MU-NLPC/Calc-aqua_rat huggingface dataset:
Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time W it could take for 10 cars to be complete? Options.
A) 111 1/9 minutes B) 115 2/5 minutes C) 116 minutes D) 120 minutes E) 125 minutes

Solution: A builds 4 cars in 80 min   B builds 4 cars in 100 min   So A builds another car in another 20 min (i.e total 5 cars)   B builds another car in another 25 minutes (i.e, total 5 cars)   However, A can build another car in next 20 min (i.e total 6 cars)   So total time W= 125 min by B, which is > 120 min by A   B - 4 cars, A - 6 cars   Answer = 120 minutes
Answer: D
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon? Answers:
A) 60°  B) 90°  C) 180°  D) 320°  E) None of these

Solution: Sol.   Angle traced by the hour hand in 6 hours = [360/12 * 6= 
360/12 * 6 = 180
180°   Answer 180°
Answer: C
An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers. How many coins did the old man have?	Options:
A) 24
B) 26
C) 30
D) 64
E) 40

Solution: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.   x^2 - y^2 = 64(x - y) --> x + y = 64.   Answer: 64.
Answer: D
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?  Choose the correct choice from the following answers:
A) 5/6  B) 3/9  C) 5/0  D) 5/3  E) 5/9

Solution: Explanation:   Let us say the ratio of the quantities of cheaper and dearer varieties = x : y   By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6   5/6nswer: Option 5/6
Answer: A
What is the total surface area in square meters of a rectangular solid whose length is 6 meters, width is 5 meters, and depth is 2 meters?
Choose the correct option.
A) 100 m2
B) 104 m2
C) 106 m2
D) 108 m2
E) 160 m2

Solution: Surface Area of a cuboid = 2(lb+bh+lh) = 2(6*5+5*2+6*2)=2(30+10+12)=2*52= 
2*52 = 104
104 m2   Answer : 104 m2
Answer: B
The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability E that exactly two visitors will buy a pack of candy?  Options.
A) 0.343	B) 0.147	C) 0.189	D) 0.063	E) 0.027

Solution: 30.1892 * (3/10)^2 * 7/10   = 3 * 9/100 * 7/10   = 189/1000= 
189/1000 = 189/1_000 = around 0.189
0.189=E   Answer - 0.189
Answer: C
How many necklace of 12 beads each can be made from 18 beads of different colours?  Choose the correct choice from the following answers.
A) 18!(6 x 29)	B) 18!(6 x 21)	C) 18!(6 x 24)	D) 18!(6 x 22)	E) 18!(6 x 44)

Solution: Explanation:   Here clock-wise and anti-clockwise arrangements are same.   Hence total number of circular–permutations: \inline {\color{Black} \frac{18P_{12}}{2\times 12}} = \inline {\color{Black} \frac{18!}{6\times 24}}   Answer: 18!(6 x 24)) 18!(6 x 24)
Answer: C
If the sum of a number and its square is 342, What is the number?
Choose the correct option
A) 16  B) 77  C) 25  D) 87  E) 18

Solution: Explanation:   Let the integer be x.   Then, x + x2 = 342   x2 + x - 342 = 0   (x + 19) (x – 18) = 0   x = 18   ANSW18R: 18
Answer: E
What sum of money will produce Rs.70 as simple interest in 5 years at 3 1/2 percent?	Select the correct option
A) 337
B) 500
C) 266
D) 400
E) 211

Solution: 70 = (P*5*7/2)/100   P = 400   Answer: 400
Answer: D
A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If p 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 p and n? Answers.
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 < p < 151   -51 < n < 151   -102 < p+n < 302.   Only option D is in this range.   Answer: 51.
Answer: D
The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Saran and David have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?  Select:	A) $0.32	B) $0.40	C) $0.45	D) $0.48	E) $0.54

Solution: If Saran and David submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combinedno discount cost.   If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer  (80)*( 0.02)= 
 (80)*( 0.02) = 1.6
$1.60, or together, a cost of $3.20 --- that's the combinedno discount cost.   If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer=($0.40).
Answer: B
In the coordinate plane, the points F (-2,1), G (1,2), and H (2,1) lie on a circle with center P. What are the coordinates of point P ? Choose the correct answer:	A) (0,0)	B) (1,1)	C) (1,2)	D) (1,-2)	E) (2.5, -2.5)

Solution: I thought I need to find the 4th point that would lie on the circle   Hence my answer was D (1,-2)   But the the center of the circle will lie on (0,0)   (0,0)
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 10%?
Options:
A) 550
B) 882
C) 772
D) 652
E) 271

Solution: Cost price = Rs.500   profit = 10% of 500 = Rs.50   Selling price = Cost price + Profit   = 500 + 50= 
500 + 50 = 550
550   550nswer:550
Answer: A
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 220 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?	Pick
A) 220 * sqrt 2  B) 220 * sqrt (2^7)  C) 220 * sqrt (2^12)  D) 220 * the twelfth root of (2^7)  E) 220 * the seventh root of (2^12)

Solution: Let the constant be k.   F1 = 220   F2 = 220k   F3 = 220 k * k = 220 * k^2   F13= 220 * k^12   we know F13 = 2 *F1 = 2 * 220 2 * 1= 
2 * 1 = 2
2 * 220= 
2 * 220 = 440
440   440/220= k^12   k = twelfth root of 2   for F7...   F7 = 220 * k^6 ( as we wrote for F2 and F3)   F7 = 220 * (twelfth root of 2) ^ 6   F7 = 220 * sqrt (2)   The answer is 220 * sqrt 2.
Answer: A
From a bunch of nine keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys? Choose the correct choice from the following
A) 1/224	B) 1/350	C) 1/492	D) 1/504	E) 1/600

Solution: The probability is 1/9*1/8*1/7 = 1/504.   The answer is 1/504.
Answer: D
Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.7 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?	Choose one
A) 1/6	B) 1/2	C) 5/8	D) 5/4	E) 15/16

Solution: X - fraction of products Jane inspected   (1 - X) - fraction of products John inspected   0.7(X) + 0.5(1-X) = 0.75   0.2X = 0.75 - 0.5= 
0.75 - 0.5 = 0.25
0.25/0.2   X= 5/4   Therefore the answer is 5/4: 5/4.
Answer: D
If it takes 4 movers 40 minutes to unpack their van, how long would 5 movers take?
Choose the correct choice.
A) 38 minutes B) 35 minutes C) 32 minutes D) 29 minutes E) 26 minutes

Solution: 4 * 40 = 5 * x   x = 32   Answer: 32 minutes
Answer: C
The annual interest rate earned by an investment increased by 5 percent from last year to this year. If the annual interest rate earned by the investment this year was 26.25 percent, what was the annual interest rate last year?
Choose the correct choice from the following choices
A) 25%	B) 24%	C) 23%	D) 22%	E) 21%

Solution: let i = interest rate   i(this year) = i(last year) + 0.05i(last year) = 1.05i(last year)   26.25 = 1.05 x i(last year)   i(last year) = 26.25/1.05 = 2625/105= 
2625/105 = 25
25%   25%nswer : 25%
Answer: A
no.of zeros in 1*2^2*3^3*....49^49	Select:
A) 240
B) 250
C) 260
D) 270
E) 280

Solution: count the number of 5's   5^5 => 5 5's   10^10 = 2^10*5^10 => 10 5's   15^15 => 15 5's   20^20 => 20 5's   25^25 =(5^2)^25 = 5^50 => 50 5's   30^30 => 30 5's   35^35 => 35 5's   40^40 => 40 5's   45^45 -> 45 5's   total no. of 5's = 5 + 10 + 15 + 20 + 50 + 30 + 35 + 40 + 45= 
5 + 10 + 15 + 20 + 50 + 30 + 35 + 40 + 45 = 250
250   i.e. product has a term 5^250 , also no. of 2's is much more than 250   no.of zeros in 1*2^2*3^3*....49^49= 250   ANSWER:250
Answer: B
The sum of all the integers k such that –20 < k < 24 is Choose the correct choice from the following answers
A) 0 B) -2 C) -25 D) -49 E) -37

Solution: -19------------------0-----------------23   values upto+23 cancels outwe are left with only -19-18 sum of which is - 37. hence option D.   -37
Answer: E
12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 12 hours a day, the number of men required? Choose the correct choice from the following answers.
A) 11 days  B) 12 days  C) 9 days  D) 8 days  E) 10 days

Solution: That is, 1 work done = 12 × 8 × 10   Then, 12 8 × 10 = ? × 12 × 8   ? (i.e. No. of men required) = 12 × 8 × 10/12× 8 = 8 days   10 days)
Answer: E
A, B and C can do a work in 90, 30 and 15 days respectively. If they work together, in how many days will they complete the work?	Choose the correct choice from the following answers: A) 5 B) 6 C) 7 D) 8 E) 9

Solution: One days's work of A, B and C = 1/90 + 1/30 + 1/15   = (1 + 3 + 6)/90 = 1/9   A, B and C together can do the work in 9 days.   Answer:9
Answer: E
Tough and Tricky questions: Ratios
2/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip? Choices:
A) 1/2	B) 2/3	C) 11/15	D) 23/30	E) 3/5

Solution: let total no. of students be 30   students left on a field trip = 2/5(30) =12   thus 18 students left behind   1/3(18)=6 students did not want to go. thus 12 students want to go on the trip   1/2(12)=6 were able to join the other students on the field trip.   thus total number of students that went on a field trip =12+6= 
12+6 = 18
18   thus required fraction= 18/30 =3/5   3/5
Answer: E
2 trains in same direction at 50km/hr,32 km/hr.A man in slower train observes 15 sec elapse before the faster train completely passed by him what is length of faster train? Answers:
A) 65 meters
B) 75 meters
C) 85 meters
D) 95 meters
E) 55 meters

Solution: relative speed= 18k/hr= 5 m/sec   distance covered= length of faster train= 5*15= 
5*15 = 75
75 meters   ANSWER:75 meters
Answer: B
There are 6 physics books and 1 chemistry book on shelf P and 5 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?  Select the correct option.
A) 1/42 B) 1/21 C) 1/15 D) 1/12 E) 1/10

Solution: P(a chemistry book is moved to shelf Q) = 1/7   P(a chemistry book is then chosen from shelf Q) = 1/6   P(the student takes a chemistry book) = 1/7 * 1/6 = 1/42   The answer is 1/42.
Answer: A
What sum of money will produce Rs.90 as simple interest in 4 years at 3 1/2 percent?
Pick:	A) 742.85	B) 622.85	C) 632.85	D) 652.85	E) 642.85

Solution: 90 = (P*4*7/2)/100   P = 642.85   ANSW642.85R:642.85
Answer: E
If 2x = 3y = 10, then 9xy = ?	Choose the correct answer:
A) 1,200	B) 200	C) 150	D) 40	E) 20

Solution: 2x = 10;x=5   3y = 10;y=10/3   Multiply: 9xy=9*5*10/3= 
9*5*10/3 = 150
150   Answer: 150.
Answer: C
the present average age of a couple and their daughter is 35 years. Fifteen years from now, the age of the mother will be equal to the sum of present ages of the father and the daughter. Find the present age of mother?	Choose the correct choice from the following answers
A) 18 years
B) 19 years
C) 11 years
D) 45 years
E) 12 years

Solution: Explanation:   (f + m + d)/3 = 35   => f + m + d = 105 --- (1)   m + 15 = f + d   Substituting f + d as m + 15 in (1), we get   2m + 15 = 105   2m = 90 => m = 45 years.   Answer: 45 years
Answer: D
What is the area of a square field whose diagonal of length 24 m?  Choose the correct option.
A) 256	B) 289	C) 200	D) 288	E) 178

Solution: d2/2 = (24 * 24)/2= 
(24 * 24)/2 = 288
288   Answer: 288
Answer: D
The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?	Choose the correct choice from the following:
A) 40, 68 kmph
B) 40, 30 kmph
C) 90, 60 kmph
D) 40, 60 kmph
E) 90, 30 kmph

Solution: Speed downstream = 60 + 30= 
60 + 30 = 90
90 kmph   Speed upstream= 60 - 30= 
60 - 30 = 30
30 kmph   Answer: 90, 30 kmph
Answer: E
Mary and Mike enter into a partnership by investing $800 and $200 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1200 more than Mike did, what was the profit made by their business in that year?	Choices.
A) $3000	B) $3500	C) $4000	D) $4200	E) $4500

Solution: Explanatory Answer   Let the profit made during the year be $3x   Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 8 : 2.   i.e., 80% of 2x would go to Mary and 20% of 2x would go to Mike.   Hence, Mary would get (80 - 20)% of 2x more than Mike   Or60% of 2x = $1200   i.e.,(60/100)*2x = 1200   or 2x = 2000.   Hence, the profit made by the company during the year $3x = $3000.   $3000nswer : $3000
Answer: A
8+2+2^2+2^3+2^4+2^5=？ Pick.
A) (2^3-1)(2^3+2)
B) 2^6+1
C) 2^5-1
D) 2^5+1
E) 2^5-2

Solution: 8+2+2^2+2^3+2^4+2^5=64   (2^3-1)(2^3+2)=64   the correct answer is (2^3-1)(2^3+2).
Answer: A
Anand and Deepak started a business investing Rs. 25,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?  Choose the most appropriate option.
A) 2777 B) 2888 C) 8050 D) 2882 E) 2781

Solution: Ratio of their shares = 25000 : 35000 = 5:7   Deepak's share = 13800 * 7/12 = Rs. 8050.   Answer: 8050
Answer: C
In how many ways can the letters of the word RECPECT be arranged? Select.
A) 1800 B) 1920 C) 2520 D) 3453 E) 3500

Solution: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways   2520
Answer: C
Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?	Choose the correct choice from the following:
A) 19
B) 19.7
C) 19.9
D) 21.7
E) 22.8

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 Paise is given as tax   => Total tax incurred = 30 Paise = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: B
When positive integer w is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30	Pick.
A) I only  B) II only  C) I and II only  D) II and III only  E) None of the above

Solution: ans E..   we can tell the ans w/o using examples..   the units digit of product w*n is 3..   this means w and n are odd positive integers..   therefore n cannot have an even factor so 8 and 30 are out..   n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: E
On a certain date, Pat invested $6,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $24,000, in how many years total will the total value of the investment plus interest increase to $48,000?  Choose the correct answer:
A) 15  B) 16  C) 18  D) 20  E) 24

Solution: 24,000 = 6,000(1 + x)^10   4 = (1+x)^10 = 2^2   (1+x)^10 = ((1+x)^5)^2 = 2^2   Therefore, (1+x)^5 = 2   48,000 = 6000(1 + x)^n   (1+x)^n = 8   (1+x)^n = 2^3   (1+x)^n = ((1+x)^5)^3 = (1+x)^15   Therefore, n = 15.   The answer is 15.
Answer: A
What are the last two digits of 43*25*23*72*51*31? Choose the correct option
A) 54
B) 75
C) 00
D) 45
E) 32

Solution: 43*25*23*72*51*31=   We have to focus on the last two digits only, so 43*25=75*23=25*72=00   51*00= 
51*00 = 0
00 therefore   31*00= 
  31*00 = 0
00   Hence Answer is 00
Answer: C
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? Pick:
A) 18 days
B) 27 days
C) 26.67 days
D) 16 days
E) 12 days

Solution: Answer   A can complete a project in 20 days. So, A will complete 1/20th of the project in a day.   B can complete a project in 30 days. So, B will complete 1/30th of the project in a day.   Let the total number of days taken to complete the project be x days.   B worked for all x days. However, A worked for (x - 10) days because A quits 10 days before the project is completed.   In a day, A completes 1/20th of the project.   Therefore, A would have completed x−10/20th of the project in (x - 10) days.   In a day, B completes130130th of the project.   Therefore, B would have completed x/30h of the project in x days.   ∴ x−10/20+x/30= 1   Or x = 18.   Choice 18 days
Answer: A
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Select the correct option
A) 14 liters  B) 76 liters  C) 10 liters  D) 11 liters  E) 12 liters

Solution: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P =10 liters.   Answer: 10 liters
Answer: C
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :	Choose the most appropriate option.
A) 8 days  B) 10 days  C) 12 days  D) 15 days  E) 18 days

Solution: Explanation:   (A + B)'s 1 day's work =(1/15 + 1/10)=1/6   Work done by A and B in 2 days =(1/6 X 2)=1/3   Remaining work =(1-1/3)=2/3   Now,	1/15work is done by A in 1 day.   2/3work will be done by a in	(15 X 2/3)= 10 days.   Hence, the total time taken = (10 + 2)= 
(10 + 2) = 12
12 days.   ANSWER IS 12 days
Answer: C
Three grades of milk are 1 percent, 2 percent and 4 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 4 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?	Choose one
A) y + 5z B) (y +z) / 4 C) 2y + 3z D) 3y + z E) 3y + 4.5z

Solution: Based on the given information, the following equation could be dervied: 1% * x + 2% * y + 4% * z = 1.5% * (x+y+z) Then use algebra to figure out 0.5%*x = 0.5%*y + 2.5%*z. Thus, x = y + 5z.   y + 5z
Answer: A
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Select the correct option:  A) 10  B) 18  C) 36  D) 72  E) 16

Solution: Answer: Option C   Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.
Answer: C
One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?	Choose the correct choice from the following options
A) 3 B) 5 C) 7 D) 9 E) 11

Solution: x/2 – x/3 = 6 => x =6   3 + 6= 
3 + 6 = 9
9   ANSWER:9
Answer: D
If 2 = (6x)/(x - xy/z) then which of the following is true?  Options: A) y = -2z B) y = 2z C) 2y = z D) -2y = z E) y = -z

Solution: 2 = (6x)/(x - xy/z)   => 2 = (6xz)/(x*(z - y))   => 2x = (6xz)/(z - y)   => (z - y) = 3z   => y = -2z   Hence Ans is y = 2z
Answer: B
A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the
ball is white?
Choose the correct choice from the following:
A) 1
B) 1/6
C) 1/3
D) 1/2
E) None of these

Solution: Explanation:   Total cases = 50 + 10= 
50 + 10 = 60
60   Favourable cases= 10   So probability = 10/60 = 1/6   Answer: 1/6
Answer: B
In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?	Choose one:
A) 20% B) 60% C) 40% D) 75% E) 80%

Solution: Let the total survey population be 100x. Now, 56x are married.   Again, let the total no of married people in the survey be 100y. Thus, 30% of them lied about being married. Thus, 70% were honest about it.   Thus, 70y = 56x   And, therefore 100y = 80x.   Thus, 80% were actually married.   ANSW80%R:80%
Answer: E
Which answer is closest to the √151?
Choose the most appropriate option:
A) 12.1  B) 12.2  C) 12.3  D) 12.4  E) 12.5

Solution: Try filling the numbers into the answer y x y =   Find the closest to 151.   Answer 12.3
Answer: C
At a raffle, 20% of the attendees bought more than five tickets, 65% of the remaining bought four tickets or less. What percentage of the attendees bought five tickets?  Choose the correct choice:
A) 28% of the attendees bought five tickets.	B) 52% of the attendees bought five tickets.	C) 20% of the attendees bought five tickets.	D) 72% of the attendees bought five tickets.	E) None of these.

Solution: Explanation:Let total number of attendees be 100,Then, number of attendees who bought more than five tickets = 20.Number of attendees who bought four tickets or less= 65% of 80 = 52.Total number with five tickets = 100 – 20 – 52 = 28.Thus, 28% of the attendees bought five tickets.28% of the attendees bought five tickets.nswer: Option 28% of the attendees bought five tickets..
Answer: A
Thomas and Matt has some money with them in the ratio of 3:4. If their father gives Rs.30 to each of them then the ratio becomes 4:5. What would be the ratio if Thomas spend Rs.40 and Matt spend Rs. 20 from what they have now?
Options.
A) 1:2 B) 2:3 C) 3:4 D) 4:5 E) 5:6

Solution: Let money of Thomas and Matt be x and y respectively.   x/y = 3/4 => x = 3/4 y   (x+30)/(y+30) = 4/5   => 5x+150 = 4y+120 => 5x = 4y-30   But x = 3/4 y   5* 3/4 y = 4y-30   15y = 16y-120 => y = 120   => x = 3*120/4 => x=90   Ratio of their money, if Thomas spend Rs.40 and Matt spend Rs. 20 => (90-40)/(120-20) = 50/100. => 1:2   1:2nswer:1:2
Answer: A