MU-NLPC/Calc-aqua_rat huggingface dataset:
N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is
Select:
A) (a) 61250	B) (b) 65525	C) (c) 42455	D) (d) 62525	E) (e) 55425

Solution: The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question.   To start, we're given information on the sub-sets of numbers:   -The 1st set has 1 number   -The 2nd set has 2 numbers   -The 3rd set has 3 numbers   Etc.   So the 50th set will have 50 numbers in it.   Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching...   The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers   The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers   Etc.   This pattern will continue all the way down to...   The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers   Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'...   So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive...   Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)...   25(1226+1275) =   25(2501) =   62525   (d) 62525
Answer: D
A boy was asked to find 7/9 of a y. But he divided the y by 7/9, Thus he got 32 morethan theanswer. Find the y.  Select the correct option.
A) 45
B) 56
C) 48
D) 63
E) 65

Solution: x/7/9 = 9x/7 = 32 + y   Actualy he should do 7x/9 = y   y = (9x/7) - 32   y = (9x - 224)/7   (9x - 224)/7 = 7x/9   81y - 2016 = 49y   81y - 49y = 2016   32y = 2016   y = 63   63
Answer: D
X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 8. What is the value of Z? Pick one.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.   X + 3Y + 3Z = 5Y + 8   Z+2+3Z+3+3Z = 5Z+5+8   2Z = 8   Z = 4   The answer is 4.
Answer: C
8, 24, 12, 36, 18, 54, (....) Choose the correct option
A) 72  B) 68  C) 108  D) 27  E) 86

Solution: 8 × 3 = 24   24 ÷ 2 = 12   12 × 3 = 36   36 ÷ 2 = 18   18 × 3 = 54   54 ÷ 2 = 27   Answer is 27.
Answer: D
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is:  Options.
A) 276  B) 299  C) 230  D) 345  E) 395

Solution: Clearly, the numbers are (23 x 9) and (23 x 10).   Larger number = (23 x 10) = 230.   Answer: Option 230
Answer: C
What is the area of a square field whose diagonal of length 20 m?	Choose the correct choice from the following options:
A) 228
B) 271
C) 200
D) 277
E) 181

Solution: d2/2 = (20 * 20)/2= 
(20 * 20)/2 = 200
200   Answer:200
Answer: C
In how many ways can the letters {U, R, U, R, R} be arranged?  Choose the correct option
A) 10 B) 20 C) 120 D) 720 E) 840

Solution: My answer : 10   There is 5! ways to arrange those letters in total, however letter U repeats 2! times and letter R repeats 3! times   => the way to arrange without repeating = 5!/ [2!x3!] = 10
Answer: A
The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?  Choose the correct choice from the following answers.
A) 18  B) 25  C) 23  D) 29  E) 28

Solution: 39x = 5 + 12 + 15 + 19 + (x – 4)44   x   = 25   Answer:25
Answer: B
If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 27, what is the value of r-p?
Pick one:
A) 20 B) 10 C) 34 D) 40 E) 5

Solution: Arithmetic mean expression for p and q:   (p+q)/2=10 ; p+q=20 ----eq1   Arithmetic mean expression for q and r:   (q+r)/2=20 ; q+r=54 ----eq2   Subtracting eq1 from eq2 we get: r-p=34   Hence, the correct answer is 34
Answer: C
A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum? Choose the correct answer:
A) 8925 B) 8259 C) 8529 D) 8952 E) None

Solution: Sol.   Principal = Rs. [100 * 4016.25 / 9 * 5] = Rs. [401625 / 45] = Rs. 8925.   8925nswer 8925
Answer: A
On the coordinate plane , points P and T are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?  Choices:	A) (1.5,1)	B) (2,-5)	C) (0,0)	D) (1,1.5)	E) (2,2)

Solution: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.   One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).   Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PT is the diameter of the circle.   There can be a case when PT is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.   If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y COR(1,1.5)INATE and mark the ans=(1,1.5)
Answer: D
A and B start walking towards each other at 4pm at speed of 2kmph and 3kmph. They were initially 15km apart. At what time do they meet?
Choose the correct choice from the following choices:	A) 8pm	B) 6pm	C) 7pm	D) 10pm	E) 5pm

Solution: Time of meeting = distance / relative speed = 15/3+2 = 15/5= 
15/5 = 3
3 hrs after 4pm= 7pm   Answer is 7pm
Answer: C
How many seconds will a 450 m 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) 27 sec
B) 30 sec
C) 86 sec
D) 16 sec
E) 18 sec

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 450 * 3/50= 
450 * 3/50 = 27
27 sec.   27 secnswer: 27 sec
Answer: A
If a man travels f miles an hour for m hours and r miles an hour for s hours, what is his average rate in miles per hour for the entire distance traveled?
Pick one
A) fm + rs
B) (fm + rs)/2
C) m/f + s/r
D) (fm + rs)/(m + s)
E) (fm + rs)/(t - s)

Solution: Average Speed = Total (fm + rs)/(m + s)istance /Total Time Taken   Total (fm + rs)/(m + s)istance travelled in m hours = fm   Total (fm + rs)/(m + s)istance travelled in s hours = rs   Total Time taken = m+s   Therefore , Average Speed = (fm+ms)/(m+s)   Answer (fm + rs)/(m + s)
Answer: D
The average salary of 15 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $20,000 each. What is the average salary of the remaining employees? Choose the most appropriate option.
A) $19,250  B) $15,800  C) $18,000  D) $15,850  E) $12,300

Solution: total salary... 15*20k=300k   5 emp @ 25k =125k   4 emp @ 20k =80k   remaing 6 emp sal = 300k-125k-80k =95k   average300 -125 -80= 
300 -125 -80 = 95
95k   average=95k/6 = 15800   Ans:$15,800
Answer: B
Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 110 players took part in that tournament.
How many matches were played?
Select the correct option:	A) 99 matches.	B) 88 matches.	C) 77 matches.	D) 109 matches.	E) 55 matches.

Solution: Solution:   109 matches.   The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 109 matches were played.   Answer 109 matches.
Answer: D
Rani is two years older than Banu who is twice as old as Chitra. If the total of the age of Rani, Banu and Chitra be 32 years, then how old is Banu ?	Choose the correct choice from the following answers.
A) 7 years B) 10 years C) 12 years D) 13 years E) 14 years

Solution: Let Chitra's age be x years. Then, Banu's age = 2x years.Rani's age = (2x + 2) years.   (2x + 2) + 2x + x = 32   5x =30   x = 6   Hence, Banu's age = 2x = 12 years.   Answer : 12 years
Answer: C
The area of a parallelogram is 72sq m and its altitude is twice the corresponding base. Then the length of the base is?
Choose the correct choice from the following options: A) 6 B) 9 C) 7 D) 62 E) 2

Solution: 2x * x = 72 => x= 6   6nswer: 6
Answer: A
The unit digit in the product (891 * 781 * 912 * 463) is:  Choose the correct answer:	A) 2	B) 5	C) 6	D) 8	E) 10

Solution: Explanation:   Unit digit in the given product = Unit Digit in (1*1*2*3)= 
(1*1*2*3) = 6
6   ANSWER: 6
Answer: C
If x is 20 percent greater than 12, then x =
Choose the correct choice
A) 10.2	B) 12.1	C) 8.1	D) 15.6	E) 14.4

Solution: X is 20% greater than 12 means X is 1.2 times 12 (in other words 12 + 20/100 * 12 = 1.2 * 12)   Therefore, X = 1.2 * 12= 
1.2 * 12 = 14.4
14.4   ANSW14.4R:14.4
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?	Choose the correct choice from the following answers:
A) 36  B) 50  C) 28  D) 26  E) 29

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr   Answer: 50
Answer: B
There are some people in party, 1/3rd left the party . Then 2/5th of the remaining left the party , then 2/3rd of the remaining left the party . At last 6 were remaining . How many people were in total ?	Answers
A) 45	B) 27	C) 28	D) 26	E) 91

Solution: Sol:   45   If x persons were there in total , then   x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 6   x×2/3 × 3/5 × 1/3 = 6   x = 6 × 5 × 3/2 = 45   45nswer:45
Answer: A
What is the are of an equilateral triangle of side 14 cm?  Choose the correct choice from the following answers
A) 66âˆš3 cm2 B) 74âˆš3 cm2 C) 64âˆš3 cm2 D) 49âˆš3 cm2 E) 14âˆš3 cm2

Solution: Area of an equilateral triangle = âˆš3/4 S2   If S = 14, Area of triangle = âˆš3/4 * 14 * 14 = 49âˆš3 cm2;   Answer:49âˆš3 cm2
Answer: D
In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is?  Choose the correct choice from the following options.
A) 20  B) 30  C) 40  D) 43  E) 45

Solution: Number = (35 * 12)= 
(35 * 12) = 420
420   Correct quotient= 420/21= 
420/21 = 20
20   20)
Answer: A
Ravi and sunil are partners in a business. Ravi invests Rs.10,000 for 8 months and Sunil invested Rs.12000 for 10 months then after one year ratio of their profits will be Choose the correct choice: A) 1:3 B) 2:3 C) 3:2 D) 3:1 E) 3:4

Solution: =(15000*8):(8000*10)   =80000:120000   =2:3   ANSWER:2:3
Answer: B
Excluding stoppages, the speed of a bus is 70 km/hr and including stoppages, it is 40 km/hr. For how many minutes does the bus stop per hour?	Choose the correct choice: A) 118 min B) 10 min C) 18 min D) 16 min E) 25 min

Solution: Due to stoppages, it covers 30 km less.   Time taken to cover 30 km = 30/70 * 60   = 25 min.   Answer:25 min
Answer: E
The speed of a train is 120 kmph. What is the distance covered by it in 10 minutes?
Choices:
A) 26 kmph  B) 20 kmph  C) 28 kmph  D) 30 kmph  E) 40 kmph

Solution: 120 * 10/60= 
120 * 10/60 = 20
20 kmph   Answer: 20 kmph
Answer: B
Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?	Choose the correct option:	A) 2208	B) 2201	C) 2200	D) 2287	E) 2221

Solution: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.   => (90%) of (110%) of x = Rs. 2178.   => (90/100)(110/100)x = 2178   => x = (2178 * 100)/(9 * 11)   => x = Rs. 2200.Answer: 2200
Answer: C
After allowing a discount of 15% on the marked price, the selling price is $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?  Answers: A) $5400 B) $5750 C) $5000 D) $7000 E) $2000

Solution: $5000   $5000   Given SP = $6800   Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)= 
(6800 * 100)/(100 - 15) = 8_000
$8000   If SP= $8000, profit = 60%   $5000P = [SP(100)]/(100 + 60) = (8000 * 100)/160= 
(8000 * 100)/160 = 5_000
$5000
Answer: C
If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant? Select the correct option:	A) 25% loss	B) 25% profit	C) 20% loss	D) 20% profit	E) 5% profit

Solution: Let the cost price of 1 article be $1.   Therefore, cost price of 20 articles = 20 * 1= 
20 * 1 = 20
$20   The selling price of 25 articles= cost price of 20 articles = $20.   Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.   Cost price of 25 articles = 25 * 1= 
25 * 1 = 25
$25.   Therefore, profit made on sale of 25 articles= Selling price of 25 articles - cost price of 25 articles   = 20 - 25 = -$5.   As the profit is in the negative, the merchant has made a loss of $5.   Therefore, % loss = loss/cp * 100   % loss = -5/25 * 100 = 20% loss.   ANSWER:20% loss
Answer: C
I. x2 + 9x + 20 = 0,
II. y2 + 5y + 6 = 0 to solve both the equations to find the values of x and y?	Options:
A) If x < y B) If x > y C) If x ≤ y D) If x ≥ y E) If x = y or the relationship between x and y cannot be established.

Solution: I. x2 + 4x + 5x + 20 = 0   =>(x + 4)(x + 5) = 0 => x = -4, -5   II. y2 + 3y + 2y + 6 = 0   =>(y + 3)(y + 2) = 0 => y = -3, -2   = x < y.   If x < yNSWER:If x < y
Answer: A
At a certain conference, 72% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance? Pick one
A) 18.0%  B) 62.0%  C) 79.2%  D) 80.0%  E) 82.0%

Solution: 0.72A -> At least 2 weeks in advance and paid conference fee in full.   FA -> Paid the conference fee in full   0.10FA -> Not 2 weeks in advance paid but conference fee in full   => 0.90FA -> 2 Weeks in advance and paid the conference fee in full   0.90FA = 0.72A   FA/A = 72/90 * 100= 
72/90 * 100 = 80
80%   Answer - 80.0%
Answer: D
The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?  Options:
A) 6.06%  B) 6.07%  C) 6.08%  D) 6.09%  E) 6.19%

Solution: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100)= 
(106.09 - 100) = 6.09
6.09%   ANSWER:6.09%
Answer: D
The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 44 kg more than the weight of the third boy, what is the weight of the lightest boy?  Choose one.
A) 87.2 kg B) 35.2 kg C) 98.2 kg D) 65.2 kg E) 87.3 kg

Solution: Let the weights of the three boys be 4k, 5k and 6k respectively.   4k + 6k = 5k + 44   => 5k = 44 => k = 8.8   Therefore the weight of the lightest boy   = 4k = 4(8.8) = 35.2 kg.   Answer:35.2 kg
Answer: B
Find the odd man out
4, 8, 12, 16, 20, 24, 27, 32  Choose the correct choice from the following options:	A) 8	B) 27	C) 24	D) 32	E) 36

Solution: 27 is odd man out   as   all numbers in   4, 8, 12, 16, 20, 24, 27, 32 series are even except 24 which is even number.   ANSWER:27
Answer: B
You have three pills with you which you are required to take one after every thirty minutes.
How long can the pills run for you?
Select the correct option
A) 45 Min	B) 55 Min	C) 50 Min	D) 70 Min	E) 60 Min

Solution: E   60 Min   The pills can run for an hour.   Explanation:   If you had ninety minutes in mind, then you are wrong. You took the first pill at the zero minute. Then you took the second pill after 30 minutes and the third pill after 30 + 30 i.e. 60 minutes or an hour.
Answer: E
How many 4-digit positive integers are multiple of each integer from 1 to 10	Choose the correct answer.
A) 1520
B) 2520
C) 3520
D) 5140
E) 7660

Solution: Least No which could be divisible by integers [ 1,2,3,4,5,6,7,8,9,10] is the LCM of the said integers.   LCM [1,2,3,4,5,6,7,8,9,10] = 2520   No the Nos which are divisible by 2520 will be divisible by [1,2,3,4,5,6,7,8,9]   There are 3 values possible between 1000 to 9999   They are 2520 x 1= 2520   2520 x 2 = 5040   2520 x 3 = 7560   ANSWER:2520
Answer: B
John bought 2 shares and sold them for $84 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had  Pick one.
A) a profit of $10 B) a profit of $7 C) a loss of $7 D) a loss of $10 E) neither a profit nor a loss

Solution: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss   Total Selling Price = 84*2= 
84*2 = 168
$168   Total a loss of $7ost Price= 168/(0.96)= 
168/(0.96) = 175
$175   Loss= 175-168= 
175-168 = 7
$7   Answer: Option a loss of $7
Answer: C
A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:  Select.
A) 45:56	B) 45:51	C) 47:56	D) 47:51	E) None

Solution: Solution: Let the CP be 100.   Hence, SP = 100 + 12% of 100 = 112.   If the marked price be X, then   90% of X = 112   =>	X = (112*100)/90 = Rs. 1120/9   Hence,   Required ratio = 100:1120/9 = 900:1120 = 45:56.   45:56nswer: Option 45:56
Answer: A
A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If b and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of b and n?	Choose the correct choice from the following options:
A) -200
B) -130
C) -104
D) 51
E) 305

Solution: 2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to  50+2*50.5= 
 50+2*50.5 = 151
151:   -51 < b < 151   -51 < n < 151   -102 < b+n < 302.   Only option D is in this range.   Answer: 51.
Answer: D
The batting average for 40 innings of a cricket palyer is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is	Answers:
A) 165 runs
B) 170 runs
C) 172 runs
D) 174 runs
E) 176 runs

Solution: Since scores are differ by 172   let us consider the highest as x+172   lowest score would be x   x+ 172 + x=176   2x=4   x=2   so x+172=174   ANSWER:174 runs
Answer: D
If the cost price is 40% of selling price. Then what is the profit percent.	Choose one:  A) 150%  B) 120%  C) 130%  D) 200%  E) None of these

Solution: Explanation:   Let the S.P = 100   then C.P. = 40   Profit = 60   Profit% = (60/40) * 100= 
(60/40) * 100 = 150
150%. 150%nswer: 150%
Answer: A
Debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Debanshu averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives? Choose the correct choice from the following:	A) 135	B) 105	C) 95	D) 75	E) 45

Solution: Debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour.   Use formula 75 = RT   Car:   T1: 45 min   R1: 40 mph   751: [(40*45)/60= 
(40*45)/60 = 30
30 miles   Bike:   T1:?   R2: 12 - 16 mph   752: 08*751= 24 miles   T1: [(24*60)/12= 
(24*60)/12 = 120
120 min (Only 12 mph speed yields an answer given in the choices)   Therefore, 75eb has to leave 120 min - 45 min= 75 min early   ANSWER: 75
Answer: D
A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 6 kilometers per hour. It returns by the same route at an average speed of 8 kilometers per hour. What is the average speed for the round-trip in kilometers per hour? Select
A) 6.8	B) 7.1	C) 7.2	D) 7.5	E) 8.0

Solution: Pick a number which is LCM of 8 and 6 = 24.   Upstream time = 24/6= 
24/6 = 4
4 hrs   Downstream time= 24/8= 
24/8 = 3
3 hrs   Total time= 7 hrs   Total distance = 48   6.8verage Speed = 48/7 =6.8km/hr
Answer: A
If x^2 - y^2 = 2xy, then (x+y)^2 =	Choose the correct answer
A) 2x^2  B) 3x^2  C) 4xy  D) 2y^2  E) -y^2

Solution: Its B   x^2 -y^2 = 2xy   x^2 = 2xy + y^2   2x^2dd x^2 on both sides we get   x^2 +x^2 = x^2 +y^2 +2xy   2x^2 = (x+y)^2   Correct Option : 2x^2
Answer: A
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. 58?
Choices
A) Rs.3944  B) Rs.3948  C) Rs.3942  D) Rs.3965  E) Rs.3929

Solution: 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 * 58   = Rs.3944.   Rs.3944nswer: Rs.3944
Answer: A
Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point Q. Two insects start crawling at the same time from point Q: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point Q? Choose the most appropriate option.
A) 15 minutes B) 30 minutes C) 40 minutes D) 1 hour E) 1 hour, 20 minutes

Solution: Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point Q. Two insects start crawling at the same time from point Q: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point Q?   First we figure out the circumference of the circles so we can determine how long it takes to complete one revolution from point Q to point Q.   C (large) = 20pi   C (small) = 8pi   R (large) = 3pi   R (small) = 5/2pi   It takes 20/3 minutes to make one revolution around the larger circle   It takes 8/(5/2) = 16/5 minutes to make one revolution around the smaller circle   The time it takes them to intersect can be determined by finding the LCM of both times. Get the denominators of both numbers equal one another.   20/3 = 100/15   16/5 = 48/15   LCM of 48 and 100:   48 = 2*2*2*2*3   100 = 2*2*5*5   LCM = 2*2*2*2*3*5*5= 
2*2*2*2*3*5*5 = 1_200
1200   1200/15= 
1200/15 = 80
80 minutes.   (1 hour, 20 minutes) 1 hour, 20 minutes
Answer: E
Dacid obtained 81, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Choose the correct choice.
A) 29  B) 38  C) 76  D) 37  E) 75

Solution: Average = (81 + 65 + 82 + 67 + 85)/5= 
(81 + 65 + 82 + 67 + 85)/5 = 76
76.   Answer: 76
Answer: C
The smallest number which when diminished by 6, is divisible 12, 14, 16, 18 and 22 is:  Choose the correct option.
A) 11099 B) 11094 C) 11091 D) 10323 E) 10483

Solution: Required number = (L.C.M. of 12, 14, 16, 18, 22 ) + 6   = 11088 + 6= 
11088 + 6 = 11_094
11094   Answer: Option 11094
Answer: B