MU-NLPC/Calc-aqua_rat huggingface dataset:
The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 33 years, then find the age of the person sitting in the middle of the row?
Choose the correct answer.
A) 9 years	B) 22 years	C) 18 years	D) 19 years	E) 17 years

Solution: Total age seven persons = (28 * 7)years   Total age of the first three persons and the last three persons are (25 * 3) years and (33 * 3) years respectively.   Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 33 * 3 = 196 - 75 - 99= 
196 - 75 - 99 = 22
22 years.   ANSWER:22 years
Answer: B
One type of liquid contains 20% of water and the second type of liquid contains 35% of water. A glass is filled with 10 parts of 1st liquid and 4 parts of 2nd liquid. The percentage of water in the new mixture in the glass is?  Choose the correct option:  A) 22.15%  B) 23.5%  C) 24.3%  D) 25%  E) 29.6%

Solution: Required percentage = (20% of 10 + 35% of 4)/10+4 *100   = 3.4/14 * 100 = 24.3%   Answer is 24.3%
Answer: C
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Choose the correct choice from the following:
A) 3100
B) 210
C) 21300
D) 25200
E) 24400

Solution: Number of ways of selecting 3 consonants from 7 =7C3   Number of ways of selecting 2 vowels from 4 = 4C2   Number of ways of selecting 3 consonants from 7 and 2 vowels from 4   = 7C3 × 4C2   = 210   It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).   Number of ways of arranging 5 letters among themselves   =5! = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   Hence, required number of ways=210×120=25200   option - 25200
Answer: D
A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 450 bolts?	Choose the correct choice from the following choices:
A) 36
B) 72
C) 120
D) 144
E) 108

Solution: Old Machine   100 bolts in 60 mins   so,   5/3 bolts in 1 min   New Machine   150 bolts in 60 mins   so,   5/2 bolts in 1 min   together,   5/3 + 5/2 =   25/6 bolts in 1 min   so, for 450 bolts   450 * 6 / 25= 
450 * 6 / 25 = 108
108 mins   Ans 108
Answer: E
In a box, there are 9 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
Pick.
A) 2/3
B) 8/21
C) 3/7
D) 9/22
E) 10/21

Solution: Explanation:   Total number of balls = (9 + 7 + 6)= 
(9 + 7 + 6) = 22
22   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(E) = 9/22.   Answer: Option 9/22
Answer: D
Two sides of a triangle have length 5 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 12
III. 24
Select.
A) I, II, and III	B) I and II only	C) II and III only	D) I and III only	E) I only

Solution: Answer = A. I, II, and III   With dimensions of only 2 sides given (for a triangle), this becomes an open ended question   I, II, and IIIny area is possible out of the three
Answer: A
The sum of first five prime numbers is:
Choices.
A) 11
B) 18
C) 26
D) 28
E) 35

Solution: Explanation:   Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28.   Note: 1 is not a prime number.   Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.   ANSWER IS 28
Answer: D
Mixture S is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture S, how many kilograms of mixture S must be added to make a 70% material B in the new mixture?  Answers.
A) A)6	B) B)7	C) C)8	D) D)9	E) E)10

Solution: Can be done with weighted avg method.   if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .   S1=20(initial mix.)   Avg. is what we need..ie 70% of material B means 30% of oil   S2=36(36% of 10 kg mix)   w1/w2=(S2-Avg)/(Avg-S1)   (36-30)/(30-20)   6/10   means for every 10 kg of new mix. we need 6 kg of mix S   6ns 6
Answer: A
You collect baseball cards. Suppose you start out with 21. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?	Pick one
A) 17 B) 18 C) 19 D) 20 E) 27

Solution: Solution   Start with 21 baseball cards.   Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 21 + 1 which is 11,   so you're left with   21 - 11= 
  21 - 11 = 10
10.   Peter takes 1 baseball card from you:  10 - 1= 
 10 - 1 = 9
9 baseball cards.   Paul triples the number of baseball cards you have: 9 Ã— 3= 27 baseball cards.   So you have 27 at the end.   Correct answer : 27
Answer: E
What number times (1⁄2)^2 will give the value of 2^3?  Choose the correct answer:
A) 2
B) 4
C) 8
D) 16
E) 32

Solution: x*(1/2)^2 = 2^3   x = 2^2*2^3 = 2^5 = 32   The answer is 32.
Answer: E
Randy'sbar serves customers every weeknight from 4 pm to 1 am. In Randy's bar,Silvermoonbeer is sold at a constant rate except during happy hour, from 6:30 to 7:30 pm, when the rate triples.
If a keg of Silvermoon beer is half empty at 5pm on Monday, and two-thirds empty at the beginning of the happy hour, when will it be completely empty?  Options: A) Monday, 7:30 pm B) Monday, 9 pm C) Monday, 7 pm D) Monday, 6:45 pm E) Monday, 9:30 pm

Solution: Let the keg be a 150 Litre keg   At 5 pm.. There are 75 litres   At 6:30 pm there are 50 litres.   So, consumption rate is 25 litres per 1.5 hours.   So it will take 3 hours to finish 50 litres at this rate.   During happy hour it sells 3 times faster. So, rate = 1 hour per 50 litres.   So, keg becomes empty at 6:30 + 1 hour = 7 pm   Answer is Monday, 7 pm
Answer: C
An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 55 meters. How many times did the ball bounce?
Select the correct option:
A) 5  B) 6  C) 3  D) 8  E) 9

Solution: Going down = 20 m   Going Up = 10 --> Total = 30   Going down = 10 --> Total = 40   Going Up = 5 --> Total = 45   Going down = 5 --> Total = 50   Going up = 2.5 --> Total = 52.5   Going down = 2.5 --> Total =55(3aught)   No of bouncing = 3   Answer : 3
Answer: C
The difference between the compound interest and simple interest accrued on an amount at the end of three years at the rate of 12% is Rs.381.888. What is the amount?
Choose the correct choice from the following:
A) Rs. 9500
B) Rs. 8400
C) Rs.8500
D) Rs.8200
E) Rs.7200

Solution: Explanation:   C.I = P[(1+R/100)T - 1]   = P[(1+12/100)3 - 1] = P[(28/25)3 - 1]   = P[(21952/15625) - 1]   = 6327P/15625   S.I = (P x 3 x 12)/100 = Rs. 9P/25   6327P/15625 - 9P/25 = 381.888   => 702P/15625 = 381.888   => P = (381.888 x 15625)/702   = Rs. 8500   Answer: Option Rs.8500
Answer: C
14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term Y of the sequence?  Choose the correct option.
A) 360
B) 365
C) 369
D) 374
E) 383

Solution: First term , a= 14   Common difference , d = 9   nth term , tn = a + (n-1)d   41st term Y, t41 = a+ 40*d = 14 + 40*9= 
14 + 40*9 = 374
374   Answer 374
Answer: D
For all integers a and b, a%b = (a + b)(a - b). If 4%x = 7, then which of the following could be a value of x?	Choose the correct choice from the following.
A) -4	B) -3	C) 2	D) 4	E) 6

Solution: 4%x = (4+x)(4-x)   16-x^2 = 7   x^2 = 9   x=-3,3   Ans: -3
Answer: B
A invested $400 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find A shares?
Select the correct option
A) $100
B) $75
C) $20
D) $120
E) $80

Solution: A:B = 400*12:200*6   A:B = 4:1   A's share = 100*4/5= 
100*4/5 = 80
$80   Answer is $80
Answer: E
A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
Pick one
A) 480	B) 487	C) 481	D) 729	E) 268

Solution: 1/x - 1/20 = -1/24   x = 120   120 * 4= 
120 * 4 = 480
480   480nswer:480
Answer: A
A full-time employee’s hourly wage was increased by 10%. He decided to decrease the number of hours worked per week so that his total income did not change. By approximately what percent should the number of hours worked be decreased?
Pick
A) 7%	B) 9%	C) 25%	D) 50%	E) 100%

Solution: Let's plug in somenicenumbers and see what's needed.   Let's say the employee used to make $1/hour and worked 100 hours/week   So, the TOTAL weekly income was $100/week   After the 10% wage increase, the employee makes $1.10/hour   We want the employee's income to remain at $100/week.   So, we want ($1.10/hour)(new # of hours) = $100   Divide both sides by 1.10 to get:   new # of hours = 100/1.10   ≈ 90 hours   So, the number of hours decreases from 100 hours to (approximately) 90 hours.   This represents a 10% decrease (approximately) .   Answer choice 9% is the closest answer.
Answer: B
A train passes a station platform in 37 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose the correct choice from the following answers:
A) 248 m	B) 240 m	C) 277 m	D) 255 m	E) 176 m

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/37 = 15 ==> x + 300 = 555 ==> x   = 255 m.   Answer: 255 m
Answer: D
A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
Answers
A) 55 kmph  B) 45 kmph  C) 54 kmph  D) 35 kmph  E) 65 kmph

Solution: B   45 kmph   Let the distance to be travelled to catch the bus be x km   x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km   By traavelling 30 kmph time taken = 60/30= 
60/30 = 2
2 hours   By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed= 60/(4/3)= 
60/(4/3) = 45
45 kmph.
Answer: B
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is? Answers.
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: US = 25   DS = 35   M = (35 - 25)/2= 
(35 - 25)/2 = 5
5   5nswer: 5
Answer: A
Double of Quarter of 2 percent written as a decimal is :  Select:
A) 0.01 B) 0.0005 C) 0.25 D) 0.005 E) None of these

Solution: Explanation :   Solution: (2)*(1/4)*2% = 2*(1/4 * 2/100) = 0.01.   0.01nswer : 0.01
Answer: A
A shopkeeper sells 200 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? Select the correct option
A) 12  B) 27  C) 29  D) 55  E) 95

Solution: SP per metre = 18000/200 = Rs. 90 Loss per metre = Rs. 5 CP per metre = 90 + 5 = Rs. 95.Answer: 95
Answer: E
Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Choose the correct choice from the following answers:
A) 635.5	B) 635.59	C) 635.51	D) 635.56	E) 635.52

Solution: Explanation:   4000   200 ---- I   200   10 ---- II   ---------------   4410   2210   --------   2000   110 ---- III   110   5.50 ---- IV   -----------   2425.50   2210   -----------   4635.50   4000   ----------   635.50   635.5nswer:635.5
Answer: A
Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other. What is the distance between the two stations?  Choose the correct choice from the following choices.
A) 540 km  B) 767 km  C) 276 km  D) 178 km  E) 176 km

Solution: Explanation:   Let us assume that trains meet after 'x' hours   Distance = speed * Time   Distance traveled by two trains = 20x km and 25x km resp.   As one train travels 60 km more than the other,   25x – 20x = 60   5x = 60   x = 12 hours   As the two trains are moving towards each other, relative speed = 20 + 25= 
20 + 25 = 45
45 km/hr   Therefore, total distance= 45*12= 
45*12 = 540
540 km.   540 kmNSWER: 540 km
Answer: A
John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount Q of dollars he could have spent for the $12 tickets? Choose the correct choice from the following answers.
A) $48  B) $60  C) $84  D) $96  E) $120

Solution: 60 ..... 12 *5 Q= 60. (min). Thus answer .$60
Answer: B
If p^2 – 13p + 40 = s, and p is a positive integer between 1 and 10, inclusive, what is the probability that s < 0?  Choose the most appropriate option
A) 1/10  B) 1/5  C) 2/5  D) 3/5  E) 3/10

Solution: p2 – 13p + 40 = s   so (p – 8)(p – 5) = s   For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.   The correct answer is 1/5.
Answer: B
Dacid obtained 61, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?  Choose one
A) 29  B) 72  C) 39  D) 37  E) 75

Solution: Average = (61 + 65 + 82 + 67 + 85)/5= 
(61 + 65 + 82 + 67 + 85)/5 = 72
72   Answer: 72
Answer: B
Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 42 percent were employees, what percent were stockholders who were not employees?  Choices
A) 34% B) 58% C) 45% D) 53% E) 62%

Solution: Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M   were stockholders and 42% of M or 0.42M were employees, it follows that 0.62M +   0.42M = 1.04M were either stockholders, employees, or both. Since 1.04M exceeds   M, the excess 1.04M − M = 0.04M must be the number of attendees who were both   stockholders and employees, leaving the rest 0.62M − 0.04M = 0.58M, or 58%, of   the meeting attendees to be stockholders but not employees.   The correct answer is 58%.
Answer: B
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is?
Choose the correct answer
A) 70 km/hr  B) 75 km/hr  C) 84 km/hr  D) 87.5 km/hr  E) 90.5 km/hr

Solution: Let the speed of two trains be 7x and 8x km/hr.   Then, 8x = [ 400/4= 
400/4 = 100
100   x= [100/8= 
100/8 = 25/2 = around 12.5
12.5   Speed of first train= (7 x 12.5) km/hr = 87.5 km/hr.   Answer is 87.5 km/hr
Answer: D
John and David can finish a job together in 4 hours. If John can do the job by himself in 5 hours, what percent of the job does David do?  Select
A) 20%	B) 25%	C) 24%	D) 23%	E) 22%

Solution: You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 20 donuts which is the job ( I picked this as a SMART number).   John on his own works  20/5= 
 20/5 = 4
4 donuts per hour.   John and David work   20/4= 
  20/4 = 5
5 donuts per hour so David works 1 donuts/hour   To find out the percentage, David works 1 donuts/hr x 4 hours= 4 donuts per hour.   Therefore 4 donuts/20donuts = 1/5 = 20%   20%nswer : 20%
Answer: A
Mario and Nina each have a bag of marbles, each of which contains 18 blue marbles, 10 red marbles, and 12 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?  Choose the correct choice from the following answers
A) 3/4  B) 2/4  C) 1/4  D) 1/8  E) 1/16

Solution: Mario and Nina each select one marble from their respective bags.   Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble   Probability that either Mario or Nina select a red marble = (10/40)*(10/40) + (10/40)*(10/40) = 2*(1/16)   Probability that either Mario or Nina select a red marble = 1/8   Answer would be 1/8.
Answer: D
If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?  Choose the correct option
A) 5%	B) 10%	C) 15%	D) 20%	E) 25%

Solution: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%   10%
Answer: B
The average of first six multiples of 4 is :
Choose the correct choice from the following options:
A) 14	B) 9	C) 12	D) 15	E) 17

Solution: Solution   14verage = 4(1+2+3+4+5+6)/6 =84/6= 
84/6 = 14
14 14nswer 14
Answer: A
Month	Average Price
per Dozen
April $1.10
May $1.20
June $1.08
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
Pick one
A) 1.12  B) 1.16  C) 1.17  D) 1.18  E) 1.19

Solution: Say x dozen eggs were sold in May.   Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.   Total x+2x/3+4x/3=3x dozen eggs were sold in three months.   Total sales: 2x/3*1.1+x*1.2+4x/3*1.08=$3.373x. The average price per dozen 3.37x/3x=$1.124.   1.12
Answer: A
A 12% stock yielding 10% is quoted at:
Choose the correct choice from the following choices: A) Rs. 83.33 B) Rs. 110 C) Rs. 112 D) Rs. 120 E) Rs. 130

Solution: Let the Face value of the stock:Rs.100   Yield=Rs.12   Market value quoted at (12/10)*100=Rs.120   ANSWER:Rs. 120
Answer: D
A train 180 m long running at 70 kmph crosses a platform in 20 sec. What is the length of the platform?
Choose the correct choice from the following answers
A) 208 B) 277 C) 350 D) 881 E) 271

Solution: D = 70 * 5/18 = 20 = 388 – 180 = 208   208nswer: 208
Answer: A
The following questions are based on the information given. Choose the appropriate answer that suits the question based on the information. A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then colored red on the two larger faces and green on remaining. While the other is colored green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up. 21. How many cubes have only one colored face each?  Choose the correct choice from the following options.
A) 32	B) 8	C) 16	D) 24	E) 0

Solution: 16 =2^3 each cube will have 2^3 cubes painted 1 side.   ANSWER:16
Answer: C
What least number should be subtracted from 1,439 so that the remainder when divided by 5, 11, and 13 will leave in each case the same remainder 3 ?  Choose the correct choice from the following answers:
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: The LCM of 5, 11, and 13 is 715. The next multiple is 2*715 = 1,430.   1,430 + {remainder} = 1,430 +3 = 1,433, which is 6 less than 1,439.   Answer: 6.
Answer: E
If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?  Pick:
A) 5:12  B) 7:12  C) 3:11  D) 5:11  E) None of these

Solution: Explanation:   a/d = (3/4)*(7/9)*(5/7) => 5/12   5:12nswer is 5:12
Answer: A
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?  Choose one
A) 10
B) 99
C) 787
D) 62
E) 22

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   D = 50 * 100/18 = 2500/9   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 2500/9 * 18/500= 
2500/9 * 18/500 = 10
10 sec   10nswer: 10
Answer: A
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 44 years now, the son's age five years back was? Pick one
A) 17years
B) 18years
C) 19years
D) 20years
E) 21years

Solution: Let the son's present age be x years. Then, (44 - x) = x   2x = 44.   x = 22.   Son's age 5 years back (22 - 5)= 
(22 - 5) = 17
17 years.   17years)
Answer: A
The population of a town increases 25% and 15% respectively in two consecutive years. After the growth the present population of the town is 1150. Then what is the population of the town 2 years ago? Choose the correct choice from the following.
A) A)400
B) B)500
C) C)600
D) D)700
E) E)800

Solution: 800xplanation:   Formula: (After =100 denominator   Ago = 100 numerator)   1150 * 100/125 * 100/115= 
1150 * 100/125 * 100/115 = 800
800   Answer: Option 800
Answer: E
In how many ways can 8 people, A, B, C, D, E, F, G, H be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other? Pick one:
A) 384 B) 396 C) 576 D) 40224 E) 696

Solution: Number of total arrangements = 8!   Restriction 1= ABC40224 not next to each other --> let say AB and C40224 are considered as one unit, respectively   Restriction 2= AB is not the same as BA + C40224 is not the same as 40224C --> the number will increase by 2*2   Total number of arrangements - Number out of restrictions = Result   8! - (4!*2*2) = 40320 - (24*2*2)= 
40320 - (24*2*2) = 40_224
40224   Answer 40224
Answer: D
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? Answers:	A) 16 2/3% loss	B) 16 2/8% loss	C) 17 2/3% loss	D) 16 87/3% loss	E) 12 2/3% loss

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
Find the probability in a group of 10 students sitting in a row , two of them
always sit next to each other	Choose the correct choice from the following answers.
A) 0.5  B) 0.4  C) 0.3  D) 0.2  E) 0.1

Solution: Assume that these 2 students are 1 and then u can sit is 9! and these 2 students can sit by 2 ways then total ways are 9!*2   and the probability is 9!*2/10! = 1/5= 
1/5 = 1/5 = around 0.2
0.2   ANSWER:0.2
Answer: D
A 270 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?
Choose the correct choice from the following answers:
A) 230  B) 883  C) 739  D) 789  E) 813

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 + 270)/9 = 500/9 => x = 230.   230nswer:230
Answer: A
While driving from A-ville to B-town, Harriet drove at a constant speed of 90 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 160 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?  Choose the correct choice from the following options.
A) 138  B) 148  C) 150  D) 162  E) 192

Solution: 5hr = 300min.   If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.   Now let plug in ans. D or E and verify which one give same distance on each leg.   D. t= 162min   * leg A-B ---> d = 90.192/60 = 17280/60   * leg B-A ----> d = 160*108/60 = 17280/60   so the correct ans. is192
Answer: E
A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is  Choose the correct choice from the following:
A) 250	B) 276	C) 280	D) 285	E) None

Solution: Solution   since the month begins with a sunday , so there will be five sundays in the month.   Required Average	= (510x5+240x25 / 30)   = (8550 / 30)= 
(8550 / 30) = 285
285   Answer 285
Answer: D