MU-NLPC/Calc-aqua_rat huggingface dataset:
Tony alone can paint a wall in 7 days and his friend Roy alone can paint the same wall in 9 days. In how many days they can paint the wall working together? Round off the answer to the nearest integer.  Choose the correct choice from the following choices: A) 2 B) 4 C) 6 D) 7 E) 9

Solution: Sol. use formula (xy / x+y)   So nearest value for 3.93 = 4   Answer: Option 4
Answer: B
Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
Choose the most appropriate option:
A) 35	B) 62	C) 68	D) 35	E) 32

Solution: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear and no other set of three points, except those that can be selected out of these 6 points are collinear.   Hence, the required number of straight lines   = ¹¹C₂ - ⁶C₂ - ⁵C₂ + 1 + 1   = 55 - 15 - 10 + 2= 
55 - 15 - 10 + 2 = 32
32   Answer: 32
Answer: E
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, BC. 116 watch A, 127 watch C, while 107 watch B. If 70 watch exactly two channels. How many watch exactly one channel?
Pick one.
A) 185	B) 180	C) 165	D) 190	E) 195

Solution: 250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)   250 = n(Exactly 1 channel) + 70 + n(Exactly 3 channels)   Let's find the value of n(Exactly 3 channels) = x   250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)   Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.   250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x   250 = 116 + 127 + 107 -70 - 2x   x = 25   250 = n(Exactly 1 channel) + 70 + 25   n(Exactly 1 channel) = 165   Answer (165)
Answer: C
N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?  Pick one
A) 5 B) 6 C) 1 D) 2 E) 3

Solution: DETAILED SOLUTION   To begin with, the question should read "find the 44th digit".   Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.   So, a number comprising 42 2's would be a multiple of 13, so would a number comprising 36 2's. So, in effect, we are left with a two digit number 2a, where a is the 44th digit. 26 is a multiple of 13, so the 44th digit should be 6.   CORRECT ANSWER 6
Answer: B
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 (in years)	Choose the correct choice from the following choices: A) 8, 20, 28 B) 16, 28, 36 C) 20, 35, 45 D) None of these E) Cannot be determined

Solution: Solution   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 16,28,36 years .   Answer 16, 28, 36
Answer: B
Rose & Raylene goes to same place for work daily from same house & they work for five days a week. Rose saves 10 minutes on a day than Raylene in her trip. In a month, how much time Rose saves compared to Raylene in traveling? Take in a month there are four weeks (20 working days)	Select:
A) 3 hours & 20 minutes B) 3 & 10 C) 3 hours D) 2 hours & 20 minutes E) 2 hours & 30 minutes

Solution: For each day rose saves 10 minutes so for a week 50 minutes (10*5) & which gives a month 200 minutes (50*4).   200 minutes = 3 hours 20 minutes   3 hours & 20 minutesnswer: 3 hours & 20 minutes
Answer: A
Goldenrod and No Hope are in a horse race with 9 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?  Choose the correct answer:	A) 362880	B) 181440	C) 120000	D) 24000	E) 21000

Solution: All 9 horses can finish the race in 9! way (assuming no tie).   If no tie is possible between No Hope and Goldenrod, then in half of these cases No Hope will be before Goldenrod and in half of these cases after (not necessarily right before or right after). How else? So, there are 9!/2=181440 different arrangements of finishes where No Hope always finishes before Goldenrod.   Answer: 181440.
Answer: B
An inspector rejects 10% of the meters as defective. How many will he examine to reject 10?	Choices:  A) 100  B) 120  C) 250  D) 200  E) 160

Solution: Then, 10% of x= 10   (10/100)x = 10   x = (10*100*)/10= 100   100nswer is 100
Answer: A
In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and four different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color?  Choose the correct choice from the following options
A) 719/720	B) 1/24	C) 2/233	D) 3/543	E) 1/720

Solution: 4 ties and 4 shirts...   red tie can take any of 4 shirts..   orange can take any of the remaining 3 shirts   yellow any of remaining 2..   and so on till last indigo chooses the 1 remaining..   Total ways= 4*3*2*1= 
4*3*2*1 = 24
24   out of this 720, ONLY 1 way will have same colour tie and shirt..   prob= 1/720   1/24
Answer: B
The speed of a boat in still water is 18 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 14 minutes is
Choose the correct choice from the following options.
A) 1.6 km
B) 2 km
C) 5.1 km
D) 4 km
E) None of these

Solution: Explanation:   Speed downstreams	=(18 + 4)= 
(18 + 4) = 22
22 kmph.   Distance travelled= (22 x 14/60)km   = 5.1km   Option 5.1 km
Answer: C
The average weight of 10 persons increases by 7.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?	Choose the most appropriate option:	A) 120 kg	B) 130 kg	C) 137 kg	D) 190 kg	E) None

Solution: Solution   Total weight increased	= (10 x 7.2)kg   = 72 kg.   Weight of new person	= (65 + 72)= 
(65 + 72) = 137
137 kg.   Answer 137 kg
Answer: C
A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1420. If a door and 2 windows occupy 8 sq. m, find the height of the room.  Choose the correct choice from the following options:
A) 4 m
B) 4.5 m
C) 5 m
D) 5.5 m
E) 6 m

Solution: Explanation:   Let breadth = x m, length = 3x m, height = H metres.   Area of the floor = (Total cost of carpeting)/(Rate/m2)=(270/5)m2=54m2.   x× (3x/2) = 54 =>x2 = (54×2/3) = 36 <=> x = 6.   So, breadth = 6 m and length =(3/2)×6 = 9 m.   Now, papered area = (1420/10)m2 = 142 m2.   Area of 1 door and 2 windows = 8 m2.   Total area of 4 walls = (142 + 8) m2 = 150 m2   2×(9+ 6)× H = 150 <=> H = 150/30= 
150/30 = 5
5 m.   Answer: Option 5 m
Answer: C
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.83. How much was lent at 5%?	Choose the correct choice from the following.
A) 388  B) 700  C) 277  D) 500  E) 271

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83   5x/100 + 90 – 6x/100 = 83   x/100 = 7   => x = 700.Answer: 700
Answer: B
If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 900. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 922.50. What is the value of X? Select.
A) 9000	B) 6000	C) 5000	D) 4000	E) 3000

Solution: Simple way to solve this question is to use options.   From SI, we know that X*y=45,000.   Now, put the value of X = 9000, we will have y = 5%   To calculate CI,   Now, we know 1st year Amount= 9000+5% of 9000= 9450.   2nd year, Amount = 9450 + 5% of 9450 = 9922.50.   We can see after 2 years Interest = 9922.50-9000= 922.50. hence, it satisfies the question. Hence 9000 is the correct answer
Answer: A
Walking at 1/3th of its usual speed a cab is 20mnts late. Find its usual time to cover the journey?	Pick one
A) 10m
B) 15m
C) 20m
D) 25m
E) 12m

Solution: New speed = 1/3th of usual speed   New time = 3 of usual time   3 UT - UT = 20m   2UT = 20m   UT = 10m   10mnswer is 10m
Answer: A
If n is an integer and n^4 is divisible by 10, which of the following could be the remainder when n is divided by 10? Choose one
A) 2
B) 5
C) 6
D) 8
E) 10

Solution: option 1   Remainder 2 means  10+2= 
 10+2 = 12
12   n^4= 12^4= 12*12*12*12/10 is not an integer   option 2   Remainder 5 means  10+5= 
 10+5 = 15
15   n^4= 15^4= 15*15*15*15/10 is not an integer   option 3   Remainder 6 means  10+6= 
 10+6 = 16
16   n^4= 16^4= 16*16*16*16/10 is not an integer   option 4   Remainder 8 means  10+8= 
 10+8 = 18
18   n^4= 18^4= 18*18*18*18/10 is not an integer   option 5   Remainder 10 means  10+10= 
 10+10 = 20
20   n^4= 20*20*20*20/10 is an integer means n^4 is divisible by 10 if we take n=10   so 10 is correct
Answer: E
If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:
Choose the correct choice from the following choices:  A) 12 years  B) 18 years  C) 16 years  D) 14 years  E) 19 years

Solution: Explanation:   The sum P becomes 3P in 4 years on compound interest   3P = P(1+R/100)4   â‡’ 3 = (1+R/100)4   Let the sum P becomes 81P in n years   81P = P(1+R/100)n   â‡’ 81 = (1+R/100)n   â‡’ (3)4 = (1+R/100)n   â‡’ ((1+R/100)4)4 = (1+R/100)n   â‡’ (1+R/100)16 = (1+R/100)n   n=16   i.e, the sum will become 81 times in 16 years   ANSWER IS 16 years
Answer: C
Jansi went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20 p. coins. When she returned she had as many one rupee notes as she originally had and as many 20 p. coins as she originally had one rupee notes. She actually came back with about one-third of what she had started out with.
How much did she spend and exactly how much did she have with her when she started out ? Select the correct option: A) 9.6 B) 10.6 C) 11.0 D) 9.4 E) 8.1

Solution: A   9.60   Let us assume that originally Jansi had X rupees and Y 20 paise coins. Going shopping she had (100X + 20 Y) paise.   She returned with only (100 Y + 20 X) paise.   This last sum, as we know, is one-third of the original and therefore   3(100 Y + 20 X) = 100 X + 20 Y Simplifying we have X = 7 Y   If Y is 1 thenX is 7. Assuming this so Jansi had 7.20 rupees when she set out for shopping.   This is wrong because Jansi actually had about 15 rupees.   Let us see now what we get if Y = 2. Then X = 14. The original sum was 14.40 rupees which accords with the condition of the problem.   If we assume that Y = 3 then the sum will be too big — 21.60 rupees.   Therefore the only suitable answer is 14.40 rupees.   After shopping Jansi had 2 one rupee notes and 14 twenty Paise coins.   This is actually l/3rd of the original sum 1,440:3 = 480. Jansi's purchases, therefore, cost 14.40 — 4.80 = Rs 9.60
Answer: A
If d is a number such that –2 ≤ d ≤ 2, which of the following has the largest possible absolute value?  Options
A) 3d – 1	B) x^2 + 1	C) 3 – x	D) x – 3	E) x^2 – x

Solution: Ans is A .. leads to the max value of 7 for d = -2
Answer: A
The smallest prime factor of 899 is xx. Which of the following is true of xx? Choose the most appropriate option:
A) 1<x≤7
B) 7<x≤14
C) 14<x≤21
D) 21<x≤28
E) 28<x≤35

Solution: 899 = 900 - 1   =30^2−1^2   = (30+1)(30-1)   = 31 * 29   29 is the smallest factor   ANSW28<x≤35R:28<x≤35
Answer: E
In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 10 per square m? Select
A) s.9500  B) s.50000  C) s.57000  D) s.60000  E) s.62000

Solution: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m   Total area of the hall to be covered with mat = 2(lb + bh + hl)   = 2(20 * 15 + 15 * 5 + 5 * 20)   =2(300 + 75 + 100)   = 2 * 475= 
2 * 475 = 950
950 sq. m   Total expenditure= 10 * 950   = Rs.9500   s.9500
Answer: A
The total marks obtained by a student in Mathematics and Physics is 20 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
Pick one:	A) 40	B) 26	C) 20	D) 28	E) 22

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + 20= 
+ 20 = 20
20 and 20 - P= 20 M + 20 / 2 = [(M + P) + (20 - P)] / 2 = (20 + 20) / 2= 
(20 + 20) / 2 = 20
20.Answer:20
Answer: C
If f(x) = k(x - k) and k is a constant, what is the value of f(4) - f(2), in terms of k?	Choose the correct choice from the following answers
A) 1
B) k
C) 2k
D) k^2 + k
E) k^2 - k

Solution: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(4) and f(2):   f(4) = k(4) - k^2 = 4k - k^2   f(2) = 2k - k^2   f(4)-f(2)=2k.. Answer 2k (4)- (2)= 
 (4)- (2) = 2
2k.. Answer 2k
Answer: C
What is the area of a triangle with the following vertices L(1, 2), M(5, 1), and N(3, 5) ?
Pick one:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: There is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem.   Though if you make a diagram minimum simple calculations will be needed:   Answer: 7.
Answer: E
Different breeds of dogs get older at different rates in “dog years.” Livonian wolfhounds age 7 times as fast as humans, whereas Khazarian terriers age 5 times as fast and Akkadian retrievers age 4 times as fast. If Dan bought a newborn Akkadian on January 1, 2008, a newborn Khazarian 1 year later, and a newborn Livonian 1 year after that, in what year will the sum of the dog-year ages of the Akkadian and the Khazarian first be exceeded by twice the age of the Livonian in dog years, rounding all ages down to the nearest integer?  Choose the correct choice: A) 2015 B) 2014 C) 2013 D) 2016 E) 2017

Solution: chart starting at 2010:   A+K=13   L=0.   Then I added 9 to a+k for each year and 14 to L for each year.   2011:AK=22 L=14   2012:AK=31 L=28   2013:AK=40 L=42   thus, 2013 is the correct answer. => 2013
Answer: C
A sum of Rs. 3000 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest?  Choose the correct choice from the following options.
A) 75%
B) 90%
C) 55%
D) 60%
E) 50%

Solution: S.I. = (9000 - 3000) = Rs. 6000   Rate = (100 * 6000) / (3000* 4)= 
(100 * 6000) / (3000* 4) = 50
50%   Answer: 50%
Answer: E
Train A and Train B began traveling towards each other from opposite ends of a 420-mile long track at 1:00 PM. If Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?	Choose the correct choice from the following answers:	A) 5:40 PM	B) 6:00 PM	C) 7:20 PM	D) 8:00 PM	E) 9:20 PM

Solution: This question tests your concepts of relative speed:   If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)   If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)   Here the trains are moving towards each other, hence in opposite direction.   Trains will cover the 500 mile track in a time of 500/(25 + 35) =420/60= 
420/60 = 7
7 hours   Trains started at 1:00 PM, there they will meet at 8:00 PM   Option 8:00 PM
Answer: D
A constructor estimates that 8 people can paint Mr khans house in 3 days. If he uses 4 people instead of 8,how long will they take to complete the job? Choose the correct choice from the following options
A) 6	B) 8	C) 3	D) 4	E) 0

Solution: Explanation:   Use formula For a work Members Ã— days = constant   8 Ã— 3 = 4 Ã— a   a = 6   so answer is 6 days   6nswer: 6
Answer: A
There are two cars. One is 100 miles north of the other. Simultaneously, the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 15 miles per hour. How many miles apart are the cars after 3 hours? Choose the correct option:
A) 125 B) 150 C) 200 D) 225 E) 250

Solution: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:   The right triangle will have a base of 75 and a height of 100. The hidden pattern here is a 3/4/5 right triangle (the 75 lines up with the '3' and the 100 lines up with the '4'). In this way, you can deduce that each side is '25 times' bigger than it's corresponding side:   3/4/5 becomes   75/100/125   Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...   Final 125nswer: 125
Answer: A
The first photo shoot takes 3 minutes long and then the following shoots are taken at a rate of 22 seconds/shoot as the model is already at the scene. What is the maximum number of photo shoots taken in 10 minutes ?	Choose the correct choice
A) 13 B) 14 C) 15 D) 16 E) 20

Solution: a must be an integer as it is the number shoots at a rate of 22sec/shoot   3*60 + 22a = 10*60   22a = 420   a = 19   The total number of shoots -->1 +19 = 20 and   21th shoot will be taken at 620 seconds which is above 10 minutes   ANSW20R: 20-- 1 +19= 
-- 1 +19 = 20
20 and   21th shoot will be taken at 620 seconds which is above 10 minutes   ANSW20R: 20
Answer: E
A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 25%. Staff are allowed a further 20% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?	Choose the correct choice:
A) 0.6D	B) 0.7D	C) 0.5D	D) 0.8D	E) 0.9D

Solution: Effective discount = a + b + ab/100 = - 25 - 20 + (-25)(-20)/100 =-40   Sale price = D * ( 1 - 40/100)   Sale price = .6 * D   0.6Dnswer (0.6D)
Answer: A
What is the twenty-fourth decimal to the right in the fraction 35/36?
Choose the correct choice.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 35/36= 0.97222222222...   The answer is 2.
Answer: B
If a coin is tossed three times, what is the probability that on the first toss the coin lands on heads and then lands on tails the next two tosses?
Choose the correct choice from the following answers.
A) 1/8	B) 1/3	C) 1/4	D) 1/2	E) 1

Solution: P(HTT) = 1/2*1/2*1/2=1/8   The answer is 1/8.
Answer: A
The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is 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 two-thirds of the males and one-third of the females in the class? Options:	A) 160	B) 168	C) 191	D) 192	E) 204

Solution: 2/3*2/5 + 1/3*3/5 = 4/15 + 3/15 = 7/15   The number of degrees is  7/15 * 360= 
 7/15 * 360 = 168
168 degrees   The answer is 168.
Answer: B
A train is 360 meter long is running at a speed of 36 km/hour. In what time will it pass a bridge of 140 meter length?
Answers:  A) 50 seconds  B) 46 seconds  C) 40 seconds  D) 97 seconds  E) 26 seconds

Solution: Speed = 36 Km/hr = 36*(5/18) m/sec = 10 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (1/10)= 
500 * (1/10) = 50
50 seconds   50 secondsnswer:50 seconds
Answer: A
In a kilometer race, A beats B by 54 meters or 12 seconds. What time does A take to complete the race?
Answers:
A) 212
B) 190
C) 277
D) 181
E) 122

Solution: Time taken by B run 1000 meters = (1000 * 12)/54 = 222 sec.   Time taken by 212 = 224 - 12= 
224 - 12 = 212
212 sec.212nswer:212
Answer: A
The events A and B are independent. The probability that event A occurs is r and the probability that event B occurs is s. Which of the following is equal to the probability that exactly one of the events A and B occurs? Choose the correct answer:	A) r − 2rs	B) s − rs	C) r + s− 2rs	D) r + s −rs	E) r + s

Solution: Probability of A occuring = p , Probability of A NOT occuring = 1-r   Probability of B occuring = s , Probability of B not occurring = 1-s   Probability of atleast of one of A and B occuring = 1-(1-r)(1-s) =r+s -rs   r + s −rs
Answer: D
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?	Select the correct option
A) 333 m	B) 277 m	C) 245 m	D) 279 m	E) 176 m

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30 = 25/2   x = 245 m.   Answer:245 m
Answer: C
7 dogs have got 7 puppies each. Each puppy has got 7 kitten as friend. They are all members of a club along with me. What is the strength of club ?
Choose the correct option
A) 300  B) 400  C) 500  D) 600  E) 700

Solution: total strength = (7+7*7+7*7*7)+1= 
(7+7*7+7*7*7)+1 = 400
400   ANSWER:400
Answer: B
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Choose the correct answer:
A) 10.18 p.m  B) 10.29 p.m  C) 11.30 p.m  D) 10.38 p.m  E) 10.32 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     4.30 + 7= 
  4.30 + 7 = 11.3
11.30 p.m.   Answer:11.30 p.m
Answer: C
The ratio of the ages of Malini and Radha is 2 : 4. The total of their ages is 2.4 decades. The proportion of their ages after 0.8 decades will be
[1 Decade = 10 years] Options.
A) 6:5  B) 3:4  C) 4:5  D) 2:3  E) 3:6

Solution: Let, Malini’s age = 2A and Radha’s age = 4A   Then 2A + 4A = 24   A = 4   Malini’s age = 8 years   and Radha’s age = 16 years   Proportion of their ages after 8 is = (8 + 8) : (16 + 8)   = 16 : 24   = 2 : 3   Answer : 2:3
Answer: D
A group of people were given 2 puzzles. 72% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?  Choose the correct choice from the following options: A) 11%, 0% B) 49%, 33% C) 68%, 57% D) 79%, 68% E) 27%, 67%

Solution: To solve this question, we don't need any formulas. Just read the question carefully. If 72% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 72%. From the given options, only D looks good   Answer 27%, 67%
Answer: E
A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 6 students hold membership in both organizations, how many different committee are possible?	Choose the correct choice from the following options:
A) 165	B) 194	C) 212	D) 236	E) 300

Solution: student government + the student advisory board consists of  9 + 8= 
 9 + 8 = 17
17 members.   6 students hold membership in both, so they were counted twice.   The total number of people to choose from is 17 - 6= 
17 - 6 = 11
11   The number of ways to choose 8 members from 11 is 11C8= 165   The answer is 165.
Answer: A
The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 2 per metre approximately Choose the correct choice from the following answers
A) 2972	B) 4567	C) 4235	D) 4547	E) 4675

Solution: Explanation:   Area = (17.56 x 10000) m2= 175600 m2.   ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.   Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.   Cost of fencing = Rs. (1485.78 x 2) = Rs. 2972.   2972nswer: Option 2972
Answer: A
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 242 runs?	Pick
A) 6.25	B) 5.25	C) 6.29	D) 6.39	E) 6.13

Solution: Required run rate   = [242 - (3.2 * 10)]/40   = 210/40= 
210/40 = 21/4 = around 5.25
5.25   Answer: 5.25
Answer: B