MU-NLPC/Calc-aqua_rat huggingface dataset:
A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?  Choices: A) 18 B) 99 C) 77 D) 55 E) 44

Solution: Let the present age of the person be x years.   Then, 3(x + 3) - 3(x - 3) = x   3x + 9 - 3x + 9 = x => x = 18   18nswer: 18
Answer: A
If A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in only median being modified not the mean.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed  Choose the most appropriate option:
A) 1) A and B
B) 2) A and E
C) 3) A,C,E
D) 4) None of them
E) 5) All of them

Solution: There are 10 equidistant numbers on the number line.   Mean and median will be the average of middle two numbers.   If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where median will change and mean will not change.   Answer: 4) None of them
Answer: D
A tank is filled in SIXTEEN hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? Choose the correct answer:  A) 56 hours  B) 28 hours  C) 55 hours  D) 66 hours  E) 47 hours

Solution: 1/A + 1/B + 1/C = 1/16 (Given)   Also given that A = 2B and B = 2C   => 1/2B + 1/B + 2/B = 1/16   => (1 + 2 + 4)/2B = 1/16   => 2B/7 = 16   => B = 56 hours.   56 hoursnswer: 56 hours
Answer: A
The sum of three consecutive multiples of 3 is 72. What is the largest number?	Choose one
A) 21  B) 24  C) 27  D) 36  E) 42

Solution: Let the numbers be 3x, 3x + 3, 3x + 6   Then, 3x + 3x + 3 + 3x + 6 = 72 ===> 9x = 63 ==> x = 7.   so the largest number is 3x + 6 = 27.   hence the correct answer is option 27) 27.
Answer: C
If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is more than 17?  Choose the correct choice from the following:
A) 1/5
B) 1/10
C) 2/15
D) 1/45
E) 2/45

Solution: The number of ways to choose two cards is 10C2=45.   There are 2 ways, {9,10} and {8,10}, to get a sum more than 17.   P(sum more than 17)=2/45   The answer is 2/45.
Answer: E
Sum of 36 odd numbers is?  Choices:
A) 1294
B) 1295
C) 1296
D) 1297
E) 1298

Solution: sum of 1st n odd no.s = 1+3+5+7+... = n^2   so, Sum of 1st 36 odd numbers = 36^2 = 1296   ANSWER:1296
Answer: C
Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?	Options:	A) 3.2 hr	B) 3.4 hr	C) 3.6 hr	D) 3.8 hr	E) 4.2 hr

Solution: let see d/t =v then x/20 + (400-x)/70 =8   x= 64 kmh   t = 64/20= 
64/20 = 16/5 = around 3.2
3.2 hr   3.2 hrNSWER:3.2 hr
Answer: A
A train passes a station platform in 31 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 one:
A) 228	B) 240	C) 165	D) 166	E) 1811

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)/31= 15 => x = 165 m.   Answer: 165
Answer: C
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?  Choose the correct choice from the following answers: A) 7 cm B) 6 cm C) 4 cm D) 3 cm E) 9 cm

Solution: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.   π(16)2 * h = (4/3)π (12)3 => h   = 9 cm   Answer: 9 cm
Answer: E
Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Select
A) 7/15  B) 14/31  C) 3/7  D) 17/35  E) 1/2

Solution: The easiest way for me is to plug in numbers.   Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.   If it takes an hour to produce a basic stereo then it will take 1.5 hours to produce a deluxe stereo.   40 basic stereos = 40 hours.   20 delux stereos = 30 hours.   Total hours = 70.   Then the fraction would be 30/70 = 3/7 Therefore answer   3/7.
Answer: C
In a six-sided polygon WQRSTV ∠W measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠W equal to, in degrees?  Choose the correct choice from the following:	A) 72	B) 80	C) 88	D) 96	E) 104

Solution: The sum of interior angle in a polygon is (n-2)*180   so for a six sided figure, (6-2)*180 = 720   let the A.M of the other 5 angles be 'm'   --> m*5 + W = 720, we know ∠W=m-48   --> m*5 + m - 48 = 720, solving we get m=128   hence ∠W= 128-48= 
128-48 = 80
80   Ans 80.
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? Choose the correct answer
A) 2888
B) 288
C) 178
D) 150
E) 2821

Solution: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9)= 
(50/3 * 9) = 150
150 m.Answer: 150
Answer: D
A person crosses a 600600 metre long street in 55 minutes. What is his speed in km per hour?
Select the correct option:
A) 8.2 B) 4.2 C) 6.1 D) 7.2 E) 9.1

Solution: Explanation:   Solution 17.2istance =600=600 metre =0.6=0.6 km   Time =5=5 minutes =112=112 hour   Speed=distancetime=0.6(112)Speed=distancetime=0.6(112) =7.2 km/hr   Answer is 7.2
Answer: D
If M/N = 6/5,then 3M+2N = ?
If p/q = 5/4 , then 2p+q= ?
If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST
Choose the correct choice from the following
A) 18/5  B) 28/5  C) 27/5  D) 26/5  E) 38/5

Solution: 3M+2N (divide by N)   3M/N+2   3*(6/5)+2   28/5 ANSWER:28/5
Answer: B
At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 2). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1?
Choose the correct option
A) $0.50  B) $1.00  C) $1.25  D) $1.50  E) $1.75

Solution: OA is definitely wrong. The answer should be $1.75.
Answer: E
If a and b are positive integers and (3^a)^b = 3^3, what is the value of 3^a*3^b?	Select:
A) 3
B) 9
C) 81
D) 27
E) 243

Solution: 3^ab =3^3 therefore ab=3 either a=1or3 or b=3 or 1   therefore 3^a* 3^b = 3^(a+b)= 3^4 =81   81
Answer: C
What is the probability that a leap year has 53 Sundays and 52 Mondays?
Choose one:
A) 1/9  B) 1/7  C) 1/2  D) 1/1  E) 1/5

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability   = 1/7   Answer:1/7
Answer: B
A man can row upstream at 55 kmph and downstream at 65 kmph, and then find the speed of the man in still water? Choices:
A) 27  B) 70  C) 60  D) 80  E) 24

Solution: US = 55   DS = 65   M = (55 + 65)/2= 
(55 + 65)/2 = 60
60   Answer:60
Answer: C
In a room with 10 people, 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?	Choose the correct choice from the following answers:	A) 5/21	B) 3/7	C) 4/5	D) 5/7	E) 16/21

Solution: (6/10)(7/9) + (5/10)(6/9) if you choose one of the 6 with one other friend, then you have a 7/9 chance of not picking their friend 2nd. If you choose one of the 5 with 2 friends, you have a 6/9 chance of not picking one of their friends second. Add them up.   42/90 + 30/90   72/90 = 4/5   C. 4/5
Answer: C
If an integer x is to be selected at random from 1 to 100, inclusive, what is probability x(x+1) will be divisible by 2?	Choose the correct option
A) 3
B) 1
C) 2
D) 4
E) 5

Solution: because x(x+1) is always an even product of even*odd or odd*even factors,   there is a probability of 1 that that it will be divisible by 2,   1*1= 
1*1 = 1
1   Answer : 1
Answer: B
The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places) Answers:
A) 77.14 cm	B) 25.14 cm	C) 84.92 cm	D) 94.94 cm	E) 23.57 cm

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(18 + 14) = 64 cm Parameter of the square = 64 cm   i.e. 4a = 64   A = 16   Diameter of the semicircle = 16 cm   Circimference of the semicircle   = 1/2(∏)(16)   = 1/2(22/7)(16) = 352/14 = 25.14 cm to two decimal places   ANSWER:25.14 cm
Answer: B
A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream?
Choose the correct option:
A) 6 hr  B) 2 hr  C) 4 hr  D) 1 hr  E) None of these

Solution: Explanation :   Speed downstream = 96⁄8 = 12 kmph   Speed of current = 4 km/hr   Speed of the boatman in still water = 12-4= 
12-4 = 8
8 kmph   Speed upstream= 8-4= 
8-4 = 4
4 kmph   Time taken to cover 8 km upstream= 8⁄4 = 2 hours. Answer : Option 2 hr
Answer: B
Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 75 marks in that test. Find the pass mark in the first test?  Pick:	A) 768	B) 243	C) 246	D) 288	E) 224

Solution: Let the maximum mark in each test be M.   The candidate failed by 75 marks in the second test.   pass mark in the second test = 249 + 75= 
249 + 75 = 324
324   45/100 M= 324   Pass mark in the first test = 40/100 M = 40/45 * 324= 
40/45 * 324 = 288
288.   Answer:288
Answer: D
Three pieces of timber 36 m, 42 m and 54 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ? Choose the most appropriate option.
A) 7 m  B) 1 m  C) 2 m  D) 6 m  E) None of these

Solution: Answer   Greatest possible length of each plank = H.C.F of 36, 42, 54 = 6 m   Correct Option: 6 m
Answer: D
A polygon has 54 diagonals. How many sides does it have?
Self made Choose the correct choice from the following answers: A) 12 B) 13 C) 14 D) 15 E) 16

Solution: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals   n*(n - 3)/2 = 54   n*(n - 3) = 108   Substitute n from the answer choices. n = 12   12nswer: 12
Answer: A
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 30%? Choose the correct choice.
A) 650 B) 882 C) 772 D) 652 E) 271

Solution: Cost price = Rs.500   profit = 30% of 500 = Rs.150   Selling price = Cost price + Profit   = 500 + 150= 
500 + 150 = 650
650   650nswer:650
Answer: A
Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary? Choose the correct choice from the following.
A) 6%  B) 8%  C) 1%  D) 2%  E) 9%

Solution: 10*10   -------- = 1%   100   Answer: 1%
Answer: C
Jill, who lives in City C, plans to visit 5 different cities, M, L, S,N,and O. She plans to visit each city exactly once and return to City C after the 5 visits. She can visit the cities in any order. In how many different orders can she visit the 5 cities? Choose the correct answer
A) 3	B) 120	C) 8	D) 9	E) 12

Solution: 5! = 120 =120
Answer: B
A pair of articles was bought for $900 at a discount of 10%. What must be the marked price of each of the article? Choose the correct choice from the following choices
A) $300	B) $500	C) $350	D) $400	E) $600

Solution: S.P. of each of the article = 900/2= 
900/2 = 450
$450   Let M.P= $x   90% of x = 450   x = 450*100/90= 
450*100/90 = 500
$500   Answer is $500
Answer: B
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is	Choose the correct option: A) 17/29 B) 17/25 C) 17/21 D) 17/20 E) 17/23

Solution: n(S) = 20   n(Even no) = 10 = n(E)   n(Prime no) = 8 = n(P)   P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20   Answer:17/20
Answer: D
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?	Choose one:  A) 88  B) 70  C) 62  D) 50  E) 54

Solution: Explanation:   Assume the length of each train = x   Total distance covered for overtaking the slower train = x+x = 2x   Relative speed = 46-36= 
46-36 = 10
10km/hr= (10×10)/36 = 100/36 m/s   Time = 36 seconds   2x/ (100/36) = 36   => (2x × 36 )/100 = 36   => x = 50 meter   Answer: Option 50
Answer: D
What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?  Select.
A) 1243
B) 1345
C) 1349
D) 1467
E) 1500

Solution: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.   First + second = third => we can eliminate 3 & 9 since  3 + 9= 
 3 + 9 = 12
12.   Last is 3 times the second=> we can eliminate option 2 & 6 since  3 * 6= 
 3 * 6 = 18
18.   Hence the number is 1349   1349
Answer: C
A man sells two articles for Rs.3640 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss?	Choose the correct choice from the following:
A) 9%loss  B) 2%loss  C) 6%loss  D) 8%loss  E) 1%loss

Solution: Explanation:   (25*25)/100   = 6%loss   Answer:6%loss
Answer: C
A merchant marks his goods up by 40% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount?  Pick.
A) 21%  B) 25%  C) 69%  D) 31%  E) 12%

Solution: Let the price be 100.   The price becomes 140 after a 40% markup.   Now a discount of 20% on 140.   Profit=112-100   12%   answer 12%
Answer: E
An athlete runs 200 metres race in 40 seconds. What is his speed?  Choose the correct choice from the following choices.
A) 23
B) 38
C) 18
D) 30
E) 28

Solution: Speed=Distance/Time = 200/40= 
200/40 = 5
5 m/s= 5 * 18/5 = 3618 km/hr   Answer :18
Answer: C
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Choose the correct option
A) 10 cm
B) 16 cm
C) 18 cm
D) 20 cm
E) 22 cm

Solution: 2(l + b)	=	5   b	1   2l + 2b = 5b   3b = 2l   b =	2	l   3   Then, Area = 216 cm2   l x b = 216   l x	2	l	= 216   3   l2 = 324   l = 18 cm.   18 cm)
Answer: C
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Select the correct option:  A) 300  B) 400  C) 500  D) 600  E) 700

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters   Answer: Option 500
Answer: C
Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Choose the correct choice from the following
A) 22 B) 77 C) 18 D) 10 E) 81

Solution: Part of the filled by all the three pipes in one minute   = 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10   So, the tank becomes full in 10 minutes.   Answer:10
Answer: D
Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5145 Nis, how much more money does Nick contribute than Archi?	Options.
A) 128 Nis
B) 212 Nis
C) 234 Nis
D) 245 Nis
E) 288 Nis

Solution: Normalising the fraction from 5:3:2.5 to 10:6:5 (Eric: Nick:Archi)   Given Nick contributes one unit more than Archi and one unit of  5145/(10+6+5)= 
 5145/(10+6+5) = 245
245   Answer is 245 Nis: 245 Nis
Answer: D
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? Select
A) 40 B) 50 C) 60 D) 70 E) 80

Solution: Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x = 50.   40nswer: Option 40
Answer: A
At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.35. What is the price of 2 doughnuts? Choose the correct choice from the following choices:
A) $ 0.55  B) $ 1.00  C) $ 1.10  D) $ 1.30  E) $ 1.80

Solution: 3D + C = 2.25......(1)   2D + C = 1.35........(2)   (1) - (2) --> D = 0.9 --> 2D = 1.8   Answer: $ 1.80
Answer: E
Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent T?
Choices.
A) 20% B) 80% C) 100% D) 180% E) 200%

Solution: C.   Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).   T=[(2 - 1)/1] * 100% = 100%.100%(2 - 1)/1  * 100= 
(2 - 1)/1  * 100 = 100
100%.100%
Answer: C
O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(5.3) + E(–6.7) + o(–7.3) + e(6.6) is:
Choose the correct choice from the following choices
A) -4	B) -2	C) 0	D) 2	E) 4

Solution: O(5.3) + E(–6.7) + o(–7.3) + e(6.6) = 7 + (-6) + (-9) + 6 = -2   The answer is -2.
Answer: B
A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business? Select the correct option.
A) 7500  B) 4366  C) 2877  D) 2768  E) 26871

Solution: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3   B's share = 25000 * 3/10   = Rs. 7500.   7500nswer: 7500
Answer: A
The area of a square field is 28808 sq m. How long will a lady take to cross the field diagonally at the rate of 7.2 km/hr?  Choose the correct choice.
A) 2.5 min	B) 3 min	C) 2 min	D) 4 min	E) 4.5 min

Solution: Area of a square field = 28808 sq m   Let the side of square = a   a^2 = 28808   => a = 169.73   Diagonal = (2)^(1/2) * a   = 1.414 * 169.73   =240   Speed of lady = 7.2 km / hour   = 7200 m / hour   = 120 m / min   Time taken by lady to cross the field diagonally = 240/120= 
240/120 = 2
2 min   Answer 2 min
Answer: C
A rectangular table seats 7 people on each of two sides, with every person directly facing another person across the table. If 14 people choose their seats at random, what is probability that person P directly faces person Q?
Select
A) 1/10
B) 1/11
C) 1/12
D) 1/13
E) 1/14

Solution: Person P will be seated somewhere at the table.   Each of the other 13 people has an equal chance of sitting opposite person P.   The probability that person Q sits across is 1/13.   The answer is 1/13.
Answer: D
A man & his wife appear in an interview for 2vacancies in the same post. The probability of husband's selection is 1/7 & the probability of wife's selection is 1/5. What is the probability that only 1 of them is selected ?  Answers
A) 1/3
B) 2/3
C) 2/7
D) 3/11
E) 4/5

Solution: Let A = Event that the husband is selected and   B = Event that the wife is selected.   Then, P (A) = 1/7   and P(B) = 1/5   ∴P(A¯) = (1 - 17/5) = 6/7   and   = (1 - 1/5) = 4/5   Required probability = P [(A and not B) or (B and not A)]   = P[(A and B¯) or (B and A¯)]   = P(A and B¯) + P(B and A¯)   = P(A).P(B¯) + P(B).P(A¯)   = (1/7* 4/5) + (1/5* 6/7)   = 10/35   = 2/7   2/7
Answer: C
If a, t, and c are consecutive even integers and a < t < c, all of the following must be divisible by 4 EXCEPT	Choose the correct choice from the following: A) a + c B) t + c C) ac D) (bc)/2 E) (abc)/4

Solution: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.   The 3 numbers can be written as   a, (a + 2)(a + 4).   If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.   A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.   C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.   D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.   E - atc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.   B - b + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.   As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.t + c
Answer: B
The difference between a two digit number and the number obtained by interchanging the positions of its digit is 36. What is the difference between the two digits of that number? Options.
A) 3
B) 4
C) 9
D) 8
E) 7

Solution: Let the ten’s digit be x   Unit’s digit be y   Then (10x+y)-(10y+x)=36   9(x-y)=36   x-y=4   Option 4
Answer: B
How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?	Select:
A) 576 numbers	B) 575	C) 620	D) 640	E) 660

Solution: 1 digit = 5   2 digits = 4* 5= 
4* 5 = 20
20   3 digits= 4*5*5= 
4*5*5 = 100
100   Now,4 digit number till 4000 can have digits 1,2,3 in thousands place ( total choices= 3 )   0,1,2,3,4 in hundreds ,tens and ones place   I.e 3*5*5*5 = 375   Now From 4000 to 4299 = 1*3*5*5= 
1*3*5*5 = 75
75   Total= 5+20+100+375+75+1= 
5+20+100+375+75+1 = 576
576 (1 for 4300)   576 numbersNSWER:576 numbers
Answer: A
A train crosses a platform of 200 m in 20 sec, same train crosses another platform of length 350 m in 25 sec. then find the length of the train?  Choose the correct choice from the following options
A) 150m	B) 180m	C) 400m	D) 250m	E) 155m

Solution: Length of the train be ‘X’   X + 200/20 = X + 350/25   5X + 1000 = 4X + 1400   X = 400m   Answer:400m
Answer: C
The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?  Options:
A) 13  B) 16  C) 27  D) 29  E) 30

Solution: 5:3:4   Total parts = 12   12 parts --> 108   1 part ---->9   The second number of the three numbers is = 3   3 parts ----> 27   27)
Answer: C