  D) 2780  E) 1911

Solution: Let the total profit be Rs. x   Amount paid to 9180 as salary = (120 x 12)   = Rs.1440   Share of each = \inline (\frac{x-1440}{2})   Interest paid by 9180 = \inline \frac{22500\times 10}{100}=Rs.2250   Total money received by A = \inline \frac{x-1440}{2}+2250   = Rs.\inline (\frac{x+3060}{2})   Total money received by 9180   \inline [(\frac{x-1440}{2})+1440-2250]= (\frac{x-3060}{2})   \inline \Rightarrow \frac{1}{2}-(\frac{x+3060}{2})-(\frac{x-3060}{2})   \inline \Rightarrow x=9180   Answer:9180
Answer: B
A 220 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?	Select.
A) 280
B) 270
C) 260
D) 250
E) 240

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 220)/9 = 500/9 => x = 280.   280nswer: Option 280
Answer: A
If a person walks at 16 km/hr instead of 12 km/hr, he would have walked 20 km more. The actual distance traveled by him is?	Choices
A) 50
B) 65
C) 70
D) 61
E) 60

Solution: Let the actual distance traveled be x km. Then,   x/12 = (x + 20)/16   x - 60 =>x = 60km.   Answer: 60
Answer: E
If Jack walked 8 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?	Options:	A) 4	B) 4.5	C) 6	D) 6.4	E) 15

Solution: 6.4istance walked in 1 hour and 15 mins = 8 miles   Speed per hour = 6.4istance/Time = 8/(5/4)= 
8/(5/4) = 32/5 = around 6.4
6.4 miles per hour   Answer 6.4
Answer: D
The average of first ten prime numbers which are odd is?	Choose one:
A) 15.5 B) 15.0 C) 15.9 D) 15.8 E) 15.1

Solution: Sum of first 10 prime no. which are odd = 158   Average = 158/10= 
158/10 = 79/5 = around 15.8
15.8   Answer:15.8
Answer: D
There are some pigeons and hares in a zoo. If heads are counted, there are 140. If legs are counted, there are 580. The number of hares in the zoo is?  Choices:  A) 120  B) 182  C) 190  D) 150  E) 137

Solution: 140*2= 
140*2 = 280
280   580   -----   300   1----2   ?----300= 150   Answer:150
Answer: D
If a population of women in a town is 40% of men . What is the population of men as a % of population of women ?
Pick one
A) A)200%	B) B)100%	C) C)50%	D) D)65%	E) E)110%

Solution: We're told that the number of Women in a town is equal to 40% of the number of Men in that town.   IF....   Men = 10   Women = 4   We're asked for the number of Men, as a percentage of the number of Women.   M/W = 10/4=5/ 2 = 250%   200%nswer is 200%
Answer: A
How can you get 81 using the digits 2, 3, 25, 50, 75, 100 only once using any of the arithmetic operators?
Choose the correct answer
A) 81	B) 82	C) 87	D) 98	E) 57

Solution: since 3^2 = 9 and 9^2 = 81,   ie , (3^2)^2 = 81   (3*3)^2 = 81   so,   [3*{(100+50-75)/25}]^2 = 81   81NSWER:81
Answer: A
A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 61, how many questions did Student A answer correctly?  Select the correct option:  A) 55  B) 60  C) 73  D) 81  E) 87

Solution: let the number of correct responses be x   then the number of incorrect responses =100-x   according to question   x-2(100-x)=61 (subtracting twice of incorrect from correct)   3x=261   x=87   ANSW87R:87
Answer: E
John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?	Choices:
A) 3 2/5 Km	B) 3 1/5 Km	C) 4 1/5 Km	D) 5 1/5 Km	E) None

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 4*6/2 * 16/6   = 24/2 * 16/60   = 8 * 2/5   = 16/5 = 3 1/5 Km   3 1/5 Km
Answer: B
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?  Choose the correct choice from the following.
A) 767 m
B) 240 m
C) 187 m
D) 176 m
E) 186 m

Solution: Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x = 240 m.   Answer:240 m
Answer: B
There is a 50% chance Jen will visit Chile this year, while there is a 25% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?[/b]	Choose one:
A) 25% B) 50% C) 62.5% D) 63.5% E) 75%

Solution: The thing to note in the question is she would not be visiting both.   Thus p(Chile)*(1-p(Madagascar))+p(Madagascar)*(1-p(Chile))   which is   (1/2*3/4) + (1/4*1/2),   3/8*1/8=1/2 =50%   Answer: 50%
Answer: B
Simple interest on a certain sum of money for 2 years at 12% per annum is half the compound interest on Rs. 6000 for 2 years at 15% per annum. The sum placed on simple interest is	Options:  A) Rs.6000  B) Rs.7935  C) Rs.8265.63  D) Rs.3967.5  E) None

Solution: Solution   C.I.	=Rs[6000x(1+15/100)Â²-4000]   Rs.(4000x115/100x115/100-6000)	= Rs.7935.   Sum	=Rs. [3967.5x100 /4x12]   = Rs.8265.63.   Answer Rs.8265.63
Answer: C
What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 60 ?
Choose the correct choice from the following choices:  A) 170  B) 128  C) 173  D) 129  E) 136

Solution: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.   Immediate two prime numbers after 60 are - 61 and 67   Sum = 61 + 67= 
61 + 67 = 128
128   Answer - 128
Answer: B
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually Select the correct option: A) 3489 B) 3109 C) 2788 D) 2776 E) 1991

Solution: Explanation:   Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.   Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]   =Rs. [8000 * (23/20) * (23/20) * (21/20)]   = Rs. 11109. .   :. C.I. = Rs. (11109 - 8000) = Rs. 3109.   Answer: 3109) 3109
Answer: B
The average consumption of petrol for a car for seven months is 110 litres and for next five months it is 86 litres. The average monthly consumption is ?	Answers:
A) 96 litres  B) 98 litres  C) 100 litres  D) 102 litres  E) None

Solution: Answer   Average = ( sum of consumption of petrol in first 7 months + sum of consumption of petrol in last 5 months. ) / 12   Average = ( 110 x 7 + 86 x 5 ) / 12   =(1200 / 12 = 100 liters   100 litresorrect Option: 100 litres
Answer: C
A train which has 430 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ? Choices:
A) 56 sec
B) 43 sec
C) 36 sec
D) 29 sec.
E) 19 sec.

Solution: Time taken to cross a moving person = length of train/ relative speed   Time taken = 430/((45-9) (5/18)   = 430/ 36*(5/18)   = 430/10= 
430/10 = 43
43 sec   ANSWER:43 sec
Answer: B
In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. what is the age of Janice after 3 years ?	Pick one
A) 12  B) 36  C) 40  D) 42  E) 45

Solution: Let Jane's age be J and daughters' age be D...   Given J   + 3= 
  + 3 = 3
3(D + 3 )=> J - 6 = 3D -> Eq1.   Given J-6 = (D-6)^2 --> Eq 2..   sub J-6 value in eq 2... 3D = D^2 - 12D + 36.   0 = D^2 - 15D + 36 => D = 12 or D = 3.   When D = 12 we get from eq 1... J+3 = 45 => J =42+ 3 = 45..   When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15+ 3= 18..   IMO option 45 is correct answer..
Answer: E
Tough and Tricky questions: Arithmetic.
(18^2 + 18^2)/6^2 = Choose the most appropriate option
A) 4
B) 8
C) 27
D) 58
E) 116

Solution: Ans is 27   my approach was:   (18^2 + 18^2)/6^2 =18(18+18)/6*6   =18*36/6*6=3*9= 
3*9 = 27
27   27
Answer: C
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?	Choose the correct answer:  A) 26  B) 27  C) 24  D) 18  E) 11

Solution: Explanation:   You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither   78 = (41-9) + (22-9) + 9 + neither.   Not enrolled students = 24   Answer: 24
Answer: C
The first five numbers in a regular sequence are 4, 9, 19, 37, and 75 What is the next number in the sequence?  Choose the correct choice from the following answers.
A) 142	B) 154	C) 176	D) 182	E) 151

Solution: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..   when we see the sequence 4, 9, 19, 37, and 75., we see that each succeeding number is some value more than twice the previous number..   9=2*4+1..   19=2*9+1..   and so on..   so next number= 2*75+1=151..   151
Answer: E
The area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm. What is the perimeter of the square? Choose the correct option:
A) 289 cm  B) 200 cm  C) 829 cm  D) 288 cm  E) 289 cm

Solution: Area of the square = s * s   = 5(50 * 10)   => s = 50   = 50 cm   Perimeter of the square   = 4 * 50= 
4 * 50 = 200
200 cm.   Answer: 200 cm
Answer: B
A can give B 50 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race? Choose one
A) 157.89	B) 157.13	C) 157.22	D) 111.0	E) 111.12

Solution: A runs 1000 m while B runs 950 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/950   = 842.10 m.   B can give C = 1000 - 842.10   =157.89m.   157.89nswer:157.89
Answer: A
The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:	Choose the correct choice from the following choices.
A) 33
B) 30
C) 38
D) 37
E) 27

Solution: Explanation:   pool : kerosene   3 : 2(initially)   2 : 3(after replacement)   \frac{Remaining\: (or \: left) \: quantity}{initial\: quantity}=\left ( 1-\frac{replaced\: quantity}{total\: quantity} \right )   (for petrol) \frac{2}{3}=\left ( 1-\frac{10}{k} \right )   \Rightarrow \frac{1}{3}=\frac{10}{K}   \Rightarrow K=30l   Therefore the total quantity of the mixture in the container is 30 liters.   Answer: 30) 30
Answer: B
The original price of a certain TV set is discounted by q percent, and the reduced price is then discounted by 2q percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
Choose the correct choice from the following answers:
A) P(1 - 0.03x + 0.02x^2)
B) P(1 - 0.03w + 0.0002w^2)
C) P(1 - 0.03x + 0.002x^2)
D) P(1 - 2x^2)
E) P(1 - 3x + 2x^2)

Solution: Youcansolve this problem with number plugging.   Say the original price was $10 and q=50. Then after the first reduction the price would become $5 and after the second reduction of   2*50= 
  2*50 = 100
100% the rprice would become $0.   Now, since P is not zero, then the expression in the brackets must be zero for q=50. Only answer choice B works.   Answer: B.   On this problem - number pluggin is not giving me the answer.. I initially used q = 10, then 2q = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.   100 (1-0.03(10) + 0.0002 (10)^2)   100 (1-0.3 + 0.0002 (100))   100 (0.7 + 0.02)   100 (0.68) = 68????   double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice P(1 - 0.03w + 0.0002w^2)..
Answer: B
Jar X is 1/2 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity? Select
A) 3/4
B) 5/6
C) 7/8
D) 5/8
E) 7/12

Solution: Let P be the capacity of Jar X.   The amount of water in Jar Y is 1/2*P/2=P/4   Then the total amount in Jar X is P/2+P/4=3P/4   The answer is 3/4.
Answer: A
In a simultaneous throw of pair of dice .find the probability of getting the total more than 7  Pick one.
A) 4/5
B) 5/12
C) 7/9
D) 12/7
E) 4/3

Solution: Here n(S)=(6*6)= 
(6*6) = 36
36   let E=event of getting a total more than 7   ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}   P(E)=n(E)/n(S)=15/36=5/12   Ans: 5/12
Answer: B
5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?  Choose one:
A) 3800
B) 4200
C) 4400
D) 4500
E) 4600

Solution: X * (95/100) * (85/100) = 3553   X = 4400   ANSWER:4400
Answer: C
On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.10 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?  Choose the correct choice
A) 0.027  B) 0.271  C) 0.417  D) 0.657  E) 0.9

Solution: Probability he hears a song is like:   Tune to A and likes what he is hearing = 0.1   Tune to A, don't find he like what they are airing, then tune to 0.271 and likes what he finds there = 0.9 * 0.1= 
0.9 * 0.1 = 0.09
0.09   Tune to A, finds crap there, Tune to 0.271, hears a similar crap, Tune to C and finally falls in love with the program= 0.9^2 * 0.1 = 0.081   Total = 0.271   Ans 0.271
Answer: B
If x is an even integer and x/18 is an odd integer, which of the following is NOT an even integer?
Choose the correct choice from the following options
A) (x^2)/54 B) (x^2)/24 C) (x^2)/9 D) (x^2)/6 E) (x^2)/2

Solution: since x is an even integer and x/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the x/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)   now, any expression in which we have 4 at the denominator will be odd. out of the given options only 24 is a multiple of 4. hence answer should be (x^2)/24
Answer: B
Convert the following unit:
3 hectares in m²	Select the correct option
A) 15000 m²  B) 18000 m²  C) 20000 m²  D) 28000 m²  E) 30000 m²

Solution: 3 hectares in m²   1 hectare = 10000 m²   Therefore, 3 hectares = 3 × 10000 m²   = 30000 m²   ANSW30000 m²R : OPTION 30000 m²
Answer: E
A began business with 6000 and is joined afterwards by B with 24000. When did B join, if the profits at the end of the year are divided equally?	Choose the correct choice from the following options.
A) 8 months
B) 9 months
C) 10 months
D) 7 months
E) None of these

Solution: Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.   ∴ Profit ratio is 12 × 6000 : (12 – x) × 24000   or 12 : 4(12 – x)   Since profit is equally divided so   12 = 4(12 – x) or x = 9. Thus B joined after 9 months.   Answer 9 months
Answer: B
On the shelf, there are four books of poetry, four novels, and six reference works. Suppose we picked two books at random. What is the probability that we pick one novel and one reference work? Pick:
A) 18/85	B) 20/87	C) 22/89	D) 24/91	E) 26/93

Solution: We could pick one novel and then one reference work, or, we could choose one reference work and then one novel.   P(one novel and one reference work) = 4/14*6/13 + 6/14*4/13 = 24/91   The answer is 24/91.
Answer: D
A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days?	Answers.
A) 327 B) 367 C) 360 D) 265 E) 171

Solution: Let xx be the number of parts the woodworker normally makes daily. In 24 days he makes 24⋅x24⋅x pieces. His new daily production rate is x+5x+5 pieces and in 2222 days he made 22⋅(x+5)22⋅(x+5) parts. This is 80 more than 24⋅x24⋅x. Therefore the equation is:   24⋅x+80=22(x+5)24⋅x+80=22(x+5)   30=2x30=2x   x=15x=15   Normally he makes 15 parts a day and in 24 days he makes 15⋅24=36015⋅24=360 parts.   Answer:360
Answer: C
At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 3 years?	Choose the correct option.
A) 4 %  B) 3 6/7 %  C) 4.76 %  D) 5 %  E) 6 %

Solution: Explanation:   250 = (1750x3xR)/100   R = 4.76 %   Answer: Option 4.76 %
Answer: C
A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/3 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
Select
A) 3/7
B) 2/7
C) 1/4
D) 2/3
E) 5/7

Solution: Rate of the small pump is 1/2 tank/hour   Rate of the larger pump is 1/(1/3) or 3 tank/hour;   Combined rate of the two pumps is 1/2+3=7/2 tank/hour, together they will fill the empty tank in 1/(7/2) = 2/7 hours (time=job/rate).   Answer: 2/7
Answer: B
There are 70 people and 3 clubs M, S, and Z in a company. 18 people joined M, 20 people joined S and 13 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?
Answers.
A) 24 B) 26 C) 28 D) 30 E) 32

Solution: Answer E.   key is 'atmost' here.   so 18 people joined M.   20 people joined S and 13 people joined Z. to get maximum people who did not join any club, 13 people who joined Z are among 20 people who joined S.   so 20+18= 
20+18 = 38
38   70-38= 
70-38 = 32
32
Answer: E
Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?	Options:
A) -33
B) 33
C) 35
D) 47
E) 49

Solution: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.   Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.   So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.   Solving this equation for d+ed+e gives d+e=−66d+e=−66.   Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.   Hence, the answer is -33: -33
Answer: A
The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?  Choose the correct choice:
A) 38 cm2  B) 85 cm2  C) 65 cm2  D) 45 cm2  E) 35 cm2

Solution: Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 36/2= 
2.5 * 36/2 = 45
45 cm2   Answer:45 cm2
Answer: D
Mike works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 500 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 62,500. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?  Select the correct option.
A) 13000  B) 12500  C) 13500  D) 14000  E) 15000

Solution: let the rate be x, then population of the bacteria after each hour can be given as 500,500x, 500(x^2), 500(x^3)   now population at 4pm =62,500   thus we have 500(x^3) = 62,500 =125   thus x=5   therefore population at 3pm = 500(25) = 12500   Answer : 12500
Answer: B
If the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ? Choose the most appropriate option:	A) 275m	B) 360m	C) 375 m	D) 420 m	E) 480 m

Solution: The distance traveled in 30 sec = 45*(5/18) *30= 
45*(5/18) *30 = 375
375m   Answer: 375 m
Answer: C
A man walks from B to C, a distance of x miles, at 8 miles per hour and returns at 10 miles per hour. What is his average speed?	Choose the most appropriate option:
A) 10 mph
B) 9.6 mph
C) 8.8 mph
D) 8.4 mph
E) 4 mph

Solution: Total distance covered = 2x   Time taken12miles / hour = x/10 hrs   Time taken @ 8 miles / hour = x/8 hrs   Avg speed = 2x / (x/8 + x/10) = 8.8 mph   Ans is 8.8 mph
Answer: C
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?  Select:
A) 5/7
B) 5/1
C) 5/2
D) 5/6
E) 5/9

Solution: P(at least one graduate) = 1 - P(no graduates)   = 1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8)   = 5/6   Answer: 5/6
Answer: D
suppose that jody drove 80 miles in 2 hours. dividing 80 by 2 tells us how many mile jody drove in each hour. the unit for this rate are miles per hour(miles/hr). if we divide 2 by 80 what information would this give us? give an interpretation of the rate. what unit would be used for this rate?	Answers.
A) mile/hours
B) hours/mile
C) minutes/mile
D) km/hours
E) none

Solution: speed= distance/time, here speed=distance covered in 1 hour. total distance 80 miles divided by total time 2 hours= 80/2. miles/ hour= 40 mile/hour. jody drove 40 miles in hour. correct answer : (hours/mile)
Answer: B
A train 110 m long running at 52 kmph crosses a platform in 30 sec. What is the length of the platform?	Choose the correct choice from the following answers:  A) 287  B) 398  C) 323  D) 245  E) 267

Solution: D = 52 * 5/18 = 30   = 433 â€“ 110   = 323   Answer: 323
Answer: C
|x+3| – |4-x| = |8+x| How many K solutions will this equation have? Choose the most appropriate option:
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: |x| = x when x >= 0 (x is either positive or 0)   |x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,   |0| = 0 = -0 (all are the same)   So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.0
Answer: A