MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 6 couples. If they will sit 12 chairs in a row such that each couple sits side by side, how many possible cases are there?
Choose the correct answer.
A) 120 B) 240 C) 1,200 D) 46080 E) 3,840

Solution: Tie the couples. Then we have 6 persons that have to be arranged in 6 places. 6! ways.   Now the couples can change position with each other. 2! ways.   6! * (2!)^6=720 *64= 
720 *64 = 46_080
46080   Answer is 46080.
Answer: D
A, B and C can do a piece of work in 30 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
Options:	A) 12 days	B) 16 days	C) 18 days	D) 11 days	E) 38 days

Solution: One day work of A, B and C = 1/30 + 1/30 + 1/40 = 1/11Work done by A and B together in the last 4 days = 4*(1/30 + 1/30) = 4/15   Remaining work = 11/15   The number of days required for this initial work = 8 days.   The total number of days required = 4 + 8= 
4 + 8 = 12
12 days.   12 daysnswer:12 days
Answer: A
The maximum number of students among them 640 pens and 520 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?	Choose the correct choice from the following answers: A) 40 B) 45 C) 50 D) 55 E) 60

Solution: number of pens = 640   number of pencils = 520   Required number of students = H.C.F. of 640 and 520= 40   40nswer is 40
Answer: A
Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent?	Select:	A) 5.26%	B) 11 7/7%	C) 11 1/9%	D) 71 1/9%	E) 11 1/2%

Solution: 950 --- 50   100 --- ? => 5.26%   5.26%nswer:5.26%
Answer: A
Simple interest on a sum at 5% per annum for 2 years is Rs.90. The C.I. on the same sum for the same period is?  Select:
A) 81.6  B) 91.5  C) 81.2  D) 81.3  E) 81.1

Solution: SI = 45 + 45   CI = 45 + 45 + 1.5= 
45 + 45 + 1.5 = 91.5
91.5   Answer: 91.5
Answer: B
A piece of ribbon is cut from a role that can now make 189 more pieces and an additional piece of 30mm. If the full role after the piece was cut is 600mm, what is the length of the ribbon that was cut?	Choose the correct choice from the following answers
A) 25
B) 270
C) 12
D) 3
E) 30

Solution: r as the length of the ribbon cut.   (189*r) +r + 30=600.   (190*r) +30=600   (190*r)=600-30 solves to (190*r)/270= 570/190   r equates to 3mm.   Answer is 3.
Answer: D
There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 6,500 milk chocolates per month, what was it one month ago?  Pick one:	A) 5,000 chocolates	B) 9000 chocolates	C) 8000 chocolates	D) 7000 chocolates	E) None of these

Solution: Let one month ago, production be x chocolates.   Then, 130 % of x = 6500   ⇒ x = 6500×100/130=5000 chocolates   5,000 chocolatesnswer 5,000 chocolates
Answer: A
Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 140 sandwiches were made, how many bologna sandwiches
were made?  Answers
A) 15	B) 30	C) 38	D) 42	E) 49

Solution: For deciding such task we should calculate all parts 5 + 7 + 8= 
5 + 7 + 8 = 20
20 parts   and we should calculate how many sandwiches holds 1 part:   140 / 20= 
140 / 20 = 7
7 sandwiches in one part   For bologna we have 7 parts so:    7 * 7= 
 7 * 7 = 49
49   Answer is 49
Answer: E
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present? Options:	A) 16	B) 20	C) 21	D) 10	E) 27

Solution: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.   Then,	((6x + 6) + 4)*10=	11*((5x + 6) + 4)   10(6x + 10) = 11(5x + 10)   5x = 10   x = 2.   Sagar's present age = (5x + 6) = 16 years   16ns- 16
Answer: A
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Choose the correct answer:
A) Rs. 375	B) Rs. 400	C) Rs. 600	D) Rs. 800	E) None of these

Solution: C's 1 day's work = 1/3-(1/6+1/8)=1/3=7/24=1/24;   A's wages: B's wages: C's wages = 1/6:1/8:1/24=4:3:1;   C's share = Rs.(1/8*3200)=Rs.400.   Correct Option: Rs. 400
Answer: B
A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 45 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?  Choose the correct choice from the following answers
A) 3.0	B) 5.0	C) 5.5	D) 6.5	E) 6.75

Solution: Construct an equation: 15/100=x/45-> x=6.75   Answer: 6.75.
Answer: E
Last year Elaine spent 20% of her annual earnings on rent. This year she earned 25% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year? Choose the correct choice from the following answers:
A) 182.5	B) 184.5	C) 167.5	D) 172.5	E) 187.5

Solution: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.   She would've spent $20 of this on rent.   This year she earned 25% more, or $125.   She would've spent 30% of this on rent, or $37.5   Do $37.5/$20   This will give you 187.5%   187.5 is the correct answer.
Answer: E
The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages.	Choices:
A) 20, 35, 55	B) 16, 28, 36	C) 20, 35, 45	D) None of these	E) 20, 15, 45

Solution: Answer: Option B   Let their present ages be 4x, 7x and 9x years respectively.   Then, (4x - 8) + (7x - 8) + (9x - 8) = 56   20x = 80 => x = 4   Their present ages are 16, 28 and 36 years respectively.
Answer: B
A man goes 50Km north , then turned left walked 40Km, then turned right ? In which direction he is?	Options
A) North  B) South  C) East  D) West  E) None

Solution: 5okm-north-->north   left-west--->west   turned right-north--->north   NorthNSWER:North
Answer: A
The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 20 years is: Choose the most appropriate option.
A) 111 × 1827 miles	B) 1174× 10^11 miles	C) 346 × 1012 miles	D) 247 × 1012 miles	E) 587 × 1012 miles

Solution: The distance of the light travels in one years is:   5,870,000,000,000 = 587 * 10 ^10   The distance of the light travels in 20 years is:   = 2*10 * 587 * 10^10   = 1174 × 10^11 miles.   Answer :1174× 10^11 miles
Answer: B
If the cost price is 86% of the selling price, then what is the profit percent?
Choose the correct choice from the following answers:
A) 5%
B) 11%
C) 16%
D) 21%
E) 19%

Solution: Let S.P. = $100   C.P. = $86   Profit = $14   Profit% = 14/86 * 100 = 25/6 = 16% approximately   Answer is 16%
Answer: C
A can do a piece of work in 4 days. B can do it in 9 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?  Select the correct option:
A) 22 days
B) 36/5 days
C) 67 days
D) 17/7 days
E) 18 days

Solution: C = 1/2 - 1/4 - 1/9 = 5/36   => 36/5 days   Answer:36/5 days
Answer: B
A side of beef lost 50 percent of its weight in processing. If the side of beef weighed 750 pounds after processing, how many pounds did it weigh before processing?  Choose the correct choice:
A) 191
B) 355
C) 737
D) 840
E) 1,500

Solution: Let weight of side of beef before processing = x   (50/100)*x = 750   => x = (750 * 100)/50= 
(750 * 100)/50 = 1_500
1500   Answer 1,500
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?	Select.
A) 356	B) 278	C) 127	D) 279	E) 150

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 9= 
50/3 * 9 = 150
150 m   Answer: 150
Answer: E
In a kilometre race, A can give B a start of 100 m or 15 seconds. How long does A take to complete the race?
Options:  A) 2min 10 sec  B) 2min 30 sec  C) 2min 40 sec  D) 2min 50 sec  E) 2min 20 sec

Solution: 100 m = 15 sec   1 m = 15/100 sec   1000 m = 15/100*1000= 
15/100*1000 = 150
150 sec=2min 30 sec   ANSWER:2min 30 sec
Answer: B
The set X = {6,7,8,9}. The set Y = {2,3,4,5}. We will randomly choose one element x from set X and one element y from set Y. What is the probability that x / y will be an integer? Choose the correct choice.
A) 5/16 B) 3/16 C) 7/8 D) 5/8 E) 3/8

Solution: The total number of x and y pairs is 4*4= 
4*4 = 16
16.   There are five pairs such that x / y is an integer.   The probability that x / y is an integer is 5/16.   The answer is 5/16.
Answer: A
The average age of 32 students in a group is 14 years. When teacherâ€™s age is included to it, the average increases by one. What is the teacherâ€™s age in years?	Choices.
A) 31	B) 36	C) 47	D) 51	E) None

Solution: Sol.   Age of the teacher = ( 33 Ã— 15 â€“ 32 Ã— 14 ) years = 47 years.   Answer 47
Answer: C
Today John is 3 times older than Mark. If in 12 years, John will be one year younger than twice the age of Mark on that day, how old is John today?  Choices
A) 13
B) 33
C) 36
D) 38
E) 39

Solution: t   Given after 12yrs john will be 1 year younger than twice mark's age   i.e 3M+12 = 2(M+12)-1   M=11   =>John's current age = 3M = 33   Answer is 33
Answer: B
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Pick.
A) 4  B) 5  C) 7  D) 8  E) 2

Solution: 7   7   1 women's 1 day work = 1/70   1 child's 1 day work = 1/140   (5 women + 10 children)'s 1 day work   = (5/10 + 10/140) = (1/14 + 1/14) = 1/7   5 women and 10 children will complete the work in 7 days.
Answer: C
A can do a piece of work in 30 days; B can do the same in 50 days. How many days will it take the work to get finished if A and B work together?
Choose the correct choice from the following answers: A) 18.75 B) 20.25 C) 21.52 D) 23.45 E) 24.58

Solution: A completes 1/30th of the work in one day and B completes 1/50th.   (1/30)+(1/50)=(1/x)   8/150=1/x => x=150/8= 
150/8 = 75/4 = around 18.75
18.75days   18.75nswer: 18.75
Answer: A
8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?
Choose the correct choice from the following answers:
A) Sunday  B) Tuesday  C) Friday  D) Tuesday  E) None of these

Solution: Explanation :   Given that 8th Dec 2007 was Saturday   Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days   365 days = 1 odd day   Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday. Answer : Option Friday
Answer: C
Present ages of Solomon and Arnald are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Arnald present age in years?  Choose the correct answer: A) A)24 B) B)25 C) C)26 D) D)27 E) E)28

Solution: Let the present ages of Solomon and Arnald be 5x and 4x years respectively.   Then, (5x + 3)/(4x + 3) = 11/9   9(5x + 3) = 11(4x + 3) => x = 6   Arnald present age = 4x = 24 years.   24NSWER:24
Answer: A
In a school 10% of the boys are same in number as 1/5th of the girls. what is the ratio of boys to the girls in the school?  Choose the correct choice from the following choices: A) 5:2 B) 2:3 C) 1:2 D) 3:7 E) 2:5

Solution: 10% of B = 1/5 G   10B/100 = G/5   B = G/2   B/G = 1/2   B:G = 1:2   Answer is 1:2
Answer: C
The compound interest on rs.30000 at 7% per annum is Rs.4347. The period is  Options
A) 2  B) 6  C) 78  D) 8  E) 9

Solution: Explanation:   2mount = Rs.(30000+4347) = Rs.34347   let the time be n years   Then,   n = 2years   2nswer: 2) 2 years
Answer: A
The sum of ages of 4 children born 4 years different each is 48 yrs. What is the age of the Elder child?	Choose the correct choice from the following choices:
A) 8 B) 9 C) 16 D) 17 E) 18

Solution: Let the ages of children be x, (x + 4), (x + 8), (x + 12) years.   Then, x + (x + 4) + (x + 8) + (x + 12) = 48   4x = 24   x =6   x+12= 6+12= 
6+12 = 18
18   Answer : 18
Answer: E
A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Answers:	A) 278 m	B) 265 m	C) 123 m	D) 270 m	E) 289 m

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 250)/26 = 20   x = 270 m.   Answer:270 m
Answer: D
The average age of a group of 12 students is 20years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is Choose the correct choice:	A) 22	B) 23	C) 24	D) 25	E) 26

Solution: total age of 12 std=20*12   total age of 16 std=21*16   total age of 4 std=(21*16)-20*12= 
(21*16)-20*12 = 96
96   avg of 4 std=(96)/4= 
(96)/4 = 24
24   ANSWER:24
Answer: C
A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 10 times per hour, and both clocks chirp for the first time at 2:03 PM, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour? Choose the correct choice from the following options
A) 2:30 PM	B) 2:45 PM	C) 3:00 PM	D) 3:15 PM	E) 3:30 PM

Solution: The question is asking when the first clock will have chirped 30 times (3*10 chirps).   The first clock chirps once every 3 minutes.   If the first chirp is at 2:03, then the 30th chirp is at 90 minutes after 2:00.   The answer is 3:30 PM.
Answer: E
A man goes downstream at 11 kmph, and upstream8 kmph. The speed of the stream is	Choose the correct choice from the following choices:  A) 1.5kmph  B) 4kmph  C) 16kmph  D) 2.5kmph  E) 26kmph

Solution: Speed of the stream = 1/2(11-8)kmph   =1.5kmph.   correct option :1.5kmph
Answer: A
How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?	Choose the correct choice.
A) 36  B) 38  C) 40  D) 42  E) 44

Solution: The total numbers between 100 and 170, inclusive, is 71.   3*34= 
3*34 = 102
102 and   3*56= 
  3*56 = 168
168 so the number of multiples of 3 is 23.   5*20= 
5*20 = 100
100 and   5*34= 
  5*34 = 170
170 so the number of multiples of 5 is 15.   However, the multiples of 15 have been counted twice.   15*7= 
15*7 = 105
105 and   15*11= 
  15*11 = 165
165 so the number of multiples of 15 is 5.   Thus the total number is  71-23-15+5= 
 71-23-15+5 = 38
38.   The answer is 38.
Answer: B
A chemical supply company has 60 liters of a 30% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
Select.
A) 12 B) 15 C) 20 D) 24 E) 30

Solution: 60 liters of a 30% HNO3 solution means HNO3 = 18 liters in 60 liters of the solution.   Now, let x be the pure HNO3 added.   As per question,   18 + x = 50% of (60 + x)   or x =24. Hence, 24
Answer: D
On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of? Choose the most appropriate option.
A) 16 2/37% B) 16 2/3% C) 16 6/3% D) 12 2/3% E) 16 3/3%

Solution: Clearly, the retailer gets 1 dozen out of 6 dozens free.   Equivalent discount = 1/6 * 100 = 16 2/3%.Answer: 16 6/3%
Answer: C
How many 4 digit number contain number 2 ?  Choose the correct choice from the following.
A) 3168	B) 3268	C) 3368	D) 3468	E) 3568

Solution: total 4 digit no. = 9*10*10*10= 
9*10*10*10 = 9_000
9000   not containing 2= 8*9*9*9= 
8*9*9*9 = 5_832
5832   total 4 digit number contain 2= 9000 - 5832= 
9000 - 5832 = 3_168
3168   3168NSWER:3168
Answer: A
Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 50 different possibilities,what is the probability that she does not pick the one correct combination.  Choose one:  A) 1  B) 0.9875  C) 0.8875  D) 3/160  E) 0

Solution: If Denise does not pick the correct combination in first 50 try, then the correct combination is one of remaining 3950. So Probability = 3950/4000 = 0.9875.   answer is 0.9875
Answer: B
The ratio of male to female in a class is 3:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?	Select the correct option:
A) a)160 degree  B) b) 168 degree  C) c)191 degree  D) d)180 degree  E) e)204 degree

Solution: here is my approach => males => 3x and females =3x => total =6x   now 6x=> 360   therefore 3x => 180 degree .   P.S => 3x is nothing but total number of students with the given prefee   aNSWER d)180 degree
Answer: D
A boat whose speed is 15 k/hr in still water goes 30 k/he downwards and come back in total 4 hr 30 min what is the speed of stream in k/hr ?  Answers: A) 1km/hr B) 2km/hr C) 3km/hr D) 4km/hr E) 5km/hr

Solution: If the speed of stream=x   Speed in downstream=15+x , Speed in Upstream=15-x,   Total time=4 hr 30 min=9/2 hr   [30/(15+x) + 30/(15-x)]=9/2,Solving x=5   x=5km/hr   ANSW5km/hrR:5km/hr
Answer: E
16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work? Select:
A) 33	B) 77	C) 20	D) 99	E) 71

Solution: 16 * 25 = 20 * x => x   = 20 days   Answer: 20
Answer: C
Of all the players in a professional baseball league, 1/2 are foreign-born, including 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?	Choose the correct choice from the following answers: A) 100% B) 75% C) 66 2/3% D) 50% E) 25%

Solution: Assume that the total number of players is 100.   1/2 are foreign born, so 50 are foreign born. 75 players are pitchers out of which 1/3 are foreign born. 25 players are foreign born and pitchers. The other 25 who are foreign born are thus not pitchers.   Thus out of 25 non pitchers, 25 are foreign born. 100%nswer: 100% - 100%   100%NSWER:100%
Answer: A
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3?  Choose the correct choice from the following options.
A) 17 kmph B) 50 kmph C) 18 kmph D) 17 kmph E) 11 kmph

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10)   = 50 kmph.   Answer:50 kmph
Answer: B
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/3 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Select the correct option
A) (a) 14/23  B) (b) 7/15  C) (c) 10/21  D) (d) 17/35  E) (e) 1/2

Solution: This problem is very good example how easy and quick plug-in method might be.   Let the total # of cups be 10.   # of small cups sold 3/5*10= 
3/5*10 = 6
6;   # of large cups sold  10-6= 
 10-6 = 4
4;   Let the price of small cup be $6, then the price of larges cup would be 7/3*6= 
7/3*6 = 14
$14;   Revenue from small cups: 6*$6=$36;   Revenue from large cups cups: 4*$14  6* 6= 
  6* 6 = 36
$36;   Revenue from large cups cups: 4*$14=$56;   Fraction of total revenue from large cups: 56/(36+56) 4* 14= 
 4* 14 = 56
$56;   Fraction of total revenue from large cups: 56/(36+56)=14/23.   (a) 14/23nswer: (a) 14/23.
Answer: A
A monkey start climbing up a tree 17 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.	Choose the correct choice from the following choices:
A) 15 hrs  B) 18 hrs  C) 19 hrs  D) 17 hrs  E) 16 hrs

Solution: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.   similarly in 14hrs it wil be 14ft.   Bt since the height of the tree is 17ft, so if the monkey hops up the tree in the next hr i.e 15th hr then it reaches at the top of the tree.   hence it takes 15 hrs for monkey to reach at the top   15 hrsNSWER:15 hrs  (3  -2  )= 
  (3  -2  ) = 1
1ft/hr.   similarly in 14hrs it wil be 14ft.   Bt since the height of the tree is 17ft, so if the monkey hops up the tree in the next hr i.e 15th hr then it reaches at the top of the tree.   hence it takes 15 hrs for monkey to reach at the top   15 hrsNSWER:15 hrs
Answer: A
If x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?
Pick one.
A) -2.4  B) 0.268  C) 1.166 repeating  D) 4.555 repeating  E) 8.125

Solution: x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?   Used process of elimination   A. -2.4   when this is multiplied by 9, x is not an integer   B. 0.268   when this is multiplied by 9, x is not an integer   C. 1.166 repeating   when this is multiplied by 9, x is not an integer   D. 4.555 repeating   E. 8.125   when this is multiplied by 9, x is not an integer   Answer choice 4.555 repeating seems to fit.4.555 repeating
Answer: D
Of the 550 people attending a conference, 300 have signed up for the Marketing workshop and 400 have signed up for the Accounting workshop. If 110 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:  Choose the correct choice from the following options.
A) 245	B) 260	C) 275	D) 280	E) 300

Solution: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:   Total = Gp.1 + Gp.2 - 260oth + Neither   550 = 300 + 400 - 260oth + 110   550 = 810 - 260oth   260oth = 260   Final Answer:   260
Answer: B
A spends 90% of his salary and B spends 85% of his salary. But savings of both are equal. Find the income of B, if sum of their incomes is Rs. 5000.  Choose the correct choice from the following choices: A) 2000 B) 2400 C) 2125 D) 2400 E) None

Solution: Explanation:   Let the incomes of A and B are x, y respectively.   Savings of A = (100 - 90)% (x) = 10% (x)   Savings of B = (100 - 85)% (y) = 15% (y)   Given, both saves equal amount.   Therefore, 10% (x) = 15% (y) ⇒xy=15%/10%=3/2   Therefore, x : y = 3 : 2   Hence, B's salary = 2/(2+3) x 5000 = Rs. 2000.   Correct Option: 2000
Answer: A
What is the tens digit of 6^19?	Select the correct option.
A) 1
B) 3
C) 5
D) 7
E) 9

Solution: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:   The tens digit of 6^2=36 is 3.   The tens digit of 6^3=216 is 1.   The tens digit of 6^4=...96 is 9.   The tens digit of 6^5=...76 is 7.   The tens digit of 6^6=...56 is 5.   The tens digit of 6^7=...36 is 3 again.   etc...   19 has the form 5n+4, so the tens digit of 6^19 is 9.   The answer is 9.
Answer: E
A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs. 760. What is A's share in the profit?
Select
A) 310	B) 330	C) 370	D) 350	E) None of these

Solution: Explanation :   Ratio of the initial capital of A and 330 = 4 : 5   Hence we can take the initial capitals of A and 330 as 4x and 5x respectively   Ratio in which profit will be divided   = (4x*3) + (3/4)*(4x)*7 : (5x*3)+ (4/5)*(5x)*7   = 12+21 : 15+28   = 33 : 43   A's share = 760 * 33/76= 
760 * 33/76 = 330
330.Answer : Option 330
Answer: B
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good
Select
A) 20/63	B) 4/56	C) 8/7	D) 6/9	E) 4/9

Solution: Explanation:   Required probability = (âµCâ‚ƒ . â´Câ‚)/â¹Câ‚„ = (10 * 4)/126 = 20/63   20/63nswer: 20/63
Answer: A