MU-NLPC/Calc-aqua_rat huggingface dataset:
Jack and Jill work at a hospital with 5 other workers. For an internal review, 2 of the 7 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?
Pick:  A) 1/3  B) 1/4  C) 1/21  D) 3/8  E) 2/3

Solution: 1/7C2=1/21.   Answer: 1/21.
Answer: C
The ratio, by volume, of bleach to detergent to water in a certain solution is 4 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?	Choices.
A) 80 B) 70 C) 60 D) 40 E) 50

Solution: B:D:W = 4:40:100   Bnew / Dnew = (1/3)*(4/40) = (1/30)   Dnew / Wnew = (1/2)*(40/100) = (1/5)   Wnew = 300   Dnew = Wnew/5 = 300/5= 
300/5 = 60
60   So, answer will be   60
Answer: C
After decreasing 24% in the price of an article costs Rs.1064. Find the actual cost of an article?
Choices.
A) 1667  B) 6789  C) 1200  D) 6151  E) 1400

Solution: CP* (76/100)   = 1064   CP= 14 * 100 => CP   = 1400   Answer: 1400
Answer: E
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?  Choose the correct option:	A) 2 : 5	B) 2 : 7	C) 5 : 2	D) 7 : 2	E) None

Solution: Solution   Let C.P. = Rs. 5x and	S.P. = Rs.7x.   Then, Gain = Rs. 2x.   ∴ Required ratio	= 2x : 5x   ‹=›2 : 5   2 : 5nswer 2 : 5
Answer: A
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? Choose one:
A) 9
B) 10
C) 12
D) 20
E) 25

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km =(9/54 x 60) min	= 10 min   Answer:10
Answer: B
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 42 ?	Choose the correct answer:
A) 4
B) 3
C) 5
D) 6
E) 2

Solution: Denote |x - 3| as y: y^2 + y = 42 --> y = -7 or y = 6. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.   y = |x - 3| = 6 --> x = 9 or x = -4. The sum = 5.   Answer: 5.
Answer: C
Two trains travelling in the same direction at 40 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?	Answers:
A) 118 m
B) 128 m
C) 231 m
D) 175 m
E) 142 m

Solution: 175 m   175 m   RS = 40 – 22 = 18 * 5/18= 
18 * 5/18 = 5
5 mps   T= 60 sec   175 m = 5 * 60= 
5 * 60 = 300
300 m   (-) 125   --------   175 m
Answer: D
When y is divided by 288, the remainder is 44. What is the remainder when the same y is divided by 24?
Pick one
A) 20  B) 21  C) 23  D) 25  E) 26

Solution: y = 288*a + 44 = (24*12)*a + 24 + 20   The answer is 20.
Answer: A
Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 30. No two digits of h are identical. How many different numbers are possible values of h?
Choose the correct choice from the following choices.
A) 24 B) 30 C) 36 D) 42 E) 54

Solution: 24nswer = 24= 24   Let number =abcd   Given that a*b*c*d = 30   a,b,c,d can be 1,2,3,5   Number of ways = 4*3*2= 
4*3*2 = 24
24
Answer: A
A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 10:30 am in the same direction at the rate of 84 km/h. At what time will the second train catch the first train? Choose the correct choice from the following
A) 4:30 B) 5:00 C) 5:30 D) 6:00 E) 6:30

Solution: In one hour and thirty minutes the first train travels 105 km.   The second train catches the first train at a rate of 84 km/h - 70 km/h = 14 km/h.   The second train will catch the first train in   105/14= 
  105/14 = 15/2 = around 7.5
7.5 hours, so at 6:00 pm.   The answer is 6:00.
Answer: D
Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
Select.
A) 15:8
B) 12:0
C) 13:9
D) 14:2
E) 13:0

Solution: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.   Let the length of train P be LP and that of train Q be LQ   given that LP = 3/4 LQ   15:8s the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,   => Speed of train P = VP = LP/30   Speed of train Q = VQ = LQ/75   LP = 3/4 LQ   => VP = 3/4 LQ/(30) = LQ/40   Ratio of their speeds = VP : VQ   = LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8   15:8nswer:15:8
Answer: A
A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 700 more than that by the previous schema, his sales were worth? Select the correct option:
A) s. 8,000
B) s. 9,000
C) s. 20,000
D) s.10,000
E) s. 50,000

Solution: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 700   X = 8000   s. 8,000NSWER s. 8,000
Answer: A
Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 50°C, what is the temperature of the pot of water in °F?  Choose the correct choice:
A) 101°F B) 108°F C) 116°F D) 122°F E) 127°F

Solution: Let F and C denote the temperature in Fahrenheit and Celsius respectively.   (F - 32) /(212 - 32) = (C - 0)/(100 - 0)   F = 9C/5 + 32   F = 9(50)/5 + 32 = 122°F   The answer is 122°F.
Answer: D
When x + p is divided by p + 1, the quotient is n and there is no remainder. Which of the following must be the value of x?  Pick one:
A) n(p +1)	B) n(p − 1)	C) p(n + 1)	D) p(n - 1) + n	E) n(p + 1) (p − 1)

Solution: Given in question (x+p)/p+1= n   => x+p= n(p+1)   =>x= np+n-p   or x= np-p+n   Now we are good to check the options   x= p(n-1) + n   Answer p(n - 1) + n
Answer: D
A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?  Choose the correct choice from the following answers: A) 100 B) 150 C) 160 D) 170 E) 180

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 120)/25 = x/15 => x = 180 m.   Answer: Option 180
Answer: E
Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 35.1 kg of zinc has been consumed in it?  Choose the correct answer
A) 78 kg B) 60 kg C) 64 kg D) 70 kg E) None

Solution: Sol.   For 9 kg Zinc, mixture melted = (9+11) kg.   For 35.1 kg Zinc, mixture, melted = [20/9 x 35.1] kg   = 78 kg.   78 kgnswer 78 kg
Answer: A
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? Options.
A) 180 degrees B) 190 degrees C) 200 degrees D) 280 degrees E) None

Solution: 180 degreesngle traced by the hour hand in 6 hours = ( 360/12 * 11/3 )degrees   =180 degrees   180 degrees
Answer: A
A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:	Choose the correct choice from the following answers.
A) 100  B) 120  C) 110  D) 130  E) 140

Solution: sax Letlheo g alnumberofworkers hex   x workers can do the wor - 100 days   (x — 10) workers can do the work in 110 days   4 100x 1u1x— 10)   1100 Q x 110   110
Answer: C
There are 300 giraffes at a large zoo. The number of giraffes is 3 times the number of all the other animals combined. How many more giraffes are there than non giraffes animals at the zoo? Choose the correct choice from the following answers:
A) 400
B) 360
C) 300
D) 290
E) 200

Solution: Answer is D.   Total giraffes= 300 = 3 * Other Animals (X)   or X = 10.   So, 290ifference in giraffes and X = 300-10= 
300-10 = 290
290.
Answer: D
Find the ratio in which rice at Rs.7.20 a kg be mixed with rice at Rs.5.80 a kg to produce a mixture worth Rs.6.30 a kg?	Options.
A) 5 : 9 B) 2 : 3 C) 3 : 4 D) 4 : 5 E) None of these

Solution: Solution   Required ratio = 50 : 90 = 5 : 9   5 : 9nswer 5 : 9
Answer: A
A customers identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?  Choose the correct answer:  A) 211  B) 216  C) 1075  D) 1080  E) 2160

Solution: A customers identification code will be of the type -,-,-,-   first digit can be selected from any of the 5 vowels in 5C1 ways   now for the remaining three digit lets consider the following two cases   case 1: when the number is greater than 200 but less than 300   number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18   now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:   211   233   244   255   266   277   288   299   here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)   thus total possible cases are 18 + 8= 
18 + 8 = 26
26   case 2: number ranging from 300 to 999   here for first digit we have 7 cases (3,4,5,6,7,8,9)   now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)   if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)   hence total number of ways= 7(18+9) = 189   thus different number of codes = 5(189+26) = 1075   hence 1075
Answer: C
A bowl of fruit contains 12 apples and 23 oranges. How many oranges must be removed so that 60% of the pieces of fruit in the bowl will be apples?	Choose one:
A) 3
B) 6
C) 15
D) 17
E) 20

Solution: Number of apples = 14   number of oranges = 23   let number of oranges that must be removed so that 60% of pieces of fruit in bowl will be apples = x   Total number of fruits after x oranges are removed = 12+(23-x) = 35-x   12/(35-x) = 6/10   =>20 = 35-x   =>x= 15   Answer 15
Answer: C
The sum of a number and its reciprocal is one-fifth of 26. What is the sum of that number and its square.	Options:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Explanation:   Let the number be x. Then,   x + 1/x = 26/5   => (x2 + 1)/x = 26/5   => 5x2 - 26x + 5 = -0   => (x - 5)(5x - 1) = 0   => x = 5 or 1/5   Answer: Option 5
Answer: C
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last? Choose the correct choice from the following choices:
A) 3 days. B) 4 days. C) 9 days. D) 8 days. E) 10 days.

Solution: Work done by X in 4 days =1/20	x 4=	1/5.   Remaining work =1 -	1/5=	4/5.   (X + Y)'s 1 day's work =1/20+1/12=8/60=2/15.   Now,	2/15	work is done by X and Y in 1 day.   So,	4/5 work will be done by X and Y in	15/2	x 4/5= 6 days.   Hence, total time taken = (6 + 4)= 
(6 + 4) = 10
10 days.   Answer: Option 10 days.
Answer: E
The average marks scored by Ganesh in English, Science, Mathematics and History is less than 20 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
Choices:
A) 80  B) 50  C) 60  D) Data inadequate  E) None of these

Solution: E+H+G+M/4âˆ’E+S+M+H/4=20   â‡’ G - S = 80   80nswer 80
Answer: A
At the opening of a trading day at a certain stock exchange, the price per share of stock K was $10. If the price per share of stock K was $15 at the closing of the day, what was the percent increase in the price per share of stock K for that day?  Pick one.
A) 1.4% B) 50% C) 11.1% D) 12.5% E) 23.6%

Solution: Opening = 10   Closing = 15   Rise in price = 5   So, percent increase = 5/10 * 100= 
5/10 * 100 = 50
50%   Answer : 50%
Answer: B
If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?  Choose the correct choice from the following options
A) 27%	B) 65%	C) 285%	D) 245%	E) 25%

Solution: Given that, cost price of 50 article is equal to selling price of 40 articles.   Let cost price of one article = Rs. 1   Selling price of 40 articles = Rs. 50   But Cost price of 40 articles = Rs. 40   Therefore, the trader made profit.\Percentage of profit = 10/40 * 100= 
10/40 * 100 = 25
25%.Answer:25%
Answer: E
A train covers a distance of 20 km in 10 minutes. If its speed is decreased by 10 km/hr, the time taken by it to cover the same distance will be?
Choose the correct choice from the following choices:
A) 20min 15sec  B) 11min 30sec  C) 15min 20sec  D) 12min 10sec  E) 9min 30sec

Solution: Speed = 20*60/10= 
20*60/10 = 120
120 km/hr   new speed= 120-10= 
120-10 = 110
110 km/hr   time taken= 20/110 = 60*2/11 = 11 min 30 sec   Answer is 11min 30sec
Answer: B
At an international conference, “Yellow” world countries and “Blue” world countries are the only participants. The ratio of “Yellow” world participants to “Blue” world participants is 3:2. If one-third of “Yellow” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed? Pick
A) 7
B) 7/15
C) 5/8
D) 9/2
E) 4/6

Solution: Yellow: 7/15lue = 3:2   Let Yellow = 3x and 7/15lue = 2x   1/3 of Yellow are left handed => 1/3 * 3x = 3x/3 Yellow left handed   2/3 of 7/15lue are left handed => 2/3 *2x = 4x/3 blue left handed   fraction of participants who are left handed = total left handed/ total participants = (yellow left handed + blue left handed)/total participants = (3x/3 + 4x/3)/(3x+2x) = (7x/15x) = 7/15   Answer : 7/15
Answer: B
A salesman gets commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as bonus of 3% on the excess of sales over Rs.10,000. If he gets total commission of Rs.1380, then the bonus he received is:
Options:
A) 22  B) 120  C) 388  D) 377  E) 272

Solution: Explanation:   Commission up to 10000 = \inline 10000\times \frac{9}{100} = 900   Again after 10000,   Commission : 120onus   9 : 3   \inline \Rightarrow 3x : x   \therefore 120onus = \inline (1380-900)\times \frac{1}{4}= Rs.120   Answer: 120) Rs.120
Answer: B
I. l-14, l, l, l, l+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following? Choose the correct choice from the following options:  A) I, II, III  B) I, III, II  C) II, III, I  D) III, I, II  E) III, II, I

Solution: S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of l or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.   I, II, III.
Answer: A
Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 3% more. She would get how much?
Choose one:  A) 9920  B) 96288  C) 26667  D) 1662  E) 2882

Solution: (8000*3*3)/100= 
(8000*3*3)/100 = 720
720   9200   --------   9920   9920nswer:9920
Answer: A
Ajay can walk 7km in 1 hour. In how many hours he can walk 80km?
Options:
A) 5hrs B) 11.4hrs C) 15.5hrs D) 20.4hrs E) 30hrs

Solution: 1 hour he walk 8km   he walk 80km in = 80/7* 1 = 11.4hours   Answer is 11.4hrs
Answer: B
Emily cut two circles from a sheet of colored paper measuring 8” by 12”. One circle had a
radius of 3 inches and the other had a radius of 2.5 inches. How many square inches of paper are
left over?
Select the correct option:	A) 48.11 sq. in.	B) 58.11 sq. in.	C) 68.11 sq. in.	D) 78.11 sq. in.	E) 88.11 sq. in.

Solution: 8 x 12 = 96 sq. in. area of paper   3.14(3)2 = 28.26 sq. in. area of one circle   3.14(2.5)2 = 19.625 or 19.63 sq. in. rounded   area of other circle    28.26 + 19.63= 
 28.26 + 19.63 = 47.89
47.89 sq. in. used for circles     96 - 47.89= 
  96 - 47.89 = 48.11
48.11 sq. in. left over   correct answer 48.11 sq. in.
Answer: A
A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast? Choose the correct option:  A) 7500  B) 5000  C) 6000  D) 3500  E) 4000

Solution: Explanation:   35%-----------L   65%-----------W   ------------------   30%----------2250   100%---------? => 7500   7500NSWER IS 7500
Answer: A
A man can row 4.5 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
Choose the correct choice
A) 1.9  B) 1.7  C) 1.2  D) 1.5  E) 1.1

Solution: Speed of boat in still water (b) = 4.5 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.5 km/hr.   Answer: 1.5
Answer: D
Two friends A and B are running up hill and then to get down! length of road is 440 yards. A on his return journey met B going up at 20 yards from top, A has finished the race 5 minutes earlier than B, then how much time A had taken to complete the race.  Choose the correct choice from the following options:
A) 50 minutes  B) 52.5 minutes  C) 55 minutes  D) 54.5 minutes  E) None of these

Solution: Explanation :   When A travels 460m (=440+20),   B travels 420m (=440-20). So, ratio of speed = 460:420   = 23:21.   Let A's speed be 23x, and that of B's be 21x.   => 23x = ((2 * 440) / t) which implies 23t = 880/x;   => 21x = ((2 * 440) / (t+5)) which implies 21(t+5) = 880/x.   From these two equations, 23t = 21(t+5). Solving, t = 52.5   Hence (B) is the correct answer.   Answer : 52.5 minutes
Answer: B
The speed of a boat in upstream is 20 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Choose the correct answer
A) 10 kmph  B) 11 kmph  C) 16 kmph  D) 30 kmph  E) 19 kmph

Solution: Speed of the boat in still water = (20+80)/2= 
(20+80)/2 = 50
50 kmph. Speed of the stream= (80-20)/2= 
(80-20)/2 = 30
30 kmph.Answer: 30 kmph
Answer: D
Two trains 140 m and 180 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Select
A) 17.9 sec	B) 11.52 sec	C) 27.7 sec	D) 10.8 sec	E) 17.8 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 180= 
140 + 180 = 320
320 m.   Required time= 320 * 9/250= 
320 * 9/250 = 288/25 = around 11.52
11.52 sec.   Answer: 11.52 sec
Answer: B
A lady bought five books namely A,B,C,D,E to distribute her 6 children. How many ways she can distribute books? Choose the correct answer
A) 6^3
B) 5^6
C) 6^5
D) 6^6
E) 3^6

Solution: 6*6*6*6*6   6^5   ANSWER:6^5
Answer: C
Evaluate: 50 - 12÷2×2 =
Choose the correct choice:
A) A)36
B) B)38
C) C)40
D) D)42
E) E)44

Solution: According to order of operations, 12÷2×2 (division and multiplication) is done first from left to right   12÷2×2 = 6 × 2 = 12   Hence   50 - 12÷6×2 = 50 - 12= 
50 - 12 = 38
38   correct answer is 38) 38
Answer: B
A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?	Options.
A) 12.6
B) 82.5
C) 12.4
D) 12.5
E) 12.0

Solution: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.   Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7   Solving the equation, the speed of man in still water is 12.5 kmph.   Answer: 12.5
Answer: D
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?  Choose the correct choice from the following choices:
A) 22277
B) 29977
C) 267676
D) 14000
E) 18811

Solution: 25*12: 30*12: 35*8   15:18:14   14/47 * 47000= 
14/47 * 47000 = 14_000
14000   Answer: 14000
Answer: D
A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 38 miles per hour, how many miles did the car travel in the third 5-minute interval?
Choose one:
A) 1.0 B) 1.5 C) 2.0 D) 2.5 E) 4.0

Solution: In the third time interval the average speed of the car was 38+5+5=30 miles per hour;   In 5 minutes (1/12 hour) at that speed car would travel   48*1/12= 
  48*1/12 = 4
4 miles.   Answer: 4.0.
Answer: E
In a simultaneous throw of 2 dice what is the probability of getting a total of 4?	Options.
A) 1/2 B) 1/4 C) 2/9 D) 1/12 E) 3/13

Solution: n(S) = 6*6= 
6*6 = 36
36   E= {(1,3),(2,2),(3,1)}   Probability = 3/36 = 1/12   Answer is 1/12
Answer: D
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is? Pick.
A) 5760
B) 5860
C) 5240
D) 5890
E) 6000

Solution: 1/x - 1/6 = -1/8   x = 24 hrs    24 * 60 * 4= 
 24 * 60 * 4 = 5_760
5760   5760NSWER 5760
Answer: A
Midas has boxes in three sizes: large, medium, and small. He puts 11 large boxes on a table. He leaves some of these boxes empty, and in all the other boxes he puts 8 medium boxes. He leaves some of these medium boxes empty, and in all the other medium boxes he puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.
How many boxes has Midas used in total?	Options:
A) 113	B) 114	C) 115	D) 116	E) 117

Solution: By keeping 8 boxes in a single box, the total number of empty boxes increases by  8-1= 
 8-1 = 7
7.   let x the number of times that 8 boxes have been kept in a box   now we know that 11 + 7x= 102   by solving we have x=13   finally 11 + 13 × 8 = 115   therefore totally 115 boxes have been used   ANSWER:115
Answer: C
How many three-digit numbers are divisible by 6 in all?	Choices: A) 149 B) 150 C) 151 D) 166 E) None

Solution: Solution   Required numbers are 102,018,114,....996.   This is an A.P with a = 102,   d= 6.   Let the number of its terms be n. Then	a+(n - 1)d   ‹=›102+(n - 1)×6 = 996   ‹=›n=150.   Answer 150
Answer: B
How many keystrokes are needed to type the numbers from 1 to 100? Choose the correct choice from the following answers:  A) 102  B) 150  C) 192  D) 208  E) 225

Solution: There are 9 one-digit numbers from 1 to 9.   There are 90 two-digit numbers from 10 to 99.   We need 3 keystrokes for the number 100.   9 + 90(2) + 3 = 192   The answer is 192.
Answer: C
The perimeter of a semi circle is 144 cm then the radius is?
Options: A) 25 cm B) 28 cm C) 30 cm D) 35 cm E) 40 cm

Solution: Explanation:   36/7 r = 144 => r = 28   ANSWER IS 28 cm
Answer: B
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p? Choose the most appropriate option:  A) 10  B) 12  C) 14  D) 16  E) 18

Solution: No need to actually find the product of 1 to 30. Just look at the numbers that have factors of 3.   3 = 3   6 = 3 * 2   9 = 3 * 3   12 = 3 * 2 * 2   15 = 3 * 5   18 = 3 * 3 * 2   21 = 3 * 7   24 = 3 * 2 * 2 * 2   27 = 3 * 3 * 3   30 = 3 * 2 * 5   There are 14 3's, so the largest factor of p for 3k is 3*14   ANSWER:14
Answer: C
At a special sale, 12 tickets can be purchased for the price of 3 tickets. If 12 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 12 tickets?  Select the correct option.
A) 20%
B) 33.3%
C) 40%
D) 50%
E) 75%

Solution: let the price of a ticket be Rs.100, so 3 tickets cost 300 & 12 tickets cost 1200   12 tickets purchased at price of 3 tickets ie., for 300, so amount saved s Rs.900,   % of 5 tickets = (900 /1200)*100= 
(900 /1200)*100 = 75
75 %   ANSW75%R:75%
Answer: E