MU-NLPC/Calc-aqua_rat huggingface dataset:
If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?  Choose the most appropriate option:
A) 986	B) 1000	C) 1200	D) 1230	E) 1365

Solution: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.   =. Required number of ways = 14C10 = 14C4   = 14!/4!x19! = 1365   1365
Answer: E
A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water?	Choices.
A) 32 kmph B) 34 kmph C) 30 kmph D) 50 kmph E) 65 kmph

Solution: US = 45   50 kmphS = 55   M = (45 + 55)/2= 
(45 + 55)/2 = 50
50   Answer:50 kmph
Answer: D
If j and k are integers whose product is 400, which of the following statements must be true? Choose the correct answer.
A) n + k > 0 B) n is not equal to k. C) Either n or k is a multiple of 10. D) If n is even, then k is odd. E) If j is odd, then k is even.

Solution: If j and k are integers whose product is 400, which of the following statements must be true?   A.n + k > 0n and k should have the same sign, but that means that they can also both be negative   B.n is not equal to k.20 x 20 = 400[i]   C.Either n or k is a multiple of 10. [i]25 x 16 = 400   D.If n is even, then k is odd.k can also be even since even x even will be even   E. If j is odd, then k is even.k must be even since odd x even = even
Answer: E
A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen?	Choose one.
A) 1.34  B) 2.84  C) 3.84  D) 4.34  E) 5

Solution: 40*(40/100)= 
40*(40/100) = 16
16 --- 50   ? --- 12=> Rs.3.84   Answer: 3.84
Answer: C
What least whole no. should be added to 532869 to make it divisible by 9?	Select the correct option:
A) 5
B) 6
C) 9
D) 10
E) 11

Solution: If a number is divisible by 9, the sum of its digits must be a multiple of 9.   Here, 5+3+2+8+6+9=33, the next multiple of 9 is 36.   3 must be added to 532869 to make it divisible by 9   9
Answer: C
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?	Answers:  A) 63  B) 12  C) 45  D) 72  E) 36

Solution: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.   63ns: 63
Answer: A
Find the least number which when divided by 18,32,48,52 leaves remainder 14,28,44,48 respectively. Choose the correct choice.
A) 2845
B) 3250
C) 3740
D) 4150
E) 5140

Solution: The difference of 18-14= 
18-14 = 4
4 , 32-28= 4 , 48-44= 4 , 52-48 = 4   L3740M of 18,32,48,52 = 3744   Required number = 3744 - 4= 
3744 - 4 = 3_740
3740   Answer is 3740
Answer: C
If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y?
Select the correct option: A) 11 B) 31 C) 21 D) 41 E) 30

Solution: x takes even values as 2,4,6,8.,   y=5x+1   x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer   30 didn't follows this condition ans is 30
Answer: E
Find the compound interest and the amount on Rs.8000 at 5% per annum for 4 years when C.I is reckoned yearly?  Answers:
A) s.1261.05
B) s.1440.05
C) s.1185.05
D) s.1346.05
E) s.1724.05

Solution: A = 8000(21/20)4   = 9724.05   = 8000   ---------   1724.05   ANSWs.1724.05R:s.1724.05
Answer: E
M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 1.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be? Select.
A) {3, 4, 5, 10, 14}
B) {3, 7, 7, 10, 12}
C) {3, 5, 5, 10, 16}
D) {1, 5, 7, 10, 18}
E) {5, 6, 7, 10, 12}

Solution: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 7 to 10 + 2*{SD} = 13.   A. {3, 4,5, 10, 14} --> only 3 numbers are in this range. Discard.   B. {3,7, 7, 10, 12} --> 4 numbers are in this range. OK.   C. {3,5, 5, 10, 16} --> only 1 number is in this range. Discard.   D. {1,5, 7, 10, 18} --> only 2 numbers are in this range. Discard.   E. {5, 6, 7, 10, 12} --> only 3 numbers are in this range. Discard.   Answer: {3, 7, 7, 10, 12}.
Answer: B
How many numbers from 10 to 50 are exactly divisible by 9? Choose the correct choice from the following:	A) 9	B) 10	C) 11	D) 12	E) 14

Solution: 10/9 = 1 and 50/9 = 5 ==> 5 - 1= 
5 - 1 = 4
4. Therefore 4   Answer : 14
Answer: E
3^11 + 3^11 + 3^11 =  Choose the most appropriate option.
A) 3^12
B) 3^13
C) 3^30
D) 9^10
E) 9^30

Solution: Since we have 3^11 added together 3 times, we can factor out a 3 and we get 3(3^11) which is equal to 3^12.   The answer is 3^12.
Answer: A
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?  Pick:  A) 600  B) 881  C) 767  D) 261  E) 121

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 30= 
1/2 * 40 * 30 = 600
600 sq.cm.   600nswer:600
Answer: A
Two family reunions are happening at the Taj hotel, the Oates reunion and the Hall reunion. All 150 guests at the hotel attend at least one of the reunions. If 70 people attend the Oates reunion and 52 people attend the Hall reunion, how many people attend both reunions?
Choose the correct choice from the following choices.
A) 2
B) 5
C) 10
D) 16
E) 28

Solution: No of people in Oates reunion=70   No of people in Hall reunion=52   Attending both=x   All guests attend at least one.   Therefore, 150=70+52-(Both)   Both=28   Answer 28
Answer: E
A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget?  Options.
A) $70 under budget B) $30 under budget C) $30 over budget D) $70 over budget E) $180 over budget

Solution: The budget for 3 months is (3/12)*$1320 = $330   The company is $70 over budget.   The answer is $70 over budget.  (3/12)* 1320= 
  (3/12)* 1320 = 330
$330   The company is $70 over budget.   The answer is $70 over budget.
Answer: D
On his drive to work, Leo listens to one of three radio stations A, B or R. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to R. If R is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?	Pick one:
A) 0.027
B) 0.09
C) 0.417
D) 0.657
E) 0.9

Solution: Probability he hears a song is like:   Tune to A and likes what he is hearing = 0.3   Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3= 
0.7 * 0.3 = 0.21
0.21   Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to R and finally falls in love with the program= 0.7^2 * 0.3 = 0.147   Total = 0.657   Ans 0.657
Answer: D
For which of the following does n(a)−n(b)=n(a−b) for all values of a and b? Choose the correct choice from the following choices.
A) n(x)=x^2	B) n(x)=x/2	C) n(x)=x+5	D) n(x)=2x−1	E) n(x)=|x|

Solution: To solve this easiest way is just put the value and see that if it equals or not.   with option 1. n(a) = a^2 and n(b) = b^2   so L.H.S = a^2 - b^2   and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.   so L.H.S not equal to R.H.S   with option 2. n(a) = a/2 and n(b) = b/2   L.H.S = a/2 - b/2 ==> 1/2(a-b)   R.H.S = (a-b)/2   so L.H.S = R.H.S which is the correct answer.   answer:n(x)=x/2
Answer: B
How many factors greater than 50, which are multiples of 3, are possible in 8400?  Choose the correct choice from the following answers:
A) 41 B) 31 C) 21 D) 11 E) 01

Solution: Prime factorisation of 8400- 2^4∗3∗5^2∗7   Number of factors of 8400 =   5*2*3*2= 
5*2*3*2 = 60
60   Number of factors of 8400 which are not multiple of 3   5*2*3= 
5*2*3 = 30
30   Number of factors of 8400 which are multiple of 3   60-30= 
60-30 = 30
30   Factors which are multiple of 3 but less than 50-   3,6,12,15,21,24,30,42,48   Total-9   Number of factors of 8400 which are multiple of 3 but more than 50 are    30-9= 
 30-9 = 21
21   Answer:- 21
Answer: C
How many seconds will a 500 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) 23 sec
B) 30 sec
C) 27 sec
D) 28 sec
E) 29 sec

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 = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer:30 sec
Answer: B
If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?
Choose the most appropriate option:
A) 3 1/13% B) 3% C) 3 11/13% D) 4% E) None of these

Solution: Explanation:   X = 125%   Y = 130%   Z = 100%   X-Y/Y * 100 = 5/130 * 100   = 500/130 %   = 3 11/13% smaller than Y   Answer: Option 3 11/13%
Answer: C
Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?	Choose the correct answer:
A) 2 <= 3x+4 <= 6
B) 24 <= 34x+4 <= 6
C) 2 <= 356x+4 <= 6
D) 2 <= 378x+4 <= 6
E) 2 <= 357x+4 <= 6

Solution: The key words in the stem are:a singleline segment offinite length   Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.   2 <= 3x+4 <= 6nswer: 2 <= 3x+4 <= 6.
Answer: A
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
Choose the correct choice from the following answers:
A) 287 m
B) 704 m
C) 168 m
D) 278 m
E) 107 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   Answer: 704 m
Answer: B
The speed of a car is 70 km in the first hour and 90 km in the second hour. What is the average speed of the car?
Select the correct option:
A) 79 kmph
B) 80 kmph
C) 34 kmph
D) 23 kmph
E) 14 kmph

Solution: S = (70 + 90)/2= 
(70 + 90)/2 = 80
80 kmph   Answer:80 kmph
Answer: B
A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?  Choose the correct choice from the following:
A) $330.00	B) $331.00	C) $332.30	D) $333.30	E) $334.60

Solution: The maximum interest in one month is 10%*$300=$30.   The combined payment (base plus interest) is $300 + $30 = $330.   The greatest possible payment is: 1.01*$330  300 +  30= 
  300 +  30 = 330
$330.   The greatest possible payment is: 1.01*$330=$333.30.   The answer is $333.30.
Answer: D
4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr? Choose the correct choice from the following options.
A) 50 B) 60 C) 70 D) 80 E) 90

Solution: 5|5, 10, 15, 20   2|1, 2, 3, 4   |1, 1, 3, 2   L.C.M of 5, 10, 15, 20 is 60   60 times   60
Answer: B
If X is to be chosen at random from the set {5,7,4,3,8} and Y is to be chosen at random from the set {6,3,4,2}, what is the probability that XY will be odd?	Choose one.
A) 12 B) 8 C) 11 D) 6 E) 1

Solution: Method-1   xy will be odd when   1) x is odd and y is even, Probability of x odd is (3/5) and Probability of y even is (3/4), so Probability of Case(1) = (3/5)*(3/4) = (15/20)=(3/4)   2) x is even and y is odd, Probability of x even is (2/5) and Probability of y odd is (1/4), so Probability of Case(2) = (2/5)*(1/4) = (2/20)   3) x is odd and y is odd, Probability of x odd is (3/5) and Probability of y odd is (1/4), so Probability of Case(1) = (3/5)*(1/4) = (3/20)   Total Favorable Probability = (15/20)+(2/20)+(3/20) = (20/20)= 
(20/20) = 1
1   Answer: option 1
Answer: E
In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70. Choose the correct choice from the following:
A) 38	B) 40	C) 27	D) 43	E) 56

Solution: Explanation:   Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x)   3*x + (70 – x)*(-1) = 38   4x = 38 + 70= 
38 + 70 = 108
108   x= 27   ANSWER 27
Answer: C
On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004? Choose one:	A) Sunday	B) Friday	C) Saturday	D) Monday	E) Tuesday

Solution: Given that 8th Feb, 2005 was Tuesday   Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)   366 days = 2 odd days   Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday   Sundaynswer:Sunday
Answer: A
A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
Options.
A) 49/153  B) 18/153  C) 49/153  D) 40/153  E) 24/72

Solution: Explanation:   Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles   2 marbles are drawn from 18 marbles at random. Therefore,   n(S) = 18C2 = 153 ways   Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event 49/153 is   n(49/153) = 6C2 + 8C2 + 4C2 = 15+28+6= 
15+28+6 = 49
49   Therefore, by definition of probability of event 49/153,   P(49/153)= n(49/153)/n(S) = 49/153   49/153NSWER:49/153
Answer: A
The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 3 years?	Choose the correct choice from the following.
A) 14300 B) 17280 C) 14500 D) 14600 E) 15400

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   10000 × 120/100^3 = 17280   17280)
Answer: B
There was a match to be held.And 100 nations were to participate in that match.It was totally an elimination match,that is if a team loses a match it must be eliminated.Find out the total number of matches played to find out the grand winner?  Choose the correct choice from the following choices:
A) 96	B) 97	C) 98	D) 99	E) 92

Solution: 100-1= 
100-1 = 99
99 as every match will eliminate one team.   ANSWER:99
Answer: D
Find the missing figures :
?% of 60 = 2.125	Choose the correct answer
A) 8.54	B) 6.54	C) 8.7	D) 3.54	E) 4.54

Solution: (i)	Let x% of 60 = 2.125. Then , (x/100)*60 = 2.125   X = (2.125 * 100/60) = 3.54   Answer is 4.54.
Answer: E
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word SUCCESS could be arranged to create a seven-letter code?	Select
A) 6! B) 6! − (3! + 2!) C) 7!/(3! × 2!) D) 7!/(3! + 2!) E) 8!/(2! x 2!)

Solution: Number of letters in word 'SUCCESS' = 7.   The letters 'S' and 'C' appear 3 times and 2 times respectively in the word 'SUCCESS'.   Therefore the mathematical solution for number of ways that the letters of the word SU7!/(3! × 2!)7!/(3! × 2!)ESS can be arranged to create seven-letter code   = 7!/(3!*2!)   Answer:7!/(3! × 2!)
Answer: C
A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 8 km in stationary water
Choose the correct choice from the following answers:  A) 40 min  B) 1hr  C) 1hr 15 min  D) 1hr 30 min  E) 2 hr

Solution: rate down stream=(1/10*60)km/hr=6km/hr   rate up stream=2km/hr   speed still water =1/2(6+2)=4km/hr   required time =(8/4)=3 hr   Answer(2 hr)
Answer: E
A rectangular lawn of length 50 m and breadth 35 m is to be surrounded externally by a path which is 2 m wide. Find the cost of turfing the path at the rate of $3 per m². Select: A) $1008 B) $1031 C) $1028 D) $1068 E) $1088

Solution: Length of the lawn = 50 m   Breadth of the lawn = 35 m   Area of the lawn = (50 × 35) m²   = 1750 m²   Length of lawn including the path = [50 + (2 + 2)= 
50 + (2 + 2) = 54
54 cm   Breadth of the lawn including the path= [35 + (2 + 2)= 
35 + (2 + 2) = 39
39 m   Area of the lawn including the path= 54 × 39 m² = 2106 m²   Therefore, area of the path = (2106 - 1750)= 
(2106 - 1750) = 356
356 m²   For 1 m², the cost of turfing the path= $ 3   For 356 m², the cost of turfing the path = $3 × 356 = $1068   ANSWER : $1068
Answer: D
A boy can reach a certain place in 45 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.  Answers:  A) 2 km/hr.  B) 6 km/hr  C) 8 km/hr  D) 14 km/hr  E) None of these

Solution: Explanation :   Solution: Let the speed be x km/hr. then,   45x - (45 * 29x/30) = 3   => 3/2X =3   X=2   2 km/hr.
Answer: A
One-fourth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?	Choose the correct choice from the following answers.
A) 4.4%  B) 5.5%  C) 6.6%  D) 11.3%  E) 16.2%

Solution: 1/4 of the switches are defective.   The defective switches that are not rejected are 1/5*1/4 = 1/20 = 4/80 of all switches.   The non defective switches that are sold are 3/4*19/20 = 57/80 of all switches.   The percent of switches sold that are defective is 4/61 = 6.6%   The answer is 6.6%.
Answer: C
If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 6/15 Find P(B|A) Choose the correct choice: A) 1/2 B) 2/3 C) 3 D) 4/5 E) 4/7

Solution: P(B|A) = P(A âˆª B)/P(A)   P(B|A) = (6/15)/(2/15)= 
(6/15)/(2/15) = 3
3.   3
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.  Choose the correct choice from the following choices.
A) 150	B) 278	C) 179	D) 200	E) 191

Solution: :   Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (200istance) = Speed * Time     (50/3) * 12= 
  (50/3) * 12 = 200
200 meter   Answer:200
Answer: D
The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 7:8 then what is the number of visitors on the 5th day of the library?	Choose the correct answer: A) 17 B) 17 C) 64 D) 19 E) 01

Solution: If number of visitors on 1st, 2nd, 3rd, 4th & 5th day are a, b, c, d & e respectively, then   a + b + c + d = 58 × 4 = 232 ----(i) &   b + c + d + e = 60 × 4 = 240 ----(ii)   Subtracting (i) from (ii), e – a = 8 ---(iii)   Given   a/e=7/8 ---(iv)   So from (iii) & (iv) a=56, e=64   Answer:64
Answer: C
A computer manufacturer produces a certain electronic component at a cost of $70 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $14,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?  Choose the correct answer:
A) 132	B) 138	C) 144	D) 128	E) 116

Solution: $14500 is a fixed cost   Each component is $74 ($70 to produce, $4 to ship)   Manufacturer will be producing and selling 250 components   so therefore the equation to find price would be   250*p = 14500+(250*70)+(250*4)   p = (14500+17500+1000)/250= 
(14500+17500+1000)/250 = 132
132   132nswer:132
Answer: A
The sum of three consecutive even numbers is 30. Find the middle number of the three? Pick
A) 14	B) 16	C) 18	D) 25	E) 34

Solution: Three consecutive even numbers (2P - 2), 2P, (2P + 2).   (2P - 2) + 2P + (2P + 2) = 30   6P = 30 => P = 5.   The middle number is: 5P = 25.   ANSWER:25
Answer: D
If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is L:	Choices: A) L=1 B) L=2 C) L=3 D) L=4 E) 5

Solution: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.   Hence p/48 should resolve to a integer.   48 -- > 2^4 * 3.   Hence p should have atleast 2^4*3 for p/48 to resolve to a int.   The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is L=2(2).
Answer: B
The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 15 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera? Choose the most appropriate option.
A) $207	B) $210	C) $230	D) $213	E) $215

Solution: Final price = (1+15/100) * Original Price   = 1.15 * Original Price   From options given only 230 is divisible by 1.10 as it is stated OP is whole dollar amount.   Hence $230
Answer: C
How many positive three-digit integers are divisible by both 3 and 7?  Answers
A) 43 B) 45 C) 47 D) 50 E) 52

Solution: A number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21.   Multiples of 21 between 100 and 999, inclusive is   (last-first)/multiple+1=(987-105)/21+1=42+1= 
42+1 = 43
43   43nswer: 43.
Answer: A
Three partners A,B,C start a business.A invested 3000 for 8 month,B invested
4000 for 9 month.and C invested 5000 for 1 years.at the end of year there is total profit of 15000 rs.what is profit share of B? Select the correct option:
A) 3000
B) 4500
C) 4000
D) 4200
E) 3500

Solution: ratio of A,B,C investment=(3000*8):(4000*9):(5000*12)   =24000:36000:60000=2:3:5.   Total annual profit=15000 rs.   profit share of B=15000*3/10= 
15000*3/10 = 4_500
4500rs.   answer 4500
Answer: B
A sum of money at simple interest amounts to $ 815 in 3 years and to $854 in 4 years. The sum is:  Choose the correct choice from the following answers:
A) $153
B) $698
C) $398
D) $549
E) $675

Solution: B   $698   S.I. for 1 year = $(854 - 815)= 
(854 - 815) = 39
$39.   S.I. for 3 years= $(39 x 3) = $117.   Principal = $(815 - 117)= 
(815 - 117) = 698
$698.
Answer: B
When n is divided by 19, the remainder is 7. Find thee difference between previous remainder and the remainder when 18n is divided by 9 ? Choose the correct choice from the following options:
A) 7  B) 5  C) 0  D) 3  E) 9

Solution: Let n=7 (leaves a remainder of 7 when divided by 19)   18n = 18(7) =126, which leaves a remainder of 0 when divided by 9.   difference = 7 - 0= 
7 - 0 = 7
7.   7nswer 7
Answer: A
There are 437 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital? Choose the correct choice from the following answers.
A) 152
B) 253
C) 57
D) 171
E) 181

Solution: Given,   The ratio of the doctors to the nurses is 8 : 11   Number of nurses = 11/19 x 437 = 253   ANSWER:253
Answer: B
In how many ways can live boys and three girls sit in a row such that all boys sit together?
Answers:
A) 3877
B) 2778
C) 2880
D) 2987
E) 1231

Solution: Explanation:   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
What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 150?  Choose the most appropriate option:
A) 10  B) 25  C) 50  D) 75  E) 100

Solution: Surprisingly no one answered this easy one.   property of a set of consecutive integerz.   mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.   So mean=median=150/2= 
150/2 = 75
75   Answer is 75
Answer: D