MU-NLPC/Calc-aqua_rat huggingface dataset:
At 15:15 pm railway time, what will be the angle between minute and hour hand?	Pick one:
A) 238	B) 360	C) 377	D) 277	E) 291

Solution: At 15:15 both minute and hour hands will be in same position. Hence the angle between them will be zero   degrees. However 360 degree also means both minute and hour hands are in same position. Hence correct answers are   both zero and 360 degrees   Answer:360
Answer: B
John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 5% and the mobile phone at a profit of 10%. Overall how much he make a profit. Choose the correct choice from the following choices.
A) s. 90
B) s. 120
C) s. 200
D) s. 50
E) s. 290

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 5/100) = 15000 - 750   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -750 + 800 = Rs. 50   As this is positive, an overall profit of Rs. 50 was made.   s. 50
Answer: D
Out of first 45 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?  Pick:
A) 17/45  B) 7/45  C) 17/9  D) 7/9  E) 17/27

Solution: n(S) = 45   n(Even no) = 22= n(E)   n(Prime no) = 14 = n(P)   P(EᴜP)   = 22/45 + 14/45 - 1/45   = 35/45=7/9   Answer:7/9
Answer: D
Two of his favorite buildings are Chicago’s Sears (Willis) Tower and
Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and
Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears?	Select:
A) 300	B) 250	C) 130	D) 303	E) 111

Solution: 830-527= 
830-527 = 303
303. Answer is 303.
Answer: D
present ages of Ram and Rahim are in the ratio of 4:3 respectively. Four years ago, the ratio of their ages was 16:11 respectively . what Ram's present age in years?  Choose the correct answer:  A) 27  B) 24  C) 40  D) 20  E) 35

Solution: Ram and Rahim be 4x years and 3x years respectively   (4x-4)/(3x-4)=16/11   11(4x-4)= 16(3x-4), 44x-44=48x-64   x=5, therefore Ram's present age : 4x= 20 years   correct answer(20)
Answer: D
In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5 feet 6 nches. Find the % correction made by the candidate from his stated height to his actual height?
Choices
A) 15	B) 20	C) 18	D) 16.5	E) 25

Solution: His height was = 5 feet 6 inch = 6 + 60= 
6 + 60 = 66
66 inch. Required % correction=66*(1.25-1)= 
66*(1.25-1) = 16.5
16.5   16.5
Answer: D
There are 6 people and 3chairs. In how many ways people can occupy the chairs? Choose the correct choice from the following answers
A) 120
B) 150
C) 240
D) 60
E) 100

Solution: total people = 6   total chairs = 3   1st chair can be occupy in 6ways   2nd chair can be occupy in 5ways   3rd chair can be occupy in 4ways   total number of ways = 6*5*4= 
6*5*4 = 120
120 ways   correct option is 120
Answer: A
A man's speed with the current is 16 km/hr and the speed of the current is 3.2 km/hr. The man's speed against the current is Choose the correct choice:  A) 9  B) 9.6  C) 11  D) 12  E) 13

Solution: Man's rate in still water = (16 - 3.2) km/hr = 12.8 km/hr.   Man's rate against the current = (12.8 - 3.2) km/hr = 9.6 km/hr.   Answer:9.6
Answer: B
A certain series is defined by the following recursive rule: Se=K(Se-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?	Choose the correct choice from the following options.
A) ROOT 2 B) ROOT 3 C) 64*ROOT 3 D) 64*3^1/3 E) 64*3^24

Solution: Ans...D   No need for any GP formula here   The rule is that eth term is K times the (e-1)th term.   1st = 64   2nd = k.64   3rd = k^2.64   .   .   .   9th term = k^8 *64   .   .   .   so 25th = k^24*64   Using this solve for k and substitute k in the equation for the 9th term
Answer: D
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  Choose the correct choice from the following answers: A) Rs.250 B) Rs.280 C) Rs.290 D) Rs.300 E) Rs.380

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 550   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250)
Answer: A
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 676 feet squared, what is the difference between the length and the width of the roof? Choose the correct choice from the following answers.
A) 39. B) 40. C) 42. D) 44. E) 46.

Solution: Let the width= x   x*4x=676   x^2= 169   x= 13   Length= 4*13= 
4*13 = 52
52   difference= 52-13= 
52-13 = 39
39   39. is the answer
Answer: A
In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 3:2:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?
Choose the correct choice.
A) $600 B) $720 C) $675 D) $450 E) $225

Solution: To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:   Household Expenses : Food : Miscellaneous = 3x : 2x : x   Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:   3x + 2x + x = 1,800   6x = 1,800   x =300   Thus, the total amount allocated to food is 2 x 300 = $600.   $600nswer $600.
Answer: A
A company has 65 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made ​​the three courses. How many employees have no training?
Options:
A) A)0  B) B)9  C) C)10  D) D)11  E) E)25

Solution: Total employees=65   studied accounting=22   studied finance=15   studied marketing=14   9 employees have been double counted and one employee has been counted thrice.   Therefore employees who have received training=22+15+14-9-(2*1)   =51-11= 
51-11 = 40
40   25mployees with no training=65-40= 
65-40 = 25
25   Ans=25
Answer: E
A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Choose the correct option:
A) 44%  B) 49%  C) 84%  D) 24%  E) 45%

Solution: g% = 20 + 20 + (20*20)/100= 
20 + 20 + (20*20)/100 = 44
44%   44%nswer: 44%
Answer: A
It takes Avery 2 hours to build a brick wall while Tom can do it in 4 hour. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Choose the correct choice from the following choices
A) 70
B) 20
C) 50
D) 60
E) 30

Solution: Avery takes 2 hours   Tom takes 4 hours   Efficiency of Avery is 1/2 units/hr   Efficiency of Tom is 1/4 units/hr   Combined efficiency of Tom and Avery is 1/2 +1/4 = 3/4 units/hr   Since they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left )   So Time taken by Tom to complete the remaining work will be 1/4/1/4 hours => 1*60= 
1*60 = 60
60 minutes...   Answer will be (60)
Answer: D
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 91 pounds?
Choose the correct choice from the following:
A) 8
B) 7
C) 12
D) 9
E) none of the above

Solution: 8ns is 8:   39 pounds --> 6 days   91 pounds --> x days   x = 91*6/39= 
91*6/39 = 14
14   the animal has already consumed food in 6 days so the the number of days for it's total consumption be 91 pounds is   14-6= 
  14-6 = 8
8
Answer: A
A football team lost 5 yards and then gained 9. What is the team's progress?  Choose the correct choice from the following options:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Solution   For lost, use negative. For gain, use positive.   Progress = -5 + 9= 
-5 + 9 = 4
4 yards   Answer 4
Answer: B
A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or doubled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $40,000 in property taxes, but did not pay until October 15th?	Select:
A) $1,400
B) $1,800
C) $2,400
D) $3,200
E) $22,800

Solution: Original amount = 40,000   Fine for July = 40,000 * 1% = 400   Fine for August = lesser of the 2 , 400+600= 1000 or  400*2= 
 400*2 = 800
800 . Pick 800   Fine for September= 800+600= 
800+600 = 1_400
1400 or  800*2= 
 800*2 = 1_600
1600. Pick 1600   Fine for October= 1600+600= 
1600+600 = 2_200
2200 or  1600*2= 
 1600*2 = 3_200
3200. Pick 3200.   The wording of the question should be have been clearer as total fines should be= 3200+1600+800+400= 
3200+1600+800+400 = 6_000
6000 and NOT 3200.   3200 is the fine ONLY for the month of October!   $3,200
Answer: D
The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 19. Find the sum : Choose the correct choice from the following.
A) 4500 B) 7600 C) 5000 D) 6000 E) None of these

Solution: Sol.(d) Let the sum be 100.   Therefore, SI = 100×5×2100=10100×5×2100=10   and CI = 100(1+5100)2−100100(1+5100)2−100   ∴ =100×21×2120×20−100=414=100×21×2120×20−100=414   Difference of CI and SI = 41⁄4 - 10 = 1⁄4   If the difference is 1⁄4 , the sum = 100   => If the difference is 19, the sum   = 400 × 19 = 7600 Answer 7600
Answer: B
According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 160 six-ounce servings of orange juice?	Choose one:
A) 20 B) 24 C) 28 D) 32 E) 36

Solution: 1 X 12 ounce can of concentrate + 3 X 12 ounce cans of water = 48 ounces of the mixture.   48 ounces of mixture gives  (48 / 6 )= 
 (48 / 6 ) = 8
8 servings.   Thus 1 x 12 ounce can of concentrate is used to produce 8 servings of the mixture.   To make 160 servings of the mixture, we need 160 / 8= 
160 / 8 = 20
20 cans of the concentrate.   The answer is 20.
Answer: A
Given A+B+C+D+E= FG. If FG is Maximum as possible and A,B,C,D,E,F,G all are distinct digits
(0-9) then what is the value of G.	Options.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: A+B+C+D+E=FG   9+8+7+6+5= 
9+8+7+6+5 = 35
35 Here E=G, So it is not possible.   again 9+8+7+6+4= 
9+8+7+6+4 = 34
34 Here also E=G, so it is also not possible   again 9+8+7+5+4= 
9+8+7+5+4 = 33
33 Here F=G   Finally 9+8+6+5+4= 
9+8+6+5+4 = 32
32 In this case condition is satisfies, so all are distinct and value of G=2.   ANSWER:2
Answer: B
If p and q are prime numbers, how many divisors does the product p^3*q^6 have? Choose the correct choice from the following answers.
A) 9 B) 12 C) 18 D) 28 E) 363

Solution: , p^2, p^3 and q, q^1, q^2.... q^6 together   Essentially there are 18 different combinations you can make (3x6)   Also you have to include the different combinations the p and q exponents can be a divisor. There are 3 different p exponents and 6 different q exponents: p, p^2, p^3, q, q^2, q^3... q^6   Also add 1 since "1" can also be a divisor.   18+3+6+1= 
18+3+6+1 = 28
28 , ANSWER:28
Answer: D
If a mixture is 3⁄5 alcohol by volume and 4⁄5 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture? Choose the correct option:
A) 1/3  B) 3/2  C) 3/4  D) 3  E) 3/5

Solution: Should be a sub-600 level Q..   volume= {3/5}/{4/5}=3/4   3/4
Answer: C
At what rate percent of simple interest will a sum of money double itself in 66 years? Choose the correct choice.
A) 6.54 %  B) 4.54 %  C) 1.51 %  D) 1.94 %  E) 5.54 %

Solution: Let sum = x. Then, S.I. = x.   Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 66)   = 100/66 = 1.51 %   ANSWER:1.51 %
Answer: C
If |2x| = 50, what is the sumof all the possible values of x?  Choices:  A) 15  B) 20  C) 25  D) -25  E) 0

Solution: There will be two cases   2x = 50 or 2x = -50   => x = 25 or x= -25   sum of both the values will be  -25 +25= 
 -25 +25 = 0
0   Answer is 0
Answer: E
By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is  Choose the most appropriate option:
A) 25%
B) 35%
C) 20%
D) 23%
E) 30%

Solution: Suppose S.P of 50 mangoes = Rs 50   Therefore, Gain = Rs 10 => C.P = Rs 40   Gain % = 10/40 x 100 = 25%   Gain = 25%   25%NSWER:25%
Answer: A
How many three-digit numbers are there such that all three digits are different and the first digit is not zero? Select: A) 504 B) 648 C) 720 D) 729 E) 810

Solution: The first digit cannot be 0, so there are 9 options for the first digit.   the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1) 9 possibilities for the 2nd digit.   The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2) 8 possibilities for the 3rd digit.   So there are  9 * 9 * 8= 
 9 * 9 * 8 = 648
648 possibilities.   ANSWER:648
Answer: B
A car is traveling at uniform speed. The driver sees a milestone showing a two digit number which is a perfect square, after traveling for an hour the driver sees another milestone with the same digits in reverse order and after another hour the driver sees another milestone containing the same two digits as part of a three digit number. What is the speed of the car?  Choose the correct choice.
A) 30 kmph
B) 40 kmph
C) 50 kmph
D) 60 kmph
E) 45 kmph

Solution: first milestone driver see is 16,second is 61,&third is 106.   so total distance traveled by him=106-16= 
106-16 = 90
90km   time taken=2h   so speed=distance/time=90/2= 
90/2 = 45
45kmph   ANSW45 kmphR:45 kmph
Answer: E
If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 4
III. ab is even
Choose the correct choice from the following choices:
A) I only B) III only C) I and II D) I and III E) I, II, and III

Solution: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even   So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.   III only.letter III only
Answer: B
A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 10 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY?	Select:
A) 6 hours
B) 8 hours
C) 30 hours
D) 12 hours
E) 15 hours

Solution: If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 10 hours in a certain point. So:   (1/3)XY= 10*y --> It took the car 10 hours to travel 1/3 of the distance at a constant speed y.   So if we solve this last equation:   XY= 3*10*y= 30*y --> It will take this car 30 hours in total to reach its final destination.   Answer: 30 hours
Answer: C
A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 5 and 7 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
Pick one:
A) Per month, with savings of $(4a + 4b)
B) Per month, with savings of $(4a - 4b)
C) The two options would cost an equal amount.
D) Per project, with savings of $(4a + 4b)
E) Per project, with savings of $(4a - 4b)

Solution: Per Project, company will pay as follows:   For 5 hours work = a+4b   For 7 hours work = a+6b   Total = 2a+10b   Per Month, company will pay for 12 hours work = a+11b   Total per contract - total per month   5a+7b - (a+11b)   4a-4b   Since a>b Amount 5a+7b(per contract amount) > a+11b (per project amount) by 4a-4b.   Hence per month payment will be cheaper by 4a-4b .   OA Per month, with savings of $(4a - 4b)
Answer: B
15 - 2 + 4 ÷ 1/2 × 8 = ?	Choose one:
A) 272
B) 77
C) 168
D) 56
E) 59

Solution: Explanation:   15 - 2 + 4 ÷ 1/2 × 8 = 15 - 2 + 4 × 2 × 8 = 15 - 2 + 64= 
15 - 2 + 64 = 77
77   Answer: Option 77
Answer: B
What is the least value of x. So that 21x57 is divisible by 3.	Choose the correct option.
A) 2
B) 0
C) 1
D) 3
E) 4

Solution: Explanation:   The sum of the digits of the number is divisible by 3, then the number is divisible by3.   2 + 1 + x + 5 + 7 = 15 + x   Least value of x may be 0   Therefore  15 + 0= 
 15 + 0 = 15
15 is divisible by 3.   Answer: Option 0
Answer: B
Pipe A can fill a tank in 20 Mins and pipe B can fill it in 30 Mins. If both the pipes are opened in the empty tank. In how many Mins will it be fill exact half of the tank? Pick one.
A) 4 mins  B) 5 mins  C) 6 mins  D) 7 mins  E) 8 mins

Solution: Part filled A in 1 hr= (1/20)   Part filled B in 1 hr= (1/30)   Part filled by (A+B) together in 1 hr=(1/20)+(1/30)=1/12   So, The tank will be full in 12 mins   Time taken to fill Exact half tank = 12/2= 
12/2 = 6
6 Mins.   Answer : 6 mins
Answer: C
The area of playground is 5800 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
Answers:
A) a) $144  B) b) $150.50  C) c) $162  D) d) $158.60  E) e) $160.70

Solution: total volume * unit cost = total cost   or, 5800 * 0.01 * 2.8 = total cost = 162=c) $162
Answer: C
A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $75000 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
Select: A) 5 B) 6 C) 9 D) 10 E) 15

Solution: Since the starting point is given as the $4000 scholarship,   Assume $4000 scholarships to be x   By the given information, $2500 scholarships = 2x   and $1250 scholarships = 6x   Gievn: Total $1250 scholarships = $75000   6x*1250 = 75000   Solve for x = 10   Option 10
Answer: D
A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?  Choose the correct answer:
A) 60km/hr	B) 54km/hr	C) 50km/hr	D) 45km/hr	E) 62km/hr

Solution: Number of gaps between 21 telephone posts = 20   distance travelled in 1 minute = 50*20= 
50*20 = 1_000
1000m= 1km   speed = 60km/hr   60km/hrnswer is 60km/hr
Answer: A
Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?	Choose the correct choice from the following choices.
A) 3 B) 3.3 C) 3.5 D) 3.6 E) None

Solution: Explanation: In this simple subtraction series, each number decreases by 0.4.   Answer: Option 3.6
Answer: D
A tempo is insured to an extent of 4/5 of its original value. If the premium on it at the rate of 1.3% amounts to $910, The original value of the tempo is? Choose the correct choice from the following.
A) 92500	B) 75230	C) 65990	D) 45280	E) 87500

Solution: Let the original value of the tempo is $x   1.3% of 4/5 of x = 910   (13/10)*(1/100)*(4/5)x = 910   x = $ 87500   Answer is 87500
Answer: E
A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? Select:	A) 27	B) 89	C) 29	D) 20	E) 22

Solution: Speed = 240/24= 
240/24 = 10
10 m/sec.   Required time= (240 + 650)/10= 
(240 + 650)/10 = 89
89 sec.   Answer:89
Answer: B
#p is defined as 2p+20 for any number p. What is p, if #(#(#p))=-4? Answers.
A) –108	B) –44	C) 10	D) -18	E) 18

Solution: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = -4 ---> 8p= -144 ---> p = -18, -18 is the correct answer.
Answer: D
When x - p is divided by p - 2, the quotient is n and there is no remainder. Which of the following must be the value of x? Choose the correct answer.
A) n(p +1)
B) n(p − 1)
C) p(n + 1) + 2n
D) p(n - 1) + n
E) n(p + 1) (p − 1)

Solution: Given in question (x-p)/p-2= n   => x-p= n(p-2)   =>x= np+2n+p   or x= np+p+2n   Now we are good to check the options   x= p(n+1) + 2n   Answer p(n + 1) + 2n
Answer: C
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder	Choose the correct answer
A) 1245	B) 1345	C) 1455	D) 1577	E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
A group of people participate in some curriculum, 25 of them practice Yoga, 15 study cooking, 8 study weaving, 2 of them study cooking only, 7 of them study both the cooking and yoga, 3 of them participate all curriculums. How many people study both cooking and weaving? Select.
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Both cooking and weaving = 15 - (2+3+7)= 
15 - (2+3+7) = 3
3   So, the correct answer is 3.
Answer: C
A walks at 30 kmph and 30 hours after his start, B cycles after him at 50 kmph. How far from the start does B catch up with A?	Choose the correct option.
A) 1200km  B) 1500km  C) 2000km  D) 2250km  E) 3600km

Solution: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.   x/30 - x/50 = 30   x = 2250 km   Answer is 2250km
Answer: D
A man cycled 25 kilometer in 1 hour 40 minutes. what was the average speed of cylcle in kilometer per hour? Choose the most appropriate option.
A) 7 miles / hour  B) 9 miles / hour  C) 10 miles / hour  D) 13 miles / hour  E) 15 miles / hour

Solution: We first convert the time of 1 hours 10 minutes in minutes   1 hours 10 minutes = 1* 60 + 40= 
1* 60 + 40 = 100
100 minutes   Average speed S is given by distance / time. Hence   S= 25 miles / 100 minutes = 0.25 mile / minute   = 15 miles / hour   correct answer 15 miles / hour
Answer: E
Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?  Choose the correct choice from the following answers:
A) 10
B) 25
C) 12
D) 20
E) 30

Solution: Explanation:   Speed of train 1 = 12 m/sec   Speed of train 2 = 8 m/sec   if they travel in opposite direction, relative speed = 12 + 8= 
12 + 8 = 20
20 m/sec   distance covered= 120 + 120= 
120 + 120 = 240
240 m   time= distance/speed = 240/20= 
240/20 = 12
12 sec   ANSWER IS 12
Answer: C
Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is? Choose the correct choice from the following options: A) 36 B) 56 C) 65 D) 75 E) 35

Solution: (3x-9):(5x-9) = 9:17   x = 12 => 3x = 36   36nswer:36
Answer: A
A man swims downstream 18 km and upstream 12 km taking 3 hours each time, what is the speed of the man in still water?	Choices:
A) 3
B) 5
C) 6
D) 4
E) 8

Solution: 18 --- 3 DS = 6   ? ---- 1   12 ---- 3 US =4   ? ---- 1 M = ?   M = (6+4)/2= 
(6+4)/2 = 5
5   Answer: 5
Answer: B
Find the number such that when 15 is subtracted from 7 times the number,the result is 10 more than twice the number? Choices:  A) 4  B) 3  C) 5  D) 2  E) 6

Solution: Let the number be x.   7x-15=2x+10   7x-2x=15+10   5x=25   x=5   answer is option 5
Answer: C
A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? Choose the correct choice from the following answers:
A) 1/13 B) 2/21 C) 5/26 D) 3/25 E) 3/28

Solution: P(Both are red),   =65/262135/262=65/262135/262   =5/26   5/26
Answer: C