MU-NLPC/Calc-aqua_rat huggingface dataset:
There are cats got together and decided to kill the mice of 999951. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?  Select:
A) 941,1009 B) 993,1007 C) 991,1009 D) 791,1009 E) 931,1009

Solution: 999951 can be written as 1000000 â€“ 49   = 10002 â€“ 72 ie of the form a2-b2=(a+b)(a-b)   =(1000+7)*(1000-7)   = (1007)*(993)   Given that number of cats is less than number if mice.   So number of cats is 993 and number of mice were 1007   Answer 993,1007
Answer: B
A’s speed is 25/18 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?  Pick one:  A) 1/18  B) 7/18  C) 7/25  D) 3/25  E) 1/25

Solution: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 25 meters, B covers 18 meters in that time. So if the race is 25 meters long, when A reaches the finish line, B would be 7 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 25 meters) would be the same as the time required by B (to cover 18 meters) to reach the finish line.   So B should get a head start of 7/25th of the race.   Answer (7/25)
Answer: C
The sequence a(1), a(2), …, a(n), … is such that a(n)=4a(n–1) –3 for all integers n>1. If a(3)=x, then a(1)=?
Select:
A) 4x–3	B) 16x–15	C) (x+3)/4	D) (x+3)/16	E) (x+15)/16

Solution: Since we know a(3) we can find a(2),   if we can find a(2) we can find a(1).   a(3)=4a(2)-3 ---> x=4a(2)-3 ---> a(2)=(x+3)/4   a(2)=4a(1)-3 ---> (x+3)/4=4a(1)-3 ---> 4a(1)=(x+15)/4 ---> a(1)=(x+15)/16   The answer is (x+15)/16.
Answer: E
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11-sided polygon)?
Select the correct option:
A) 1/2  B) 1/3  C) 1/4  D) 1/8  E) 1/11

Solution: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.   So the remaining n-3 vertices make diagonals.   There are 2 of these diagonals which are the shortest.   The probability of choosing one of the shortest diagonals is 2/8 = 1/4.   The answer is 1/4.
Answer: C
The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 98, and last 6numbers is 65 then find 6th number?	Answers:
A) A)318
B) B)65
C) C)58
D) D)62
E) E)48

Solution: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s   answer = 6*98+6*65-11*60= 
6*98+6*65-11*60 = 318
318   318nswer is 318
Answer: A
Solution A is 20% sugar and Solution B is 80% sugar. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% sugar solution? Answers: A) 6:4 B) 6:14 C) 4:4 D) 4:6 E) 3:7

Solution: Forget the volumes for the time being.   You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use   w1/w2 = (A2 - Aavg)/(Aavg - A1)   w1/w2 = (80 - 50)/(50 - 20)= 
(80 - 50)/(50 - 20) = 1
1/1   So the volume of the two solutions will be equal. Answer has to be 4:4=4:4
Answer: C
In a group of 90 students, 30 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
Answers:
A) 9	B) 19	C) 33	D) 27	E) 31

Solution: Number of students taking history =H=30   Number of students taking statistics =S= 32   Total number of students =T= 90   Number of students taking History or Statistics or both =B= 59   Number of students taking neither history nor statistics =N= 90-59= 
90-59 = 31
31   LetXbe the number of students taking both history and statistics.   Then   T= H + S + N - X   or 90 = 30+ 32 +31 - X   or X = 3   Now,   Number of students taking only history will be   H-X   or  36-3= 
 36-3 = 33
33   Answer:- 33
Answer: C
Two bullet train s are running in opposite directions with the same speed. If the length of each bullet train is 120 metres and they cross each other in 12 seconds, then the speed of each bullet train (in km/hr) is:
Select
A) 46 km/hr.  B) 36 km/hr.  C) 56 km/hr.  D) 76 km/hr.  E) 66 km/hr.

Solution: B   36 km/hr.   Let the speed of each bullet train be x m/sec.   Then, relative speed of the two bullet train s = 2x m/sec.   So, 2x = (120 + 120)/12   --> 2x = 20   --> x = 10.   --> Speed of each bullet train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.
Answer: B
A nickel is placed flat on a table. What is the maximum number of nickels that can be placed
around it, flat on the table, with each one tangent to it?  Choose the correct choice from the following options
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: Connect the midpoints of the given nickel and two others placed around it so that   all three touch. This creates an equilateral triangle with 60 degree angles. Since 360=60 = 6,   six nickels can be placed around the given nickel.   correct answer 6
Answer: C
What is the remainder when 750*810*830*790 is divided by 13?
Choose the correct answer.
A) 4
B) 9
C) 10
D) 8
E) 6

Solution: OA is 'C'.   OE:   take the remainder from each of 750/15, 810/15 and so on..   750/13 gives remainder = 9   810/13 gives remainder = 4   830/13 gives remainder = 11   790/13 gives remainder = 10   the net remainder is the product of above individual remainders. i.e = 9*4*11*10   break them into pairs 9*4/13 gives remainder 10   and 11*10/13 gives remainder 6   so 10*6/13 gives remainder 8.   Answer: 10
Answer: C
If a and b are the two values of t that satisfy
the equation t^2 â€“ 10t + 16 = 0, with a > b, what is the value of a â€“ b?
Choose the correct choice from the following
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Factor the left side of the equation:   t^2 â€“ 10t + 16 = 0   (t â€“ 2)(t â€“ 8) = 0   t = 2, t = 8   Thus, a = 8 and b = 2. So a â€“ b = 8 â€“ 2 = 6.   The answer is 6.
Answer: C
k = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?  Choose the correct choice from the following choices:  A) 2^n - 8  B) 2^n - 4  C) 2^n  D) 2^n + 4  E) 2^n + 5

Solution: Given: k, M and N are integers   If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)   We're told that 9 is a divisor of 2^n + 5   We also know that 9 is a divisor of9.   So, applying the aboverule, 9 is a divisor of 2^n + 5 +9, and 9 is a divisor of 2^n + 5 -9 = 2^n-4   2^n - 4
Answer: B
A certain distance is covered by a cyclist at a certain speed. I a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is:  Choices
A) 1:2  B) 2:1  C) 1:4  D) 4:1  E) None of these

Solution: let the distance covered by the cyclist be x and the time taken be y. Then, Required ratio=1/2x/2y:x/y=1/4:1=1:4.   1:4orrect Option: 1:4
Answer: C
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?	Select.
A) 5:18  B) 5:12  C) 5:10  D) 5:11  E) 5:16

Solution: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.   a2 = 4096 = 212   a = (212)1/2 = 26 = 64   L = 2a and b = a - 24   b : l = a - 24 : 2a = 40 : 128 = 5:16   Answer:5:16
Answer: E
A and B start a business, with A investing the total capital of Rs.100000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.10000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?	Choose the correct choice from the following choices: A) A)2520000 B) B)2620000 C) C)2820000 D) D)2920000 E) E)2420000

Solution: Interest received by A from B = 10% of half of Rs.100000 = 10% * 50000 = 5000.   Amount received by A per annum for being a working partner = 10000 * 12 = Rs.120000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (5000+ 120000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of 2620000   (5000 + 120000 + P) = 2(P)   P = 125000   Total profit = 2P + 120000   = 2*125000 + 120000 = 2620000   Answer:2620000
Answer: B
An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of B? Choose the correct choice.
A) 360  B) 358  C) 356  D) 514  E) 504

Solution: Let the shares of A, B and C be a, b and c respectively.   a : b : c = 1/2 : 1/3 : 1/4   Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.   a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.   Share of B = 4/13 * 1638 = Rs. 504   Answer: 504
Answer: E
A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?  Select the correct option.
A) $200  B) $333.33  C) $100.25  D) $277.78  E) $377.00

Solution: Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 )   $25000 is 60% of total amount.   So total amount = 25000 * 100/60   Remaining amount is 40% of total amount.   40% of total amount = 25000 * (100/60) * (40/100) = 50000/3   This amount has to be divided by 50( remaining people are 50 )   So per head amount is 50000/3 / 50 = 32000/180 = 333.33;   ANSWER:$333.33
Answer: B
In a company of 11 employees, 5 employees earn $32,000, 4 employees earn $45,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 11 employees is $48,000, what is the annual salary for each of the highest-paid employees? Choose one.
A) $90,000  B) $94,000  C) $98,000  D) $102,000  E) $106,000

Solution: 5*32,000+4*45,000+2x=11*48,000   2x=528,000-160,000-180,000   2x=188,000   x=94,000   The answer is $94,000.
Answer: B
Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Pick one
A) 54 B) 59 C) 63 D) 71 E) 62

Solution: Total = 70   Thrower = 46   Rest = 70 - 46= 
70 - 46 = 24
24   Left Handed= 24/3= 
24/3 = 8
8   Right handed= 16   If all Thrower are right handed then total right handed is   46 + 16= 
  46 + 16 = 62
62   so E. 62 is the right answer
Answer: E
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is: Select the correct option.
A) 70 km/hr	B) 75 km/hr	C) 84 km/hr	D) 87.5 km/hr	E) 77.5 km/hr

Solution: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours,   then the speed of the first train = 400/4= 
400/4 = 100
100 kms/hr   then the speed of the first train is:100*7/8= 700/8= 
700/8 = 175/2 = around 87.5
87.5 km/hr   ANSWER:87.5 km/hr
Answer: D
One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?
Select the correct option
A) 11 km  B) 13 km  C) 16 km  D) 18 km  E) 19 km

Solution: Let the distance travelled on foot be x km.   Then, distance travelled on bicycle = (61 -x) km.   So, x + (61 -x) = 9   4 9   9x + 4(61 -x) = 9 x 36   5x = 80   x = 16 km.   16 km
Answer: C
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?	Choose the correct answer.
A) 9
B) 12
C) 14
D) 15
E) 60

Solution: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?   3! / 1!2! * 6! / 3!3!   =3*20= 
3*20 = 60
60   E. 60
Answer: E
There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange?
Choices.
A) R=7/10 B) R=3/5 C) R=2/5 D) R=3/10 E) 1/10

Solution: Method 1   Probability R that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10   Method 2   Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10   Method 3   Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue   = 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)   = 1 - 3C2/5C2   = 1-(3/10) = 7/10   R=7/10nswer :R=7/10
Answer: A
Which of the following options is an arithmetic sequence?
I. m-9, n-5, o-9,p-9, q-9, r-9
II. m^5, n^5, o^5, p^5, q^5
III. 4m,4n,4o,4p,4q
Answers: A) I only B) I and II C) I and III D) II and III E) III only

Solution: lets look at the three choices...   I. m-9, n-5, o-9,p-9, q-9, r-9   since the difference is not constant, it is not an arithmetic sequence...   II. m^5, n^5, o^5, p^5, q^5   since the difference is not constant, it is not an arithmetic sequence   III. 4m,4n,4o,4p,4q   since the difference is constant it is an arithmetic sequence...   The answer is III only)
Answer: E
Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was? Choose one
A) Rs. 692.80 B) Rs. 905 C) Rs. 990 D) Rs. 1385 E) None

Solution: Answer   Income of the deceased = Total income of 4 members - total income of remaining 3 members.   = 735 x 3 - 650 x 2 Rs.   = 905 Rs.   Correct Option: Rs. 905
Answer: B
In how many ways the word "RITUAL" can be arranged?
Choose one:
A) 120 B) 240 C) 720 D) None E) Cannot be determined

Solution: Explanation :   The required number of ways = 6!   = 720   Answer : 720
Answer: C
210 reputed college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
Choose one
A) 25	B) 40	C) 50	D) 60	E) 75

Solution: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.   So, if we use your formula it should be: 210={Mac}+{Windows}-{40oth}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: B
5 identical snow plows can clear an iced parking lot in 24 hours. How long would it take 6 such snow plows to clear the same parking lot? Pick one
A) 1 hour, 15 minutes	B) 2 hours, 30 minutes	C) 3 hours	D) 7 hours, 30 minutes	E) 20 hourss

Solution: 6/5 as many plows will take 5/6 as many hours --> 24*5/6=20 hours.   Answer: 20 hourss.--  24*5/6= 
--  24*5/6 = 20
20 hours.   Answer: 20 hourss.
Answer: E
If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ?
Choices: A) 4 B) 3 C) 2 D) 1 E) 0

Solution: Explanation:   Let n ÷ 4 = p , remainder = 3   => n = 4p + 3   2n = 2(4p + 3)   = 8p + 6   = 8p + 4 + 2   = 4(2p + 1) + 2   Hence, if 2n is divided by 4, we will get 2 as remainder.   Answer: 2
Answer: C
Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
Choose the correct choice.
A) 27 sec	B) 87 sec	C) 67 sec	D) 47 sec	E) 37 sec

Solution: Explanation:   Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 300 / (15 + 25)5/18 = 300x 18 / 40 x 5 = 27 seconds.   27 secnswer: 27 sec
Answer: A
How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.
Choose the correct answer:
A) 648
B) 720
C) 890
D) 980
E) None of these

Solution: Explanation :   Since, there is no repetition, numbers 1 to 6 will always be present in the 6 digit number.   We will go through this step by step.   Divisible by 1 and 1 at the unit place:   _ _ _ _ _ 1   This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.   Divisible by 2 and 2 at the unit place:   _ _ _ _ _ 2   This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.   Divisible by 3 and 3 at the unit place:   _ _ _ _ _ 3   Since, any number will have all the digits from 1 to 6 and the sum  1 + 2 + 3 + 4 + 5 + 6= 
 1 + 2 + 3 + 4 + 5 + 6 = 21
21 is divisible by 3   This gives us total of 5 x 4 x 3 x 2 x 1= 120 numbers.   Divisible by 4 and 4 at the unit place:   _ _ _ _ _ 4   Here, there are two cases   _ _ _ _ 2 4   This gives 4 x 3 x 2 x 1 = 24 numbers.   _ _ _ _ 6 4   This gives 4 x 3 x 2 x 1 = 24 numbers.   This gives us total of   24 + 24= 
  24 + 24 = 48
48 numbers.   Divisible by 5 and 5 at the unit place:   _ _ _ _ _ 5   This gives us total of 5 x 4 x 3 x 2 x 1= 120 numbers.   Divisible by 6 and 6 at the unit place:   _ _ _ _ _ 6   As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even.   This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.   None of these cases will have numbers overlapping with each other.   So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120= 
120 + 120 + 120 + 48 + 120 + 120 = 648
648   648nswer : 648
Answer: A
A car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?  Choices:
A) 6
B) 8
C) 10
D) 12
E) 14

Solution: Let T be the total time of the trip.   35*4 + 44(T-4) = 38T   6T = 176-140   T = 6   The answer is 6.
Answer: A
A store sells a certain product at a fixed price per unit. At the product's current price, v units cost a total of exactly $300. If the price were lowered by $5 from its current value, then v + 2n units would cost exactly $300; if the price were raised by $5, then v – n units would cost exactly $300. What is the value of v?	Pick.
A) 10	B) 15	C) 20	D) 25	E) 30

Solution: It got too complicated when I used algebra. Using plugging in, it was quite fast.   Price Quantity total value   p v pv = 300   p-5 v+2n (p-5)(v+2n) = 300   p+5 v-n (p+5)(v-n) = 300   Solving three equations for three unknowns. Tough!!   Plugging in, I always start with C. 20 was the answer here, so saved calculation!   Putting values in above equations:   Price Quantity total value   15 20 300   10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5   20 15 300   So v = 20 satisfies all equations!!
Answer: C
It would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?	Choose the correct choice.
A) 72/17
B) 17/72
C) 14/24
D) 24/56
E) 34/56

Solution: The rate of the first machine is 1/9 job per hour;   The rate of the second machine is 1/8 job per hour;   Thus, the combined rate of the machines is 1/9+1/8=17/72 job per hour, which means that it takes 1/(17/72)=72/17 hours both machines to do the job.   72/17nswer: 72/17.
Answer: A
find the average of first 20 multiples of 7?  Choose the correct choice:  A) 73.5  B) 70.5  C) 63.5  D) 54.5  E) 40.5

Solution: Required average =7(1+2+3+…….+20)/20   (7*20*21)/(20*2)   (147/2)=73.5.   73.5NSWER 73.5 73.5
Answer: A
Out of 8 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?  Choose the correct answer
A) 7/8	B) 9/10	C) 11/12	D) 13/14	E) 15/16

Solution: P(no graduates) = 4C3 / 8C3 = 4/56 = 1/14   P(at least one graduate) = 1- 1/14 = 13/14   The answer is 13/14.
Answer: D
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 $0.51 more than Jane, what was the original price of the dish?	Choose the correct choice from the following
A) 24 B) 34 C) 37.8 D) 42 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 = 0.51--> 15p - 13.5p = 51 --> p = 34.   Answer: 34.
Answer: B
Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z? Choose one.
A) y + 3z B) (y +z) / 4 C) 5y + 3z D) 3y + z E) 3y + 4.5z

Solution: Soln:   The resulting equation is   => (.01x + .05y + .03z)/(x+y+z) = 1.5/100   => x + 5y + 3z = 1.5x + 1.5y + 1.5z   taking x to one side and y and z to other side we get   => x = 5y + 3z   Ans is 5y + 3z
Answer: C
If x is divisible by 3, 14, and 15, which of the following must be the least multiple of x? Choose the correct choice from the following answers
A) 308  B) 210  C) 200  D) 120  E) 100

Solution: If x is divisible by 3, 14, and 15, then x must be a multiple of 3,14 and 5.   Hence,the least multiple of x will be   3*14*5= 
  3*14*5 = 210
210.   ANSWER:210
Answer: B
Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1450?
Pick.
A) Rs.1000 B) Rs.1250 C) Rs.1010 D) Rs.10000 E) None of these

Solution: Explanation:   1450 = P [1 + (5*16/5)/100]   P= 1250   Answer: Option Rs.1250
Answer: B
How many different section of 4 books can be made from 10 different books if two particular books are always selected?	Choices
A) 36
B) 38/
C) 26
D) 28
E) 24

Solution: This means two books are seclected out of the remaining 8 books. Required number of ways = 8C2= 8!/6!x2!=28. Ans: 28.
Answer: D
4 couples are seating at a round tables how many ways can the 4 women sit together	Choose the correct choice from the following:  A) 4!*4!  B) 3!*4!  C) 4!*3!  D) 5!*4!  E) 6!*4!

Solution: 4 men can be arranged around a table in (4-1)= 
(4-1) = 3
3! ways;   Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.   So, total # of ways is 3!*4*4!=4!*4!   4!*4!NS:4!*4!
Answer: A
If the radius of a circle is increased by 60% then the area is increased by:
Choose the correct answer.
A) 44%	B) 120%	C) 156%	D) 40%	E) None of the above

Solution: initially A=pi*r2   now R2=160/100r   then area=Pi*(160R/100)2   area=256R/100   that is area increases from 100 to 256=increase in area=156%   ANSWER:156%
Answer: C