MU-NLPC/Calc-aqua_rat huggingface dataset:
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 3 and 4 are not together ?
Pick one
A) 48 B) 36 C) 60 D) 72 E) 120

Solution: Reqd ways = (Total No. of ways - cases when both 3 and 4 are together)   5 numbers can be arranged in 5 places in 5! ways. Now tie 3 and 4 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.   Reqd. Answer = 5! - 4!2! = 120 - (24*2)= 
120 - (24*2) = 72
72   Answer: 72
Answer: D
A car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip?
Choose the correct choice from the following choices.
A) 8  B) 10  C) 12  D) 14  E) 16

Solution: Let T be the total time of the trip.   30*6 + 46(T-6) = 34T   12T = 276-180   T = 8   The answer is 8.
Answer: A
A 1100 m long train crosses a tree in 110 sec, how much time will It take to pass a platform 700 m long?  Choose the correct option.
A) 288	B) 190	C) 188	D) 180	E) 12

Solution: L = S*T   S= 1100/110= 
1100/110 = 10
10 m/Sec.   Total length (180)= 1800 m   T = 180/S   T = 1800/10= 
1800/10 = 180
180 Sec   Answer:180
Answer: D
The area of a square field is 625 km2. How long will it take for a horse to run around at the speed of 25 km/h ? Answers
A) 12 h  B) 10 h  C) 8 h  D) 4 h  E) None of these

Solution: Explanation Area of field = 625 km2. Then, each side of field = √625=25km 4 histance covered by the horse = Perimeter of square field = 25 × 4 = 100 km ∴ Time taken by horse = distances/peed=100/25= 
100/25 = 4
4h Answer 4 h
Answer: D
For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (9,0) and center at the point (3,3), what are the coordinates of the remaining vertex?
Options:  A) (3,4)  B) (3,6)  C) (0,9)  D) (6,4)  E) (9,6)

Solution: Let (a,b) be the remaining vertex.   x: 0 + 9 + a = 3*3. Then a = 0.   y: 0 + 0 + b = 3*3.= 
3*3. = 9
9.   The answer is (0,9).
Answer: C
The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ? Choose the correct choice:
A) 71 years	B) 72 years	C) 74 years	D) 77 years	E) 79 years

Solution: The total of the ages of Amar, Akbar and Anthony is 80 years.   total of their ages three years ago = 80-3*3= 
80-3*3 = 71
71 yrs   71 yearsNSWER:71 years
Answer: A
Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is?
Select the correct option.
A) 5 days  B) 6 days  C) 7 days  D) 8 days  E) 9 days

Solution: If A can complete a work in x days and B can complete the same work in y days, then, both   of them together can complete the work in x y/ x+ y days.   That is, the required No. of days = 10 × 40/50 = 8 days.   8 days)
Answer: D
The number of diagonals of a polygon of n sides is given by the formula z=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have? Choose the correct choice from the following options:
A) 3 B) 5 C) 6 D) 7 E) 8

Solution: z=n(n-3)   z=2*n   2n=n(n-3)   =>2=n-3   =>n=5   Answer 5
Answer: B
The ratio of the ages of three people is 4:6:7. Eight years ago, the sum of their ages was 61. Find their present ages.
Answers.
A) 12,18,21  B) 16,24,28  C) 20,30,35  D) 24,36,42  E) 28,42,49

Solution: Let the present ages be 4x, 6x, 7x.   (4x-8) + (6x-8) + (7x-8) = 61   17x = 85   x = 5   Their present ages are 20, 30, and 35.   The answer is 20,30,35.
Answer: C
In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability E that the worker is under 25 years old?	Select the correct option:
A) 0.30	B) 0.25	C) 0.45	D) 0.70	E) 0.90

Solution: Percentage of male worker = 48   Percentage of female worker = 52   Let total number of workers = 1000   number of male workers= 480   number of female workers = 520   Number of male age 25 or older = (4/10)*480= 
(4/10)*480 = 192
192   Number of female age 25 or older=(2/10)*520= 
(2/10)*520 = 104
104   Total number of workers 25 or older= 192+104= 
192+104 = 296
296   Total number of workers under 25= 1000 - 296= 
1000 - 296 = 704
704   Probability that a worker randomly selected is under 25 years old= 704/1000= 
704/1000 = 88/125 = around 0.704
.704   Alternatively , since the answer options are not close , we can use estimation here .   Percentage of male worker 25 or older= (4/10)*48 = 20 % approx   Percentage of female worker 25 or older = (2/10)*52 = 10 % approx   Percentage of total worker 25 or older = 30 %   Percentage of total worker under 25 = 70 %   Probability that a worker randomly selected is under 25 years old E= .7   Answer 0.70
Answer: D
When you multiply a number by 4 and
then subtract 3, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 9. What
is the number?	Choose the correct choice from the following options:
A) A)23  B) B)13  C) C)19  D) D)12  E) E)10

Solution: Let x equal the number and then change the words into an equation and solve for x:   4x – 3 = 9(x – 7)   4x – 3 = 9x – 63   60 = 5x   12 = x   correct answer 12)12
Answer: D
One half of the workers at the biscuit company is technician,quarter is clerk,one-fifth are administrative and the other 25 are supervisors. How many workers total are there in the biscuit company?	Options:
A) 250
B) 366
C) 400
D) 500
E) 2500

Solution: 1/2x + 1/4x +1/5x = 19/20x   Remaining 1/20 x= 25   x= 25*20= 
25*20 = 500
500   500 is the answer.
Answer: D
In Chess game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?	Choose the correct choice from the following answers:
A) 1/3
B) 4/9
C) 5/9
D) 2/3
E) 3/4

Solution: In Chess game,Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:   P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.   Answer: 5/9.
Answer: C
A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? Choose the correct choice:
A) 22	B) 88	C) 10	D) 99	E) 27

Solution: 400 --- 31   400 --- 3   120 --- ?   400*3 = 120*x => x =10 days   Answer: 10
Answer: C
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?	Select the correct option:
A) 16  B) 17  C) 12  D) 18  E) 12

Solution: T = 9/45 * 60= 
9/45 * 60 = 12
12   Answer: 12
Answer: C
The instructions state that Cheryl needs 2 square yards of one type of material and 1/2 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 5/10 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?	Choose the correct choice from the following choices.
A) 1/12 B) 1/9 C) 2 D) 1 1/9 E) 2 1/9

Solution: total bought = 2+1/2   left part 5/10--->1/2   so used part  2+1/2-1/2= 
 2+1/2-1/2 = 2
2   Ans 2
Answer: C
The number of students enrolled at school XX this year is 7 percent more than it was last year. The number of students enrolled at school YY this year is 3 percent more than it was last year. If school XX grew by 40 more students than school YY did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school YY last year?
Choose the correct choice from the following: A) 480 B) 1600 C) 1920 D) 2080 E) 2400

Solution: Given Info:   No. of students enrolled in school X is= 7% more than previous year's strength= 7X/100   No. of students enrolled in school Y is= 3% more than previous year's strength= 3Y/100   Given that "THIS YEAR" school X have 40 students more than school Y. So the increase in strength can be written as   7X/100= 40 + 3Y/100   7X= 4000 + 3Y....................(1)   And total students on previous year are X + Y=4000......................(2)   2400quating & Solving we get, Y=2400   ANS is 2400
Answer: E
In how many ways can live boys and three girls sit in a row such that all boys sit together? Choose the correct choice from the following:
A) 2888
B) 2885
C) 2880
D) 2876
E) 2224

Solution: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.   Required number of arrangements = 4! * 5! = 24 * 120= 
24 * 120 = 2_880
2880.   Answer:2880
Answer: C
There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?  Select:	A) Rs. 1500	B) Rs. 1800	C) Rs. 2000	D) Rs. 2400	E) None of these

Solution: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.   In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.   But present price of the article is Rs. 2288   for 114.4 ---> 100 ; 2288 ---> ?   Required price = (2288 * 100)/114.4 = 20 * 100 = Rs. 2000.   ANSWER:Rs. 2000
Answer: C
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?  Choose the correct choice from the following options:
A) 12 days B) 15 days C) 16 days D) 18 days E) 20 days

Solution: Explanation:   A's 2 day's work =(1/20 x 2)=1/10   (A + B + C)'s 1 day's work =(1/20 +1/30+1/60)=6/60=1/10   Work done in 3 days =(1/10 +1/10)=1/5   Now,	1/5work is done in 3 days   Whole work will be done in (3 x 5) = 15 days.   ANSWER IS 15 days
Answer: B
Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 18 as remainder Choose the correct choice from the following answers
A) 1235
B) 1346
C) 1378
D) 1634.4
E) 1489

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 18   5x = 1347   x = 269.4 number = 269.4+1365= 
269.4+1365 = 1_634.4
1634.4   1634.4
Answer: D
All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 154 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?	Choose one:	A) 1232	B) 1723	C) 1129	D) 2613	E) 1372

Solution: A   B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.   Quantity of milk in B = 8k - 5k = 3k.   Quantity of milk in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of milk in container C= 8k - 3k = 5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 154 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 1548  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of milk: 8k 3k 5k   It is given that if 154 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.   5k - 154= 3k + 154 => 2k = 308 => k = 154   The initial quantity of milk in 1232 = 8k = 8 * 154= 
8 * 154 = 1_232
1232 liters.
Answer: A
What least number must be subtracted from 7538 so that remaining no.is divisible by 14
Choices:
A) 3
B) 5
C) 6
D) 8
E) 9

Solution: Explanation:   On dividing 7538 by 14 we get the remainder 6, so 6 should be subtracted   Option 6
Answer: C
A is 2 times as fast as B. A alone can do the work in 20 days. If A and B working together in how many days will the work be completed?
Choose the correct choice from the following choices
A) 23 B) 13 C) 21 D) 24 E) 25

Solution: A can finish 1 work in 20 days   13 can finish 1/2 work in 20 days - since A is 2 faster than 13   This means   13 can finish 1 work in 20*2= 
20*2 = 40
40 days   Now using the awesome GMAT formula when two machines work together they can finish the job in= A13/ (A+13) = 20*40/(20+40) = 13 days   So answer is 13
Answer: B
What is the difference between the place value and face value of 1 in the numeral 54315?	Choose one.
A) 9
B) 11
C) 5
D) 1
E) 10

Solution: Difference between the place value and face value of 1 = 10-1= 
10-1 = 9
9   9nswer is 9
Answer: A
There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is	Choices.
A) 6
B) 9
C) 12
D) 15
E) 17

Solution: Sol.   Let the numbers be x and y.   Then, 2x + 3y = 39 ................(i)   3x + 2y = 36 .................(ii)   On solving (i) and (ii), we get : x = 6 and y = 9.   ∴ Larger number = 9.   Answer 9
Answer: B
If (3^4)(5^6)(7^3) = (35^n)(x), where x and n are both positive integers, how many different possible values of n are there?  Answers:
A) 1
B) 2
C) 3
D) 4
E) 6

Solution: Notice that the power of 7 in LHS is limiting the value of n, thus n cannot be more than 3 and since n is a positive integer, then n could be 1, 2, or 3.   Answer: 3.
Answer: C
A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze? Choose the correct choice from the following answers
A) 1211  B) 1218  C) 1210  D) 1212  E) 1229

Solution: π (232 – 122)   = 1210   Answer: 1210
Answer: C
What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
Pick:
A) 1267	B) 2876	C) 1865	D) 2506	E) 1812

Solution: Explanation:   358/179 â€¦.. 895/179   179(2 + 3 + 4 + 5) => 2506   Answer:2506
Answer: D
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are	Choose the correct option
A) 42,30 B) 42,31 C) 42,32 D) 42,33 E) None of these

Solution: Explanation:   Let their marks be (x+9) and x.   Then, x+9 = 56/100(x + 9 +x)   => 25(x+9)   => 14 (2x + 9)   => 3x = 99   => x = 33.   So, their marks are 42 and 33   Option 42,33
Answer: D
In a survey of parents, exactly 9/10 of the mothers and 3/4 of the fathers held full-time jobs. If 40 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?	Choices:
A) 27%
B) 21%
C) 19%
D) 18%
E) 16%

Solution: Fathers without full-time jobs are 1/4*3/5 = 3/20 of all the parents surveyed.   Mothers without full-time jobs are 1/10*2/5 = 2/50 of all the parents surveyed.   The percent of parents without full-time jobs is 3/20 + 2/50 = 19/100 = 19%   The answer is 19%.
Answer: C
The average age of a class of 20 students is 14 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
Select the correct option.
A) 40 years B) 41 years C) 42 years D) 43 years E) 36 years

Solution: If age of the teacher was 14, average would not have changed.   Since average increased by 2,   Age of the teacher=14+22×1=36   ANSW36 yearsR:36 years
Answer: E
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is Choose the correct choice:
A) 35 B) 37 C) 39 D) 41 E) 46

Solution: Explanation:   Let B's age = x years.   Then, As age = (x+ 9) years.   (x+9+10)=2(x�10)   hence x=39.   Present age of B = 39 years   Answer: Option 39
Answer: C
Three pipes A, B and C can fill a tank in 5 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. How many hours will take C alone to fill the tank? Choose the correct choice from the following options
A) 8
B) 10
C) 12
D) 14
E) 16

Solution: The rate of A+B+C is 1/5 of the tank per hour.   After 2 hours, the tank is 2/5 full.   The rate of A+B is 3/5 * 1/6 = 1/10 of a tank per hour.   The rate of C is 1/5 - 1/10 = 1/10   C can fill the tank in 10 hours.   The answer is 10.
Answer: B
The ratio of 2 numbers is 2:3 and their H.C.F. is 10. Their L.C.M. is ?  Choose the correct choice from the following options:
A) 30
B) 60
C) 20
D) 10
E) 40

Solution: Let the numbers be 2x and 3x   Their H.C.F. = 10   so the numbers are 2*10 , 3*10 = 20,30   L.C.M. = 60   Answer is 60
Answer: B
Truck X is 14 miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 57 miles per hour and Truck Y is traveling at an average speed of 63 miles per hour, how long will it take Truck Y to overtake and drive 4 miles ahead of Truck X?	Pick one:  A) 5 hours  B) 3 hours 20 minutes  C) 3 hours  D) 2 hours 45 minutes  E) 8 hours

Solution: Relative speed = 63-57= 
63-57 = 6
6 miles per hour   Dist required= 14+4= 
14+4 = 18
18 miles   Time taken to overtake= 18/6= 
18/6 = 3
3 hours. 3 hours is the answer.
Answer: C
A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw?  Pick:
A) 64  B) 36  C) 52  D) 86  E) 24

Solution: We may have (1 black and 2 non black) or (2 black and 1 non black) or (3 black)   Required number of ways = 3C1*6C2+3C2*6C1+3C3 = 64   64nswer is 64
Answer: A
9 points are marked on a straight line and another 10 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points? Choose the correct answer:
A) 91 B) 105 C) 196 D) 27 E) 14

Solution: assuming that the top line can have either 2 points or 1 point...   9! / 1!8! - 9! / 2! 7! yields 27.   27
Answer: D
Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job?	Choose the correct choice from the following answers.
A) 4 days
B) 6 days
C) 8 days
D) 2 days
E) 9 days

Solution: Sandy can do 1/6 of the job each day.   Molly can do 1/12 of the job each day.   The combined rate is 1/6 + 1/12 = 1/4 of the job each day.   The job will take 4 days.   The answer is 4 days.
Answer: A
If each edge of cube increased by 15%, the percentage increase in
Pick one:
A) 30.25
B) 32.25
C) 38.25
D) 37.25
E) 41.25

Solution: 100 × (115)/100 × (115)/100 = 132.25 => 32.25%   Answer is 32.25.
Answer: B
Find the value of x in (x+1)/(x+3)=5	Choose the most appropriate option:
A) 2.5	B) -2.5	C) 3.0	D) 3.5	E) -3.5

Solution: (x-1)/(x+3)=5   Multiplying both sides with x+3 gives x+1=5(x+3)   = x+1=5x+15   Subtracting x from both sides gives 4x+15=1   Subtracting 15 from both sides gives 4x=-14   Dividing by 4 on both sides gives x=-3.5   Answer: -3.5
Answer: E
What will be the compound interest on a sum of Rs. 21,000 after 3 years at the rate of 12% p.a.?	Choose the correct answer.
A) Rs. 8503.49
B) Rs. 9720
C) Rs. 10123.20
D) Rs. 10483.20
E) None

Solution: Amount = [21000 * (1 + 12/100)3]   = 21000 * 28/25 * 28/25 * 28/25 = Rs. 29503.49   C.I. = (29503.49 - 21000) = Rs. 8503.49   Rs. 8503.49NSWER:Rs. 8503.49
Answer: A
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?  Choose the correct choice from the following:
A) 10	B) 12	C) 14	D) 16	E) 18

Solution: Part filled in 2 hours = 2/6 = 1/3.   Remaining part = 1 - 1/3 = 2/3   (A + B)'s 1 hour work = 2/21   C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]   = (1/6 - 2/21) = 1/14   C alone can fill the tank in 14 hours.   ANSWER:14
Answer: C
If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution?	Choices
A) 9.3% B) 17.3% C) 26.67% D) 35.5% E) 41.3%

Solution: Let X be the quantity of non-vinegar in the strong vinegar solution   Thus vinegar quantity will be 12 - X   When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100   From this equation X = 7.04   Answer (12-7.04)/12 = 41.3%   ANSW41.3%R:41.3%
Answer: E
If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers?	Select.
A) It is a multiple of 3  B) It is a multiple of 4  C) It is a prime number  D) It is a multiple of 5  E) It is a multiple of 2

Solution: n+12 is a positive odd integer. This means n will be an odd integer   The next 4 integers would be: n + 12, n + 13, n + 14, n + 15   Sum = 4n + 54   This sum will always be even.   Option It is a multiple of 2
Answer: E
Which of these expressions has the greatest value? Answers
A) 1673211/1663212
B) 1356741/1356745
C) 1245671/1245675
D) 1124471/1124476
E) 1217861/1217864

Solution: Using elimination method on options   1673211/1663212 = 1.00601186139...   1673211/1663212NSWER:1673211/1663212
Answer: A
Replace X with the appropriate number in
5 , 6 , 8 , 9 , 13 , 15, 16, X
Choose the correct choice.
A) 22	B) 20	C) 21	D) 17	E) 18

Solution: 18   list of consecutive numbers that has an 'i' in the spelling
Answer: E
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 45 seconds. What is the length of each train (in meters)?	Choose the correct choice from the following options.
A) 48.5
B) 62.5
C) 73.5
D) 87.5
E) 96.5

Solution: The relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr= 10 * 5/18 = 25/9 m/s   In 45 seconds, the relative difference in distance traveled is  45 * 25/9= 
 45 * 25/9 = 125
125 meters   This distance is twice the length of each train.   The length of each train is  125/2= 
 125/2 = 125/2 = around 62.5
62.5 meters   The answer is 62.5.
Answer: B
. Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a?	Choose the correct choice from the following answers
A) Rs.228  B) Rs.229  C) Rs.220  D) Rs.200  E) Rs.221

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 15000(1 - 4/100) = 15000 - 600   m = 8000(1 + 10/100) = 8000 + 800   Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800   = Rs.200   As this is positive, an overall profit of Rs. 200 was made.   Answer:Rs.200
Answer: D
A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market? Choose the most appropriate option: A) 8 B) 12 C) 15 D) 16 E) 18

Solution: Say the # of eggs the cook originally got was x;   he price per egg then would be 12x and the price per dozen would be 12∗12/x.   Now, since the cook talked the seller into adding two more eggs then he finally got x+2 eggs (notice that x+2 is exactly what we should find);   So, the price per egg became 12/x+2 and the price per dozen became 12∗12/x+2 .   As after this the price per dozen went down by a dollar then 12∗12/x−12∗12/x+2=1, which simplifies to 144/x−144/x+2=1. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choices E fits: if x+2=18 then 144/16−144/18=9−8=1 .   Answer: 18
Answer: E