MU-NLPC/Calc-aqua_rat huggingface dataset:
Jane and Thomas are among the 8 people from which a committee of 3 people is to be selected. How many different possible committees of 3 people can be selected from these 8 people if at least one of either Jane or Thomas is to be selected?  Options: A) 24 B) 28 C) 32 D) 36 E) 40

Solution: The total number of ways to choose 3 people from 8 is 8C3 = 56.   The number of committees without Jane or Thomas is 6C3 = 20.   There are  56-20= 
 56-20 = 36
36 possible committees which include Jane and/or Thomas.   The answer is 36.
Answer: D
An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 8. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?  Choose the correct option:
A) s 1200  B) s 1500  C) s 1600  D) s 1900  E) s 1700

Solution: Explanation :   Let P = Faruk, Q = Vasim, R = Ranjith   Let P = 3x, Q = 5x and R = 8x.   Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2400.   Hence, (R - p) = (2400 - 900)= 
(2400 - 900) = 1_500
1500   Answer : s 1500
Answer: B
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere?
Choose the correct choice.
A) 6/π  B) 9/π  C) 6  D) 9  E) 12

Solution: Given Area of the base of a hemisphere is 3 = PI * R^2   Thus R = Sqrt ( 3 / PI ) .   Surface area of whole sphere = 4*PI*R^2 .   = 4 * PI * 3 / PI   = 12 .   Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2= 
12 / 2 = 6
6 ( curved part , not including the flat rounded base ) .   But the total surface area= 6 + Area of the base of a hemisphere .   = 6 + 3= 
6 + 3 = 9
9.   Answer is 9 !!
Answer: D
A group of 4 investment bankers and 5 clients recently frequented the Bonbon Ribs Restaurant. The total bill for the meal, including 20% gratuity, came to $756. On average, how much did the meal of each individual cost before gratuity?	Choose the correct option
A) $160
B) $70
C) $90
D) $80
E) $55

Solution: 4 IBs and 5 clients - so total 9 people   The bill $756 includes 20% gratuity... so the actual cost of dinner was $630   Now, the cost per person will be $630/9 which is $70   Option $70
Answer: B
Two water pumps, working simultaneously at their respective constant rates, took exactly six hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate? Choices
A) 8  B) 10  C) 12  D) 14  E) 16

Solution: Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.   Both pumps together can fill 1/6 of the pool each hour.   2.5x = 1/6   x = 1/15   1.5x = 1.5/15 = 1/10   The faster pump could fill the pool in 10 hours.   The answer is 10.
Answer: B
A boat having a length 4 m and breadth 3 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: Choose the correct choice from the following choices:
A) 12 kg B) 120 kg C) 72 kg D) 96 kg E) None of these

Solution: Explanation:   Volume of water displaced = (4 x 3 x 0.01) m3   = 0.12 m3.   ∴ Mass of man = Volume of Water displaced x Density of water   = (0.12 x 1000)kg   = 120 kg.   Answer: 120 kg
Answer: B
A sum of money lent out at S.I. amounts to Rs. 850 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?  Choose the correct choice from the following choices
A) s.440
B) s. 500
C) s. 540
D) s. 782
E) s. 840

Solution: S.I for 5 years = (1020 - 850) = Rs. 170.   S.I. for 2 years = 170/5 * 2 = Rs. 68.   Principal = (850 - 68) = Rs. 782.   ANSWER:s. 782
Answer: D
When Robert discontinued his retainer-ship contract with a Pvt Company, management held his fees Rs. 15000/- for one month. Earlier Robert had taken an advance fees of 7280/- from company. But Robert forget that. After one month Robert asked his fees and accountant gives Rs.18500/- to him. What is the incentive amount given to Robert?	Choose the correct choice from the following answers.
A) A)9500  B) B)12500  C) C)10780  D) D)10500  E) E)8600

Solution: Total fees = Rs.15000/-   Advance Money = 7280/-   Balance Salary = 15000-7280= 
15000-7280 = 7_720
7720   Paid amount= 18500/-   Incentive amount = 18500-7720= 
18500-7720 = 10_780
10780/-   Answer is 10780
Answer: C
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Choices.
A) 2	B) 4	C) 5	D) 67	E) 8

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer: 4
Answer: B
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 146 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?  Select the correct option.
A) 2  B) 3  C) 4  D) 1  E) 5

Solution: We have to work with multiples of 20 and 25.   First, we must know the limits of this multiples, so:   146/25= 5....so the max is 5   146/20=7...so the max is 7   146-145= 
146-145 = 1
1 ( 6 small box +1 big box)   Answer : 1
Answer: D
Three cards are randomly selected, one at a time (without return), from a standard deck of 52 cards. What is the probability that all three cards are hearts? (Answer in lowest terms).	Choose the correct choice from the following answers:
A) 11/850 B) 1/4 C) 1/16 D) 1/107 E) 20/21

Solution: A standard deck has 52 cards of which 1/4 are hearts, so the probability of getting a heart is P(H) = 1/4 on the first selected card.   Because selection is (without return), the P(H) has changed for following selections. Now, there are 51 cards and number hearts is dependent upon whether first card was a heart, or not... and so on.... Therefore, conditional probability! The probability that event B occurs, given that event A has already occurred is:   Formula = P(A\B) = P(A and B)/P(B).   P(11/850\B) = (13/52)(12/51)(11/50) = 1716/132600 = 11/850   11/850nswer: 11/850
Answer: A
If a/b = 1/2, then the numerical value of which of the following expressions cannot be determined?  Pick one:
A) 2a/b
B) (a + b)/a
C) (a + 1)/(b + 1)
D) (a - 3b)/(a + b)
E) 6a – 3b

Solution: a/b = 1/2   => b = 2a   A.	2a/b   = 2*(a/b)   (a + 1)/(b + 1)an be determined   B.	(a + b)/a   Dividing numerator and denominator by a ,   1+(b/a)   (a + 1)/(b + 1)an be determined   (a + 1)/(b + 1).	(a + 1)/(b + 1)   = (a + 1)/(2a+1)   Numerical value can't be determined   D.	(a - 3b)/(a + b)   Dividing numerator and denominator by b,   =(a/b - 3 )/ (a/b+ 1 )   (a + 1)/(b + 1)an be determined   E.	6a – 3b   = 6a - 3*2a = 0   Answer (a + 1)/(b + 1)6  - 3*2= 
6  - 3*2 = 0
0   Answer (a + 1)/(b + 1)
Answer: C
The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?
Choose the correct option:
A) 14 years	B) 17 years	C) 19 years	D) 21 years	E) None

Solution: Solution   Sum of the ages of 14 students	= (16 x 35) - (14 x 21)   = 560 - 294.= 
560 - 294. = 266
266.   ∴ Required average= 266 / 14= 
266 / 14 = 19
19 years.   Answer 19 years
Answer: C
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?	Choose the correct choice.
A) 10 lr
B) 9 lr
C) 12 lr
D) 13 lr
E) 15 lr

Solution: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150= 
20/100 * 150 = 30
30 liters.   P liters of water added to the mixture to make water 25% of the new mixture.   Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).   (30 + P)= 25/100 * (150 + P)   120 + 4P = 150 + P => P = 10 liters.   10 lrNSWER 10 lr
Answer: A
If six persons sit in a row, then the probability that three particular persons are always together is ?	Choose the correct choice from the following options: A) 1/6 B) 1/2 C) 1/5 D) 1/2 E) 1/1

Solution: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5   Answer: 1/5
Answer: C
A car that moves at an average speed of 60 kmph, reaches its destination on time. When its average speed becomes 50 kmph, then it reaches its destination 45 minutes late. Find the length of journey.	Choose the most appropriate option
A) 189 km
B) 225 km
C) 255 km
D) 199 km
E) None

Solution: Sol.   Difference between timings = 45 min = 3/4 hr.   Let the length of journey be x km.   Then, x/50 - x/60 = 1/4   â‡” 6x - 5x = 225   â‡” x = 225 km.   Answer 225 km
Answer: B
Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?  Answers:	A) 1/3	B) 1/30	C) 1/10	D) 1/45	E) 1/60

Solution: Pete covered 5*60= 
5*60 = 300
300 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/300=1/60.   Answer: 1/60.
Answer: E
Find the number of square tiles to cover the floor of a room measuring 3.5 m * 12.5 m leaving 0.25 m space around the room. A side of square tile is given to be 60 cms?	Choose the correct choice from the following.
A) 36
B) 100
C) 36
D) 1000
E) 212

Solution: 3 *12 = 6/10* 6/10 * x => x =100   Answer: 100
Answer: B
A boat can travel 1.8 times the distance down the stream than up the stream in the same time. If the speed of the current is 3 KMPH, Find the speed of the boat in still water	Select:
A) 5
B) 10.5
C) 15
D) 20
E) 25

Solution: Simple question, messy language.   Lets say boat's speed is B and current's speed is C.   Upstream speed : B - C   Downstream speed : B + C   Distance will be the same both times. lets say D.   given : time it takes upstream = 1.8 times time it takes downstream   D/(10.5 + C) = 1.8 * [D/(10.5 - C)]   Solving 10.5 = 3.5 C   given : C is 3 KMPH   So 10.5 is 10.5 KMPH   10.5
Answer: B
Average of all prime numbers between 30 to 45 Choose the correct choice from the following options
A) 38  B) 37.8  C) 39  D) 39.8  E) 40

Solution: Explanation:   Prime numbers between 30 and 45 are:   31, 37, 41, 43   38verage of prime numbers between 30 to 45 will be   (31+37+41+43 / 4)=152 / 4= 
152 / 4 = 38
38   Option 38
Answer: A
A and B can together finish a work in 40days. They worked together for 10days and then B left. After another 18 days, A finished the remaining work. In how many days A alone can finish the job? Select the correct option
A) 10
B) 24
C) 60
D) 30
E) 20

Solution: A+24 10days work = 10*1/40 = 1/4   Remaining work = 1-1/4 = 3/4   3/4 work is done by A in 18 days   whole work will be done by A in  18*4/3= 
 18*4/3 = 24
24 days   Answer is 24
Answer: B
There are 20cm, 21cm, 22cm,23cm, 24cm,25cm rods of quantities 2,3,6,4,3,2 respectively. Find average of this data.  Pick
A) 32.25
B) 21.45
C) 45
D) 22.45
E) 22

Solution: Average = ( 20*2+21*3+22*6+23*4+24*3+25*2 )/20= 
( 20*2+21*3+22*6+23*4+24*3+25*2 )/20 = 449/20 = around 22.45
22.45 Answer : 22.45
Answer: D
A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %.
Choose the correct option:
A) 7% B) 4% C) 5% D) 9% E) 8%

Solution: cp=rs27.50, sp=rs 28.50   gain=rs(28.50 –27.50)=rs1.10   so gain%={(1.10/27.50)*100= 
(1.10/27.50)*100 = 4
4%   Ans:4%
Answer: B
The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?  Choose the correct option:
A) 6:8 B) 6:9 C) 6:5 D) 6:2 E) 6:3

Solution: 4:5   3:2   -------   12:15:10   12:10   6:5   Answer:6:5
Answer: C
Ramesh start a bike at 1pm. and rides it at 50kmph. Mahesh started at 2pm with his car at 70kmph. When will Mahesh overtake Ramesh? Answers:	A) 4:30	B) 5:10	C) 3:00	D) 6:10	E) 5:30

Solution: Suppose bike is overtaken by car xhrs after 1pm   Distance covered by the bike in x hrs = distance covered by the car in x-1 hr   50x = 70(x-1)   20x = 70   x = 7/2 hrs   Required time = 1+3.5 = 4:30pm   4:30nswer is 4:30
Answer: A
When the integer k is divided by 7, the remainder is 3. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 7
II. 6k + 1
III. 8k + 5	Answers
A) I only B) II only C) III only D) I and II only E) I, II and III

Solution: k = 7j + 3   4k + 7 = 28j + 12 + 7 = 28j + 14 + 5   6k + 1 = 42j + 18 + 1 = 42j + 14 + 5   8k + 5 = 56j + 24 + 5 = 56j + 28 + 1   The answer is I and II only.
Answer: D
Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $229  Select:
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: Taking the prices of products in ascending order(already arranged)   $50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $229   we see that median value is the 6th value as there in total 11 values given   Arithmetic mean = total/number of entries = 1418/11 =128.9090   We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price   as we can clearly see that there is one value between $120 and $128.90, answer is 1 unit   Correct Answer - 1
Answer: B
A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder?
Choose the correct choice from the following choices.
A) 199
B) 200
C) 28
D) 12
E) 25

Solution: If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required largest number   9997 - 7654= 
9997 - 7654 = 2_343
2343   9997 - 8506= 
9997 - 8506 = 1_491
1491   8506 - 7654= 
8506 - 7654 = 852
852   Hence, the greatest number which divides 7654, 8506 and 9997 and leaves same remainder= HCF of 2343, 1491, 852   = 213   Now we need to find out the common remainder.   Take any of the given numbers from 7654, 8506 and 9997, say 7654   7654 ÷ 213 = 35, remainder = 199   199nswer is 199
Answer: A
The population of a small beach town on Australia's east coast grows by 50% from May 1 to June 1 and then grows by another 50% from June 1 to July 1. The population then decreases by 11.11% from July 1 to August 1. By approximately what percentage has the population grown from May 1 to August 1?
Options.
A) 50%  B) 90%  C) 100%  D) 200%  E) 225%

Solution: Pop Aug1 = Pop May1 * (3/2) * (3/2) * (8/9) = Pop May1 * 2   Population of August is twice the population of May. So it has grown by 100%.   Answer (100%)
Answer: C
If 5a + 7b = m, where a and b are positive integers, what is the largest possible value of m for which exactly one pair of integers (a, b) makes the equation true? Answers.
A) 35	B) 48	C) 69	D) 70	E) 74

Solution: 5*a1 + 7*b1 = m   5*a2 + 7*b2 = m   5*(a1 - a2) = 7*(b2 - b1)   since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.   Lets check how it works for our numbers, starting from the largest:   E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 from a and add 5 to b respectively, so a2 = 5 and b2 = 7, second pair - bad   70)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 toawe will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 froma, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus   70 is the answer
Answer: D
The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then  Options:	A) x = y + z	B) 2x = y + z	C) 3x = 2y - 2z	D) 3x = 9y - 2z	E) 3x = 2y - 1z

Solution: Explanation:   Clearly, we have : x = (3y + 3z ) / 6 or 2x = y + z   Answer: 2x = y + z
Answer: B
n the given series, you can find a set of numbers. Of course, there is a particular pattern that has been followed here with every progressing set.
Find the pattern and complete the series.
(2 + 6), (21 + 6), (58 + 6), (119 + 6), ___ Choose one
A) 215  B) 216  C) 217  D) 218  E) none

Solution: Solution:   (210 + 6)   Explanation:   If you add the numbers, you will find that they add up to be 8, 27, 64 and 125.   8 = 2^3   27 = 3^3   64 = 4^3   125 = 5^3   Thus the next sum should be 6^3 = 216.   Since 6 has been added in each set, the first number will be   (216 - 6)= 
  (216 - 6) = 210
210.   Hence, the missing set will be (210 + 6).   Answer 216
Answer: B
How many different positive integers exist between 10^6 and 10^7, the sum of whose digits is equal to 2? Choose the correct choice from the following answers: A) 6 B) 7 C) 5 D) 8 E) 18

Solution: So, the numbers should be from 1,000,000 to 10,000,000   The following two cases are possible for the sum of the digits to be 2:   1. Two 1's and the rest are 0's:   1,000,001   1,000,010   1,000,100   1,001,000   1,010,000   1,100,000   6 numbers.   2. One 2 and the rest are 0's:   2,000,000   1 number.   Total = 7 numbers.   Answer: 7.
Answer: B
A tailor trims 7 feet from opposite edges of a square piece of cloth, and 5 feet from the other two edges. If 45 square feet of cloth remain, what was the length of a side of the original piece of cloth?	Choose one:
A) 13
B) 15
C) 17
D) 19
E) 21

Solution: Let the original side of the square be x.   (x-14)*(x-10) = 45 = 5*9   x = 19   The answer is 19.
Answer: D
If z is not equal to zero, and z=6zs−9s2−−−−−−−−√z=6zs−9s2, then z equals: Pick one:
A) s	B) 3s	C) 4s	D) -3s	E) -4s

Solution: squaring on both the sides gives Z^2 = 6ZS -9S^2   = Z^2-6ZS+9S^2   = Z(Z-3S) -3S(Z-3S)   = (Z-3S) (Z-3S)   = Z = 3S   Answer = 3s
Answer: B
For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [7]*[4] equivalent to?
Choose the most appropriate option:
A) [28]
B) [84]
C) [42]
D) [48]
E) [14]

Solution: [7]*[4] = 21*2= 
21*2 = 42
42= (1/2)(84) = [84]   The answer is [84].
Answer: B
A 6 litre sol is 25% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
Choose the correct choice from the following choices
A) A.0.6 B) B.1 C) C.2.1 D) D.3 E) E.5.4

Solution: 25% of 6 = 1.5   50% of 6 = 3   shortage is 1.5   so we need to have 1.5/50% to get 50% alcohol content.   = 3 D.3
Answer: D
6 wires are by average 80 cm long each. If the average length of one third of the wires is 70 cm, what is the average of the other wires?
Pick
A) 75.	B) 85.	C) 90.	D) 94.	E) 100.

Solution: Edit:   Given ( X1 + X2 ... + X6 ) / 6 = 80   ( X1 + X2 ... + X6 ) = 480 --> Eq 1.   Now given avg length of one third wires is 70. That means out  6 / 3= 
 6 / 3 = 2
2 wires.   let the avg length of two wires be ( X1 + X2 ) / 2= 70 .   ( X1 + X2 ) = 140. --> eq 2.   Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )   Substitute eq 2 in eq 1 then we get   140 + X3 + X4 + X5 + X6 = 480   => X3 + X4 + X5 + X6 = 340   Now divide 340 by 4 we get 85.   => ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining wires.   IMO correct option is 85..
Answer: B
Three numbers are in the ratio 4 : 5 : 6 and their average is 36 . The largest number is: Choose the correct choice.
A) 28  B) 32  C) 43.2  D) 42  E) 45

Solution: Explanation:   Let the numbers be 4x, 5x and 6x. Therefore,   (4x+5x+6x)/3 = 36   15x = 108   x = 7.2   Largest number = 6x = 43.2.   ANSWER 43.2
Answer: C
If A and B together can finish a work in 16 days.A can finish same work alone in 24 days then B alone can finish same work alone in how many days?  Choose the correct choice from the following answers:
A) 30 days
B) 48 days
C) 40 days
D) 36 days
E) 50 days

Solution: (A+B) work in 1 day = 1/16, A work in 1 day= 1/24   B work in 1 day=[1/16-1/24]=1/48.   B alone can finish same work in 48 days.   Answer 48 days
Answer: B
A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
Options
A) 90 cm
B) 1 dm
C) 1 m
D) 1.1 cm
E) None of these

Solution: Explanation:   Let the thickness of the bottom be x cm.   Then , [(330 - 10) × (260 - 10) × (110 - x)] = 8000 × 1000   => 320 × 250 × (110 - x) = 8000 × 1000   => (110 - x) = 8000×1000/320=   100   => x = 10 cm = 1 dm.   Answer: 1 dm
Answer: B
A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.  Choose the most appropriate option:
A) 20 seconds
B) 27 seconds
C) 30 seconds
D) 40 seconds
E) 50 seconds

Solution: Speed = 45 Km/hr = 45*(5/18) m/sec   = 25/2 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= 40 secondsistance/speed   =500∗2/25=40seconds   answer :40 seconds
Answer: D
In an examination, 40% of total students failed in Hindi, 40% failed in English and 15% in both. The percentage of these who passed in both the subjects is :  Options:
A) 10%  B) 20%  C) 30%  D) 40%  E) 50%

Solution: pass percentage = 100 - (40+45-15) = 100-70= 
100-70 = 30
30   ANSWER:30%
Answer: C
The speed of a car is 60 km in the first hour and 30 km in the second hour. What is the average speed of the car?	Answers.
A) 45 kmph
B) 65 kmph
C) 75 kmph
D) 85 kmph
E) 90 kmph

Solution: Explanation:   S = (60 + 30)/2= 
(60 + 30)/2 = 45
45 kmph   45 kmph)
Answer: A
K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 550?
Answers
A) 10  B) 11  C) 12  D) 13  E) 15

Solution: 550 = 2*222 + (22*4) + 9*2   K weight of 600 = 2 +4+9= 
2 +4+9 = 15
15   Answer 15
Answer: E
For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 96 Θ 33 ) Θ 17 ) - ( 94 Θ (33 Θ 17)) ?
Choices:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: (( 96 Θ 33 ) Θ 17 )   The remainder of 96 divided by 33 is 30;   The remainder of 30 divided by 17 is 13;   ( 97 Θ (33 Θ 17))   The remainder of 33 divided by 17 is 16;   The remainder of 94 divided by 16 is 1.   13 - 2= 
13 - 2 = 11
11.   Answer: 11.
Answer: D
An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 9. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?	Pick one:
A) s 1800
B) s 1500
C) s 1600
D) s 1900
E) s 1700

Solution: Explanation :   Let P = Faruk, Q = Vasim, R = Ranjith   Let P = 3x, Q = 5x and R = 9x.   Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2700.   Hence, (R - p) = (2700 - 900)= 
(2700 - 900) = 1_800
1800   s 1800nswer : s 1800
Answer: A
The length of a rectangular floor is more than its breadth by 200%. If Rs. 100 is required to paint the floor at the rate of Rs. 2 per sq m, then what would be the length of the floor?	Choose the most appropriate option.
A) 12.25
B) 44
C) 18
D) 16
E) 14

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   12.25rea of the floor = 100/2= 
100/2 = 50
50 sq m   l b= 50 i.e., l * l/3 = 150   l2 =150 => l = 12.25   12.25nswer:12.25
Answer: A
Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?	Pick one:	A) 630	B) 1260	C) 2520	D) 3780	E) 5040

Solution: The number of ways to seat 7 people is 7! = 5040.   Child C will sit to the left of Child D in exactly half of these arrangements.   The total number of possible arrangements is 5040/2= 
5040/2 = 2_520
2520   The answer is 2520.
Answer: C