MU-NLPC/Calc-aqua_rat huggingface dataset:
Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 40 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
Choices
A) 80 lakh	B) 50 lakh	C) 40 lakh	D) 64 lakh	E) None of these

Solution: Let the incomes of two companies A and B be 5x and 8x respectively.   From the question,   5x+40/8x=5/4 ⇒ 20x + 160 = 40x   ∴ x = 8   ∴ Income of company B = 8x = 64 lakh   Answer 64 lakh
Answer: D
The dimensions of a rectangular solid are 4 inches, 5 inches, and 10 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
Choose the correct choice from the following answers:
A) 10:17	B) 2:5	C) 10:19	D) 25:7	E) 32:25

Solution: Answer: 10:19.
Answer: C
Dimitri weighs 2x-x pounds more than Allen weighs. Together, Allen and Dimitri weigh a total of y pounds. Which of the following represents Allen’s weight?
Choose the correct answer.
A) y - x/2 B) 2x - y/2 C) (y - x)/2 D) y - 2x E) 2x - y

Solution: These type of multi-variable story problems are usually perfect for TESTing VALUES.   Here, we're told that Dimitri weighs 2X-X or X pounds more than Allen weighs and that they weight a combined TOTAL of Y pounds.   IF....   Dimitri = 30   Allen = 20   X = 10   Y = 50   We're asked for Allen's weight, so we're looking for an answer that equals 20 when X = 10 and Y = 50.   Answer A:  50 - (10/2)= 
 50 - (10/2) = 45
45 NOT a match   Answer B: 20 - (50/2)= -5 NOT a match   Answer (y - x)/2: (50-10)/2 = 20 This IS a match   Answer D:   50 - 20= 
  50 - 20 = 30
30 NOT a match   Answer E: 20 - 50= -30 NOT a match   Final Answer:   (y - x)/2
Answer: C
In how many ways can the letters of the word MECHANIC be arranged?
Choose the correct option
A) 2580
B) 2500
C) 20160
D) 2520
E) 3420

Solution: MECHANIC has 8 words, but C is repeated two times. Thus ways = 8! / 2! = 20160 ways   20160
Answer: C
If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ?	Choose the correct choice from the following options:	A) 27/4	B) 27/8	C) 3/4	D) 3/8	E) 1/4

Solution: Say a = 3. Then:   a/b = 1/3 --> b = 9;   b/c = 2 --> c = 9/2;   c/d = 1/2 --> d = 9;   d/e = 3 --> e = 3;   e/f = 1/2 --> f = 6.   abc/def = (3*9*9/2)/(9*3*6) = 3/4.   Answer: 3/4.
Answer: C
A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ? Choose the correct choice:
A) 4 days  B) 5 days  C) 6 days  D) 7 days  E) 8 days

Solution: Explanation:   (A+B)'s 1 day work = 1/4   A's 1 day work = 1/12   B's 1 day work =   (1/4−1/12)=3−1/12=1/6   So B alone can complete the work in 6 days   Option 6 days
Answer: C
How many seconds will a 100 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?  Choose the correct option:
A) 11 sec
B) 6 sec
C) 77 sec
D) 14 sec
E) 12

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 = 100 * 3/50= 
100 * 3/50 = 6
6 sec.   Answer: 6 sec
Answer: B
A person has his own coach & whenever he goes to railway station he takes his coach. One day he was supposed to reach the railway station at 5 O'clock. But he finished his work early and reached at 3 O'clock. Then he rung up his residence and asked to send the coach immediately. He came to know that the coach has left just now to the railway station. He thought that he should not waste his time and started moving towards his residence at the speed of 3miles/hr. On the way, he gets the coach and reaches home at 6 o'clock. How far is his residence from railway station.	Choose the correct choice from the following answers.
A) 17 miles  B) 18 miles  C) 19 miles  D) 16 miles  E) 15 miles

Solution: He walked for 1.5 hrs and coach travelled in one side for 1.5 hrs instead of 2 hrs to save 0.5 hrs one side journey of coach.   So Coach speed is 3 times speed of man i.e. 9 mph.   Total distance of stn from Home = 1.5( 3+9) = 1.5*12= 
1.5*12 = 18
18 miles   ANSWER:18 miles
Answer: B
The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in? Options.
A) 2.98 min B) 5.28 min C) 1.97 min D) 2.88 min E) 2.77 min

Solution: Clearly, the two will meet when they are 726 m apart.   To be (4.5 + 3.75)= 
(4.5 + 3.75) = 8.25
8.25 km apart, they take 1 hour.   To be 726 m apart, they take (100/825 * 726/1000) hrs= (242/2750 * 60)= 
(242/2750 * 60) = 132/25 = around 5.28
5.28 min.   Answer: 5.28 min
Answer: B
A train 200 m long passes a man, running at 6 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
A) 36	B) 50	C) 78	D) 66	E) 22

Solution: Speed of the train relative to man   = (200/10) m/sec = 20 m/sec. [20 * (18/5)] km/hr   = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 6) km/hr. x - 6   = 72 ==> x   = 78 km/hr.   Answer:78
Answer: C
M and N started a business by investing Rs.4000/- and Rs.5000/- respectively. Find the M’s share out of a total profit of Rs.1800: Choose the correct choice from the following answers.
A) Rs.500/-  B) Rs.550/-  C) Rs.600/-  D) Rs.650/-  E) Rs.800/-

Solution: M = Rs.4000/-   N = Rs.5000/-   M share 4 parts & N share 5 parts   Total 9 parts -----> Rs.1800/-   ----> 1 part -------> Rs.200/-   M share = 4 parts -----> Rs.800/-   Rs.800/-
Answer: E
What is the distance covered by a car if it travels with a speed of 160 kmh for 5 hours?  Choose the correct choice: A) 350 km B) 400 km C) 800 km D) 600 km E) 650 km

Solution: Distance= Time x Speed   5 x 160 = 800   Answer: 800 km
Answer: C
A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 100 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
Pick:
A) 3/16,000 B) 1/4,800 C) 3/1,600 D) 1/90 E) 2/45

Solution: Solution provided by stanford2012 is correct: 100/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=100/800*1/600=1/4,800.   Answer: 1/4,800.
Answer: B
A boy sitting in a train which is travelling at 30 kmph observes that a goods train travelling in a opposite direction, takes 18 seconds to pass him. If the goods train is 350 m long, find its speed.  Choose the correct choice from the following:  A) 25  B) 30  C) 35  D) 40  E) 45

Solution: Relative speed = (350/18)m/s = (350/18)*(18/5)= 
(350/18)*(18/5) = 70
70 kmph   speed of goods train= 70-30= 
70-30 = 40
40 kmph   Answer is 40
Answer: D
There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all three secretary are assigned at least one report?
Choose the correct choice from the following choices.
A) 8/9	B) 64/81	C) 12/27	D) 16/81	E) 5/9

Solution: "We havé total possibilities N =3^4"   What are these total possibilities? They are the ways in which the 4 reports can be distributed among 3 secretaries so that all reports may go to one secretary, the reports may be distributed among 2 secretaries or they may be distributed among all 3. So such cases are included (4, 0, 0), (0, 4, 0), (2, 2, 0), (1, 3, 0), (1, 1, 2), etc   In how many ways can you give 4 reports to only 1 secretary? You choose the secretary who will get the reports in 3C1 = 3 ways   In how many ways can you give 4 reports to only 2 secretaries? Choose the 2 secretaries in 3C2 ways. Each secretary must get at least one report so you can distribute them in 2 ways:   '1 and 3' - Choose one report in 4C1 ways and give it to one secretary in 2C1 ways. The other secretary gets the other 3 reports.   or   '2 and 2' - Choose 2 reports in 4C2 ways and give to the first secretary. The other secretary gets the other two reports.   Total number of ways is 3C2 * (4C1*2C1 + 4C2) = 42 ways   Note that in your method 2^4 is incorrect. It includes the ways in which all 4 reports go to one secretary.   So this means that in  3 + 42= 
 3 + 42 = 45
45 ways, at least one secretary gets no report. In the rest of  81 - 45= 
 81 - 45 = 36
36 ways, each secretary gets at least one report.   Required Probability= 36/81 = 12/27   ANS:12/27
Answer: C
John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish?	Choose the correct option:
A) 24
B) 34.8
C) 37.8
D) 40
E) 84

Solution: The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:   0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40.   Answer: 40.
Answer: D
A welder received an order to make a 1 million liter cube-shaped tank. If he has only 2x4 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)	Choose the correct choice from the following answers
A) 92	B) 90	C) 82	D) 75	E) 78

Solution: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)   In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.   A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).   The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.   The question tells us:he has only 2x4 meter sheets of metal that can be cut.   Each sheet has an area of 8 sq m. How many of these need to fill up 600 sq m?  600/8= 
 600/8 = 75
75. He needs 75 sheets.   Answer=75
Answer: D
John and David can finish a job together in 6 hours. If John can do the job by himself in 8 hours, what percent of the job does David do?
Choose the correct choice from the following choices.
A) 35%  B) 45%  C) 25%  D) 30%  E) 20%

Solution: You can also plug in numbers. For example, Bob and Alice work at a donut factory and make 24 donuts which is the job ( I picked this as a SMART number).   John on his own works  24/8= 
 24/8 = 3
3 donuts per hour.   John and David work   24/6= 
  24/6 = 4
4 donuts per hour so David works 1 donuts/hour   To find out the percentage, David works 1 donuts/hr x 6 hours= 6 donuts per hour.   Therefore 6 donuts/24donuts = 1/4 = 25%   Answer : 25%
Answer: C
8 noun, 3 verbs and 2 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??  Pick.
A) 128
B) 188
C) 218
D) 248
E) 288

Solution: we have to choose one from each set. 1 from 8 nouns and 1 from 3 verbs and 1 from 2 adjectives.   then we have to arrange 3 different sets in 3! ways.   so,   8c1*3c1*2c1*3!=288   ANSW288R:288
Answer: E
In a class of 30 students, 5 students did not borrow any books from the library, 12 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?  Pick.
A) 5	B) 8	C) 15	D) 18	E) 20

Solution: The average number of books per student was 2means that total of   2*30= 
  2*30 = 60
60 books were borrowed;   5+12+8= 
5+12+8 = 25
25 students borrowed total of  5*0+12*1+8*2= 
 5*0+12*1+8*2 = 28
28 books;   So  60-28= 
 60-28 = 32
32 books are left to distribute among 30-25= 
30-25 = 5
5 students, these 5 arethe rest who borrowed at least 3 books;   Tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed. Minimum these 4 students could have borrowed is 3 books per student, so total number of books they could have borrowed is 4*3= 
4*3 = 12
12 books. So the 5th student could have borrowed is  32-12= 
 32-12 = 20
20 books.   Answer: 20.
Answer: E
In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?	Options:	A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Let the number of papers be x. Then, 63x + 20 + 2 = 65x   or 2x = 22 or x = 11.   Answer 11
Answer: D
Fill in the missing number:
18 14 12 11 ? 10.25
Choose the correct option.
A) 10.1
B) 10.4
C) 10.2
D) 10.5
E) 10.3

Solution: 10.5   10.5   10.5ivide each number by 2 and then add 5 to it.
Answer: D
A diner is having lunch at a salad bar. There are four types of lettuce to choose from, as well as four types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad? Choose the correct choice from the following answers:
A) 20
B) 40
C) 60
D) 80
E) 100

Solution: 4*4*5= 
4*4*5 = 80
80   The answer is 80.
Answer: D
The distance between Delhi and Mathura is 200 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?  Select:
A) 10.50 a.m.  B) 12.00 a.m.  C) 10.30 a.m.  D) 11.40 a.m.  E) 1.40 a.m.

Solution: D = 200 â€“ 20 = 180   RS = 20 + 25= 
20 + 25 = 45
45   T= 180/45= 
180/45 = 4
4 hours   8 a.m. + 4 hrs 00 min= 12.00 a.m.   ANSWER:12.00 a.m.
Answer: B
In what time will a car 10 m long moving at the rate of 36 kmph pass a telegraph post on its way?  Answers
A) 8 sec B) 1 sec C) 9 sec D) 6 sec E) 2 sec

Solution: T = 10/36 * 18/5= 
10/36 * 18/5 = 1
1 sec   Answer:1 sec
Answer: B
If 2^(2w) = 8^(w−3), what is the value of w?
Choose the correct answer:
A) 3
B) 6
C) 9
D) 12
E) 15

Solution: 2^(2w) = 8^(w−3)   2^(2w) = 2^(3*(w−3))   2^(2w) = 2^(3w-9)   Let's equate the exponents as the bases are equal.   2w = 3w-9   w = 9   The answer is 9.
Answer: C
Pipe A can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes. How long it will take to fill the tank if both pipes are operating together?
Choose the correct choice from the following: A) 30 B) 35 C) 40 D) 45 E) 50

Solution: Pipe A fills 1/30th of the tank in a minute and pipe B empties 1/90th of the tank   (1/30)-(1/90)=(1/x)   2/90=1/x => x=45   Answer: 45
Answer: D
An MBA admissions committee is to be formed randomly from 6 second year MBAs for the 3 positions. If Albert and Jane are applicants, what is the probability that Albert will be selected but Jane will not?
Choose the most appropriate option.
A) 10% B) 17% C) 25% D) 30% E) 44%

Solution: Probability of selecting Albert but not Jane =   Prob(A,J',J')   = 3* 1/6 * 4/5 * 3/4 (J' is Jane is not selected and we multiply by 3 because A , J' and J' can occur in 3 distinct ways)   = 3/10   =30%   Answer 30%
Answer: D
The average age of students in section A of 125 students is 23 years and the average age of students in section B of 162 students is 25 years. Find the average age of students in both sections taken together? Choose the correct choice from the following answers
A) 26 years B) 30years C) 15years D) 24years E) 20years

Solution: The required average = (125*23+162*25)/125+162 = 24 years   Answer is 24years
Answer: D
A ratio between two numbers is 4:5 and their L.C.M. is 200. The first number is
Choices
A) 60  B) 40  C) 20  D) 15  E) None

Solution: Sol.   Let the required numbers be 4x and 5x. Then, their L.C.M. is 20x.   ∴ 20x = 200⇔ x = 10. Hence, the first number is 40.   Answer 40
Answer: B
If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?  Select
A) 141  B) 200  C) 312  D) 391  E) 412

Solution: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).   We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...   A + (A+2) + (A+4) = 3A + 6   We know that 3A + 6 COULD equal one of those five answers; we just have to find it...   Could 3A + 6 = 141   3A = 135   A = 45   This is NOT an EVEN INTEGER, so 141 is NOT the answer   Could 3A + 6 = 200   3A = 194   A = 64.6666   This is NOT an EVEN INTEGER, so 200 is NOT the answer   Could 3A + 6 = 318   3A = 312   A = 102   This IS an EVEN INTEGER! The numbers would be 102, 104 and 106. This IS the answer   Final Answer:   312
Answer: C
A football field is 8400 square yards. If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards?
Pick.
A) 450 B) 600 C) 500 D) 2400 E) 3200

Solution: Answer A) 4800 yards need 1200 lbs   1 Yard will need 1200/8400 = 1/7 lbs   3600 Yards will need   1/7* 3500= 
  1/7* 3500 = 500
500lbs   500
Answer: C
A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 20 months? Pick one:
A) 18:11
B) 18:15
C) 20:11
D) 18:121
E) 18:112

Solution: A invests Rs.8000 for 20 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.   A : B   8000*20 : (8000*4) + (4000*14)   160000 : 88000   A:B = 20:11.Answer:20:11
Answer: C
If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be odd? Choices:
A) 1/6  B) 1/3  C) 1/2  D) 2/3  E) 5/6

Solution: Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 1/3.   Answer: 1/3.
Answer: B
In how many different number of ways 4 boys and 1 girls can sit on a bench?  Choose the correct choice from the following:
A) 120
B) 140
C) 160
D) 180
E) 200

Solution: npn = n!   5p5= 5 × 4 × 3 × 2 × 1 = 120   120
Answer: A
A rectangular lawn of dimensions 90 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?  Choose the correct choice:
A) A)4200	B) B)930	C) C)9309	D) D)3900	E) E)8302

Solution: Explanation:   4200rea = (l + b – d) d   (90 + 60 – 10)10 => 1400 m2   1400 * 3 = Rs.4200   4200nswer: Option 4200
Answer: A
If 22 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?  Answers:
A) 95
B) 90
C) 88
D) 80
E) 75

Solution: Let x be the number of students in the school. 0.22x students went to the trip and took more than 100$. They compose   (100-75)= 
  (100-75) = 25
25% of all students who went to the trip. Therefore the toal of 0.22x/0.25=0.88x students went to the camping which is 88%.   The answer is 88  0.22 /0.25= 
  0.22 /0.25 = 0.88
0.88x students went to the camping which is 88%.   The answer is 88
Answer: C
Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity Q for the round trip?	Select the correct option:	A) 24 miles per hour	B) 48 miles per hour	C) 50 miles per hour	D) 53 1/3 miles per hour	E) 68 miles per hour

Solution: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.   Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.   D = (R)(T)   120 = (40)(T)   120/40= 
120/40 = 3
3= T   3 hours to drive to SD   On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.   D = (R)(T)   120 = (60)(T)   120/60= 
120/60 = 2
2= T   2 hours to drive to SD   Total Distance = 240 miles   Total Time = 3+2= 
3+2 = 5
5 hours   Average Speed= 240/5= 
240/5 = 48
48 miles/hour   Final Answer:   48 miles per hour
Answer: B
If the area of circle is 314 sq cm then its circumference?  Choose the correct answer.
A) 10
B) 61
C) 65
D) 56
E) 62

Solution: 22/7 r2 = 314 => r = 10   2 * 22/7 * 10 = 62   Answer: 62
Answer: E
The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?	Choose the correct answer:
A) 90cm
B) 95cm
C) 100cm
D) 110cm
E) 122cm

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (135/360 * 2 * 22/7 * 28) + 2(28)   = 66 + 56= 
66 + 56 = 122
122 cm   Answer:122cm
Answer: E
A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 960 grams. Find the profit percent. Options:	A) 4.166	B) 3.1	C) 2.1	D) 1.256	E) 3.759

Solution: Explanation:   (100 + g) / (100 + x) = True measure / Faulty measure   x = 0   true measure = 1000   faulty measure = 960   100 + g / 100 + 0 = 1000 / 960   100+g = 100/96*100   g = 4.166   4.166NSWER: 4.166
Answer: A
When the positive integer A is divided by 5 and 8, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 8, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B? Choose the most appropriate option:
A) 32 B) 35 C) 36 D) 40 E) 50

Solution: A = 5k+3 = 8j+4   B 5 +3= 
5 +3 = 8
8j+4   B= 5m+3 = 8n+4   A-B 5 +3= 
5 +3 = 8
8n+4   A-B= 5(k-m) = 8(j-n)   Thus A-B is a multiple of 5 and 8, so it is multiple of 40.   The answer is 40.
Answer: D
Narendra started a business, investing 30000. Six months later, Chandan joined him with 10000. If they make a profit of 10000 at the end of the year, what should be the share of Narendra?	Choose the correct choice from the following answers
A) A)Rs.7000
B) B)Rs.8000
C) C)Rs.8500
D) D)Rs.8571
E) E)Rs.8700

Solution: The ratio of their investments = 30000 × 12 : 10000 × 6 = 6: 1.   :. Narendra’s share on profit of Rs.10000 = 10000 × 6/7 = Rs.8571.   Rs.8571)
Answer: D
In an engineering class that contained 50 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?  Select:  A) 4  B) 6  C) 10  D) 12  E) 24

Solution: 1st Question : Three fifths of the students answered the first question correctly - so 3/5∗50=30   2nd Question : four fifths of the remainder answered the second question correctly so 4/5∗(50−30)=45∗20=16   total students who answered at least one Q correct =30+16= 
30+16 = 46
46   so students who answered BOTH incorrectly= 50−46=4   4NSWER:4
Answer: A