MU-NLPC/Calc-aqua_rat huggingface dataset:
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 0.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
Select.
A) 2.04%
B) 4.12%
C) 5%
D) 8.25%
E) 10%

Solution: Per quarter, interest = 0.5% So for a year, interest = 2% Due to quarter cumulation, effective yield (YTM) would be slight higher than 2% 2.04%nswer = 2.04% =2.04%NSWER:2.04%
Answer: A
A set consists of 15 numbers, all are even or multiple of 5. If 8 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10? Select the correct option:	A) 0	B) 1	C) 2	D) 3	E) 5

Solution: {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.   Since{Neither}=0(allare even or multiple of 5) then:   15 = 8 + 10 - {Both} + 0;   {Both}=3(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).   Answer: 3.
Answer: D
A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.20 per kg. What will be his gain percent?  Choose the correct choice
A) 8 1/7 %
B) 2 1/3 %
C) 3 1/3 %
D) 8 1/8 %
E) 8 1/9 %

Solution: C.P. of 1 kg = 420/70 = Rs. 6   S.P. of 1 kg = Rs. 6.20   Gain % = 0.20/6 * 100 = 10/3   = 3 1/3 %   Answer:3 1/3 %
Answer: C
What should be the least number to be added to the 51234 number to make it divisible by 9?
Choose the correct choice from the following options
A) 12
B) 17
C) 18
D) 77
E) 26

Solution: Explanation:   The least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits.   Sum of digits = 15.   Nearest multiple of 9 greater than sum of digits = 18.   Hence 3 has to be added.   Answer: 18
Answer: C
A set of numbers has the property that for any number t in the set,t+2 is in the set. If -2 is in the set, which of the following must also be in the set? I. -3 II. 1 III. 4
Choose the correct answer: A) II only B) I,III only C) III only D) II,III only E) I only

Solution: question is asking for must be there elements.   According to the question if t is there t+2 must be there.   if -2 is the starting element the sequence is as follows.   S ={-2,0,2,4,6....}   if -2 is not the starting element the sequence is as follows   S = {...-4,-2,0,2,4,6...}   By observing the above two sequences we can say that 4 must be there in set S.   Answer : III only
Answer: C
After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?  Options:
A) Rs.2989  B) Rs.5029  C) Rs.5000  D) Rs.5197  E) Rs.5029

Solution: Given SP = Rs. 6800   Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)   = Rs. 8000   If SP = Rs. 8000, profit   60%   Rs.5000P = [SP(100)]/(100 + 60)   = (8000 * 100)/160   = Rs.5000   Answer: Rs.5000
Answer: C
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? Choose the correct choice from the following answers:
A) 90%
B) 50%
C) 60%
D) 70%
E) 80%

Solution: circumference of A = 2(pie)r = 8 so r = 4/pie   volume = pie(4/pie)^2*10 = 160/pie   circumference of B = 2(pie)r = 10 so r = 5/pie   volume = pie(5/pie)^2*8 = 200/pie   so ratio of capacities = 160/200= 
160/200 = 4/5 = around 0.8
0.8   so capacity of A will be 80% of the capacity of B   ANSW80%R:80%
Answer: E
If x, y, and z are positive integers, and 2x = 5y = 7z, then the least possible value of x + y + z is	Choose the correct choice:
A) 15
B) 28
C) 37
D) 42
E) 59

Solution: Take LCM of 2,5 and 7 = 70   Now 2x = 70 => x =35   5y = 70 => y = 14   7z = 70 => z =10   35+14+10= 
35+14+10 = 59
59.   Option 59.
Answer: E
What is the least number of squares tiles required to pave the floor of a room 2 m 42 cm long and 1 m 76 cm broad? Pick:  A) 88  B) 82  C) 84  D) 44  E) 54

Solution: Length of largest tile = H.C.F. of 242 cm and 176 cm = 22 cm.   Area of each tile = (22 x 22) cm2.   Required number of tiles =242 x 176/(22^2)= 88.   88NSWER:88
Answer: A
A money lender finds that due to a fall in the annual rate of interest from 8% to 7 ¾ % his yearly income diminishes by Rs.61.50. his capital is	Choices:
A) 22378	B) 3778	C) 24600	D) 27888	E) 12771

Solution: Explanation:   24600apital = Rs.x , then   x = 24600   Answer: 24600) Rs.24600
Answer: C
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place? Choose one:
A) 2.89 B) 2.88 C) 2.82 D) 2.84 E) 2.83

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer:2.88
Answer: B
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?	Choices.
A) 272	B) 111	C) 822	D) 150	E) 379

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150
Answer: D
Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?  Choose the correct choice
A) 1
B) 2
C) 7
D) 4
E) 9

Solution: 2500 = 4(100/4)2   4 = 4   Answer:4
Answer: D
x = y - (1/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
Choices:
A) decrease B) stay the same C) increase four fold D) just more than double E) increase to more than five times

Solution: Alternate approach   Plug in some values of y > 0   Let y = 10   So, x = y - (1/y)   Or, x = 10 - (1/10)= 
10 - (1/10) = 99/10 = around 9.9
9.9   Let y= 20   So, x = y - (1/y)   Or, x = 20 - (1/20)= 
20 - (1/20) = 399/20 = around 19.95
>19.95   So, x increases from 9.9 to 19.95   Hence the number increases 2 times, thus the correct answer will be (just more than double)
Answer: D
A tourist purchased a total of $3,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?  Options:
A) $1,430
B) $2,310
C) $2,290
D) $3,270
E) $4,150

Solution: Let the number of $10 checks cashed beT   Let the number of $50 checks cashed beF   7 checks cashed;   T+F=7   Now; T can be F+1 OR T can be F-1   Let's check both conditions;   T=F+1   T+F=7   F+1+F=7   2F=6   F=3   T=4   Value cashed = 3*50+4*10=150+40= 
150+40 = 190
$190   Let's check the other condition as well;   T=F-1   T+F=7   F-1+F=7   2F=8   F=4   T=3   Value cashed = 4*50+3*10=200+30= 
200+30 = 230
$230   The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.   Value cashed= $230   Value lost = 3000-230 = $3270   Ans:$3,270
Answer: D
Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?	Choose the correct choice:
A) 2
B) 3
C) 5
D) 8
E) 13

Solution: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence   X + Y = 20   If X is the number of cards at $0.25, then the X cards cost   0.25 X   If Y is the number of cards at $0.15, then the Y cards cost   0.15 Y   The total cost of the X cards and the the Y cards is known to be $4.2 and also given by   0.25 X + 0.15 Y = 4.2   We now need to solve the system of equations   X + Y = 20   0.25 X + 0.15 Y = 4.2   The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve   0.25 X + 0.15 (20 - X) = 4.2   X(0.25 - 0.15) + 3 = 4.2   0.1 X = 1.2   X = 12 and Y = 20 - 12= 
20 - 12 = 8
8   correct answer 8
Answer: D
What is vasu salary if salary of vasu is more than rajan salary working in same company i)vasu salary is 100 more than rajan salary. ii)rajan found 2000 allowns which is 50 less than vasu. (iii)basic salry of rajan is 1000.  Choose the correct choice from the following answers:
A) only i is required	B) i & ii is required	C) i& iii is required	D) i&ii&iii is required	E) none of these

Solution: i and iii is enough   ANSWER:i & ii is required
Answer: B
The distance light travels in one year is approximately 5,850,000,000,000 miles. The distance light travels in 100 years is
Select the correct option:
A) A) 587 × 108 miles B) B) 587 × 1010 miles C) C) 587 × 10-10 miles D) D) 585 × 1012 miles E) E) 587 × 10-12 miles

Solution: The distance of the light travels in 100 years is:   5,850,000,000,000 × 100 miles.   = 585,000,000,000,000 miles.   = 585 × 1012 miles.   The answer is (585 × 1012 miles)
Answer: D
A box contains four nickel coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
Choose the correct choice from the following options.
A) 3/5	B) 2/5	C) 4/5	D) 1/5	E) 3/4

Solution: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)   How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)   Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)   = 4/5   4/5
Answer: C
The owner of a furniture shop charges his customer 60% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table?	Choose the correct choice from the following answers
A) 750  B) 650  C) 625  D) 115  E) 400

Solution: CP = SP * (100/(100 + profit%))   = 1000(100/160) = Rs. 625.   Answer: 650
Answer: B
If x is an integer and 3.134 × 10^x is less than 31,000 what is the greatest possible value for x? Choose the correct choice from the following
A) 7
B) 6
C) 5
D) 4
E) 3

Solution: If x=4   3.134 × 10^4 = 31340 > 31000   So, x = 3   Answer : 3
Answer: E
For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 75N in one hour, where N is a positive integer?
Choose the correct choice
A) 12 + 50N  B) 12 + 3N  C) 62N  D) 37N  E) 25

Solution: 25 units = 1 worker;   75N units = 75N/25 = 3N workers.   So, the answer is 3N workers plus 12 managers.   Answer: 12 + 3N.75 /25= 
75 /25 = 3
3N workers.   So, the answer is 3N workers plus 12 managers.   Answer: 12 + 3N.
Answer: B
calculate the time required to become sum 2 times of itself at rate of 10%.  Choose the correct choice from the following options:
A) 5year B) 15year C) 10year D) 8year E) 12year

Solution: if sum become 2 time then simple interest equal to x.   x=x*10*t/100   t=100/10= 
100/10 = 10
10year   answer 10year
Answer: C
find 3 consecutive odd integers, all less than 100, such that the sum of their squares forms a Unidigit (that is, all its digits are the same). Thus, for integer abc, a^2 + b^2 +c^2 equals a Unidigital. Choose the correct choice from the following options.
A) 39,43,45 B) 43,45,47 C) 45,47,49 D) 41,43,45 E) 41,43,47

Solution: If numbers are x,x-2,x+2, then   x^2+(x+2)^2 =(x-2)^2 = x^2+2x^2+8 = 3x^2+8   Now 3x^2+8 should be unidigital.   checking different combinations , we get   x=43.   so numbers are 41,43,45   ANSWER:41,43,45
Answer: D
A train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds. What is the length of the train in metres?	Choose the correct choice from the following answers
A) 375 m  B) 750 m  C) 250 m  D) 600 m  E) 300 m

Solution: Let Length of Train = L   Case-1: Distance = 1500+L (While crossing the bridge)   Time = 70 Seconds   i.e. Speed = Distance / Time = (1500+L)/70   Case-2: Distance = L (While passing the lamp post)   Time = 20 Seconds   i.e. Speed = Distance / Time = (L)/20   But Since speed has to be same in both cases so   (1500+L)/70 = (L)/20   i.e. 1500 + L = 3.5 L   i.e. 2.5L = 1500   i.e. L = 600   Answer: option 600 m
Answer: D
A train passes a station platform in 55 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:
A) 180 m
B) 525 m
C) 240 m
D) 320 m
E) None

Solution: Sol.   Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x metres.   Then, x + 300 / 55= 15 ⇔ x + 300 = 825 ⇔ x = 525 m.   Answer 525 m
Answer: B
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?  Choose the correct choice from the following answers:
A) 28788  B) 2788  C) 1000  D) 2877  E) 28881

Solution: X * (110/100) * (95/100) = 1045   X * (11/10) * (1/100) = 11   X = 1000   Answer: 1000
Answer: C
If the sum of three consecutive even numbers is 48 more than the average of these numbers, then the largest of these numbers is?	Choose the correct choice from the following answers:
A) 20
B) 24
C) 22
D) 26
E) 27

Solution: Explanation:   Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).   x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 48   3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 144   9x + 18 = 3x + 150   6x = 132   x = 22   Therefore, the largest number is 26.   ANSWER 26
Answer: D
A basketball player succeeds with 60% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Answers.
A) 0.856	B) 0.872	C) 0.936	D) 0.952	E) 0.985

Solution: P(missing all 3 free throws) = 0.4^3 = 0.064   P(succeeding at least once) = 1 - 0.064= 
1 - 0.064 = 0.936
0.936   The answer is 0.936.
Answer: C
A five-character password consists of three letter of the alphabet and two different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?	Choose the most appropriate option.
A) 225,040 B) 18,443,720 C) 26,337,000 D) 28,337,440 E) 28,473,120

Solution: 5 character password: DLDLL   First digit can be chosen in 10 ways.   The letter can be chosen in 26 ways.   Next digit can be chosen in 9 ways.   The letter can be chosen in 25 ways.   The letter can be chosen in 24 ways.   This gives us 10*26*9*25*24ways   Now, the letter can also be DDLD so there will be another 10*9*26*25*24 ways   Total = 10*26*9*25*24*2 = 28,473,120 ways   28,473,120
Answer: E
What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?	Choose the correct option:
A) 814
B) 820
C) 842
D) 844
E) 848

Solution: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.   Area of each tile = (41 x 41) cm2.   Required number of tiles = (1517×902)/ (41×41) = 814   answer :814
Answer: A
The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?  Choose the correct choice from the following answers:
A) 91.5 cm B) 11.5 cm C) 91.8 cm D) 92.5 cm E) 99.5 cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 21) + 2(21)   = 49.5 + 42= 
49.5 + 42 = 91.5
91.5 cm   91.5 cmnswer:91.5 cm
Answer: A
A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?  Choose the correct choice from the following answers.
A) 46 seconds
B) 36 seconds
C) 38 seconds
D) 26 seconds
E) 18 seconds

Solution: Distance = 240+ 120= 
240+ 120 = 360
360 m   speed= 36 km/hr = 36×10/36 = 10 m/s   Time = distance/speed = 360/10= 
360/10 = 36
36 seconds   answer : 36 seconds
Answer: B
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 56?
Pick.
A) 3944
B) 920
C) 3808
D) 6928
E) 3729

Solution: Explanation:   Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 56 = Rs. 3808.   Answer: Option 3808
Answer: C
What is the remainder when (55)(57) is divided by 7?
Pick:	A) 1	B) 2	C) 3	D) 5	E) 6

Solution: (55)(57) = (56-1)(56+1) = 56^2 - 1 which is 1 less than a multiple of 7.   Then the remainder will be 6.   The answer is 6.
Answer: E
After decreasing 24% in the price of an article costs Rs.684. Find the actual cost of an article?	Choices:
A) 218	B) 777	C) 900	D) 2688	E) 1991

Solution: 900P* (76/100) = 684   900P900 * (76/100)= 
900 * (76/100) = 684
684   900P= 9 * 100= 
9 * 100 = 900
> 900P= 900   Answer: 900
Answer: C
A man is 36 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is  Pick:
A) 28 years	B) 22 years	C) 18 years	D) 16 years	E) 15 years

Solution: Let's Son age is x, then Father age is x+36.   => 3(x+3) = (x+36+3)   => 3x+9 = x+39   => 2x = 30 years = 15 Y15 yearsARS   Answer: 15 years
Answer: E
(3 x 10^5) + (2 x 10^3) + (4 x 10^2) =	Options:
A) 302400  B) 32400  C) 30240  D) 3240  E) 324

Solution: When you multiply a number by 10 you just add a zero   => 3 x 10^5 => add 5 zeros => 3 x 10^5 = 300000   =>2 x 10^3 = 2000   => 4 x 10^2 = 400   =>3 x 10^5 + 2 x 10^3 + 4 x 10^2 = 300000 + 2000 + 400= 
300000 + 2000 + 400 = 302_400
302400=> answer is 302400 ( 302400)
Answer: A
Ravi, Gagan and Nitin are running a business firm in partnership. What is Gagan’s share in the profit earned by them?
I.Ravi, Gagan and Nitin invested the amounts in the ratio of 2 : 4 : 7.
II.Nitin’s share in the profit is Rs. 8750.
Options
A) I alone sufficient while II alone not sufficient to answer
B) II alone sufficient while I alone not sufficient to answer
C) Either I or II alone sufficient to answer
D) Both I and II are not sufficient to answer
E) Both I and II are necessary to answer

Solution: Explanation:   Let us name Ravi, Gagan and Nitin by R, G and N respectively.   I. R : G : N = 2 : 4 : 7.   II. N = 8750..   From I and II, we get:   When N = 7, then G = 4.   When N = 8750, then G = ( 4/7 x 8750) = 5000.   Thus, both I and II are needed to get the answer.   answer is (Both I and II are necessary to answer).
Answer: E
There are C girls in a class, and their average height is M inches. In the same class, there are D boys with an average height of N inches. What is the average height of all the students in the class?	Choose the correct answer:
A) (X + Y)/(M + N)  B) (M + N)/(X + Y)  C) (XM + YN)/(M + N)  D) (CM + DN)/(C+ D)  E) MN/XY

Solution: Total height = CM+(CM + DN)/(C+N   No of students = C+(CM + DN)/(C+   Avg = (CM+(CM + DN)/(C+N)/(C+(CM + DN)/(C+)   Answer is (CM + DN)/(C+
Answer: D
When x is multiplied by 3, the result is 10 more than the result of subtracting x from 26. What is the value of x?	Pick one:
A) -4  B) 9  C) 11  D) 13  E) 22

Solution: The equation that can be formed is:   3x-10=26-x   or, 4x=36   or, x=9.   9 answer.
Answer: B
A boat can move upstream at 50 kmph and downstream at 100 kmph, then the speed of the current is?	Pick one
A) 10  B) 45  C) 25  D) 40  E) 20

Solution: US = 50   DS = 100   M = (100- 50)/2= 
(100- 50)/2 = 25
25   Answer:25
Answer: C
A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
Pick
A) 5 hours 45 min
B) 5 hours 55 min
C) 6 hours 45 min
D) 7 hours 45 min
E) 8 hours

Solution: ----------------------------------------------------------------   Solution 1   ----------------------------------------------------------------   Given that time taken for riding both ways will be 2 hours lesser than   the time needed for waking one way and riding back   From this, we can understand that   time needed for riding one way = time needed for waking one way - 2 hours   Given that time taken in walking one way and riding back = 5 hours 45 min   Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min   7 hours 45 min
Answer: D
The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by	Choose the correct option.
A) 25%  B) 20%  C) 80%  D) 75%  E) None

Solution: Solution: Let the initial expenses on Sugar was Rs. 100.   Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,   = (100 + 25% of 100) = Rs. 125.   But, They want to keep expenses on Sugar, so they have to cut Rs. 25 in the expenses to keep it to Rs. 100.   Now, % decrease in Consumption,   (25/125)*100= 
(25/125)*100 = 20
20%.   Mind Calculation Method;   100-----25%↑---→125------X%↓---→100.   Here, X= (25/125)*100= 
(25/125)*100 = 20
20%.   Answer: Option 20%
Answer: B
How many integers between 300 and 1100 are there such that their unit digit is odd?
Choose the correct choice from the following choices:
A) 200	B) 300	C) 400	D) 500	E) 600

Solution: There are 800 numbers from 301 to 1100 (inclusive).   Half of the numbers are odd, so there are 400 odd numbers.   The answer is 400.
Answer: C
At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:50 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?  Choose the correct choice from the following answers:
A) 0.5 + (p - 0.5s)/(r + s)
B) (p - 0.5s)/(r + s)
C) 0.5 + (p - 0.5r)/r
D) (p - 0.5r)/(r + s)
E) 0.5 + (p - 0.5r)/(r + s)

Solution: The distance 0.5 + (p - 0.5s)/(r + s) is going to cover between 1:00 and 1:30   = .5r   now the distance between the two trains = (p-.5r)   the relative velocity = (r-(-s)) = r+s   From 1:30, time is going to take when they meet = (p-.5r)/(r+s)   số thẻ ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 tờ 1:30]   ans is 0.5 + (p - 0.5s)/(r + s)
Answer: A
On dividing number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?
Answers.
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Let x be the number and y be the quotient.   Then, x = 357 * y + 39   = (17 * 21 * y) + (17 * 2) + 5   = 17 * (21y + 2) + 5.   Required remainder = 5.   ANSWER:5
Answer: B
In 10 years, A will be twice as old as B was 10 years ago. If A is now 7 years older than B the present age of B is	Choose the correct choice from the following answers: A) 37 B) 38 C) 39 D) 40 E) 41

Solution: let present age of 37 be a and B be b   a+10 = 2*(b-10)   => 2b-a = 30 ......(i)   a = b+7   =>2b-b-7 = 30   b=37   so the present age of b is 37 years   37NSWER:37
Answer: A
In a class of 60 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 most appropriate option:	A) 6	B) 15	C) 24	D) 33	E) 54

Solution: Formula for calculating two overlapping sets:   6 + B - both + NOT(6 or B) = Total   so in our task we have equation:   41 (french) + 22 (german) - 9 (both) + NOT = 60   54 + NOT = 60   NOT = 60 - 54= 
60 - 54 = 6
6   So answer is 6
Answer: A