MU-NLPC/Calc-aqua_rat huggingface dataset:
A box contain Red, Blue and Green colored balls. The number of Red balls is 80 and the number of Blue balls is 60.
The number of Green balls subtracted from the number of Red balls is the same as the number of Green balls added with the number of Blue balls. Then the number of Green balls is?	Choices:	A) 80	B) 70	C) 60	D) 85	E) 140

Solution: Answer   Let the number of Green balls be x.   Then, x - 60= 80 - x   â‡’ 2x = 80+ 60= 
80+ 60 = 140
140   â‡’ 2x= 140   âˆ´ x = 70   Correct Option: 70
Answer: B
On the x y plane, there are 8 points of which 4 are collinear. How many straight lines can be formed by joining any 2 points from the 8 points ?	Options:  A) 28  B) 22  C) 20  D) 23  E) 56

Solution: Each line is defined by two points.   4 points are collinear => 1 line passes through those.   Now each of those points form 5 line => 4 lines with the "out" points and 1 line is the common one   but this is counted (the common) so we just add 4(point)*4(lines)=16 to the sum.   Finally the 4 points "out" of the common line form 4C2 = 6 different lines    1+16+6= 
 1+16+6 = 23
23 totals	ANS:23
Answer: D
three men invested sum. and their ratio is 5:7:6. profit is 9000.then b's share Pick
A) 2000	B) 2100	C) 2200	D) 2300	E) 3500

Solution: b's share =7/18*9000= 
7/18*9000 = 3_500
3500   ANSW3500R:3500
Answer: E
The average runs of ten batsmen is 25. If three players whose marks are 3,8 and 4 are removed , then find the approximate average runs of the remaining players. Choose the correct choice
A) 28  B) 34  C) 55  D) 29  E) 52

Solution: Exp. Total runs of 10 players = 25*10= 
25*10 = 250
250,   Total runs after the removal of 3 players= 250 –(3 + 8 + 4)   = 250 – 15 = 235   Approximate average runs = 235/(10-3) = 235/ 7 = 34   Answer: 34
Answer: B
Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?	Choose the correct choice from the following choices:
A) 338
B) 237
C) 197
D) 285
E) 171

Solution: Explanation:   Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5   SP = CP[(100 + profit%)/100]   = 237.5 * [(100 + 20)/100] = Rs. 285.   Answer: 285
Answer: D
James and David work at a grocery shop with 6 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen?  Pick one:
A) 1/20
B) 1/22
C) 1/23
D) 1/25
E) 1/15

Solution: Probability that James and David will both be chosen out of 6 workers   = (2/6)*(1/5)   = 1/15   Answer 1/15
Answer: E
A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.	Choose the correct choice from the following:
A) 240  B) 88  C) 77  D) 266  E) 121

Solution: (3*8 + 2*4):(4*8 + 5*4)   8:13   8/21 * 630= 
8/21 * 630 = 240
240.   240nswer: 240
Answer: A
You collect pens. Suppose you start out with 7. Mike gives you another 22 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 19 pens. How many pens do you have at the end?	Select the correct option:
A) 39  B) 40  C) 41  D) 42  E) 43

Solution: Solution   Start with 7 pens.   Mike gives you 22 pens:  7 + 22= 
 7 + 22 = 29
29 pens.   Cindy doubles the number of pens you have: 29 × 2= 58 pens.   Sharon takes 19 pens from you:  58 - 19= 
 58 - 19 = 39
39 pens.   So you have 39 at the end.   Correct answer: 39
Answer: A
A drum contains 4 red balls, 3 blue balls and 2 white balls. Three balls are removed (no replacement) what is the probability that there will be one of each?	Answers
A) 22 B) 21 C) 24 D) 25 E) 28

Solution: 4*3*2 / 9*8*7.   There is a 4/9 chance of taking a red ball first; if you do, ther'es a 3/8 chance of taking a blue ball next, and if you get that far, there's a 2/7 chance of getting a white ball third.   Or you might get white first, blue second and red third: 2/9, followed by 3/8 and then 4/7. No matter what order it might occur, the multiplication will always be (4*3*2)/(9*8*7).   Since 4*2= 
4*2 = 8
8 and 3 is a factor of 9, you can cancel out the entire top row to leave 1 / (3*1*7) ie. 1 chance in 21.   answer 21
Answer: B
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck. Choose one:
A) $204
B) $231
C) $156
D) $145
E) $200

Solution: Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 145.   So after completing the 1st week she will get $ (x+145).   Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.   = $ (x + 145 + 145)   = $ (x + 290)   So in this way end of every week her salary will increase by $ 145.
Answer: D
Sivagami is 2 years elder than Meena. After 6 years the total of their ages will be 7 times of their current age. Then age of Sivagami is :  Choose the correct choice from the following
A) 19 years	B) 17 years	C) 15 years	D) data inadequate	E) 16 years

Solution: Explanation:   Let Meena’s age = A.   Then Sivagami’s age = A + 2   After 6 years the total of their ages will be 7 times of what?   Not clear.   So the given data are inadequate. Answer: data inadequate
Answer: D
The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the sum and the number if the ratio between the digits of the number is 1:2 ? Choose the correct choice from the following answers:
A) 6	B) 8	C) 10	D) 14	E) 15

Solution: Let the number be xy.   Given xy – yx = 36.   This means the number is greater is than the number got on reversing the digits.   This shows that the ten’s digit x > unit digit y.   Also given ratio between digits is 1 : 2 => x = 2y   (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.   Hence, (x + y) – (x – y) = 3y – y = 2y = 8   8
Answer: B
The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 25%?	Choose the correct choice from the following choices:  A) 37.5%  B) 37.6%  C) 38.5%  D) 17.1%  E) 37.2%

Solution: Let marked price = Rs. 100.   Then, C.P. = RS. 64, S.P. = Rs. 75   Gain % = 11/64 * 100 = 17.1%.   Answer: 17.1%
Answer: D
In a bucket there are 3 green balls and 2 yellow balls. What is the probability of drawing at least one green ball when drawing two consecutive balls randomly?	Choose the correct choice from the following answers:
A) 16/20
B) 9/10
C) 2/5
D) 3/5
E) ½

Solution: P(at least one green) = 1 - P(no green, so 2 yellow) = 1- 2/5*1/4 = 9/10.   Answer: 9/10.
Answer: B
The points A(0, 0), B(0, 4a - 5) and C(2a + 3, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
Options:
A) 114
B) 116
C) 118
D) 119
E) 120

Solution: 1/2bh=1/2(2a+3)(2a+6)   Now 4a-5=2a+6   2a=11   Therefore,   A(0,0); B(0,17); C(14,17)   1/2*14*17= 
1/2*14*17 = 119
119   Answer: 119
Answer: D
A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 108 runs, thereby increasing his average by 6 runs. His new average is?  Choices:
A) 11 runs
B) 27 runs
C) 48 runs
D) 28 runs
E) 29 runs

Solution: Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 6 => 11x + 66 = 10x + 108 => x = 42.   New average = (x + 6) = 48 runs.   Answer: 48 runs
Answer: C
The average of five numbers id 27. If one number is excluded,the average becomes 25. The excluded number is  Options
A) 25  B) 27  C) 30  D) 35  E) 34

Solution: given x/5=27 so x=135 and y/4=25 so y=100. excluded no is x-y=135-100= 
135-100 = 35
35.   ANSWER:35
Answer: D
Two men Amar and Bhavan have the ratio of their monthly incomes as 6:5. The ratio of their monthly expenditures is 3:2. If Bhavan saves one-fourth of his income, find the ratio of their monthly savings?
Choose the correct answer:
A) 3:19
B) 3:10
C) 3:16
D) 3:11
E) 3:12

Solution: Let the monthly incomes of Amar and Bhavan be 6x and 5x respectively.   Let the monthly expenditures of Amar and Bhavan be 3y and 2y respectively.   Savings of 3:10havan every month = 1/4 (5x)   =(his income) - (his expenditure) = 5x - 2y   => 5x = 20x - 8y => y = 15x/8   Ratio of savings of Amar and 3:10havan   = 6x - 3y : 1/4 (5x) = 6x - 3(15x/8) : 5x/4   = 3x/8 : 5x/4 => 3:10   Answer: 3:10
Answer: B
Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?	Choose the most appropriate option:	A) (1/3)	B) (1/8)	C) (2/8)	D) (1/16)	E) None

Solution: Explanation: This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result.   4/2= 
4/2 = 2
2   2/2= 
2/2 = 1
1   1/2= 1/2   (1/2)/2 = 1/4   (1/4)/2 = 1/8 and so on.   Answer: Option (1/8)
Answer: B
If x/(11p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?  Options
A) 22 B) 33 C) 44 D) 66 E) 99

Solution: x/(11p) = odd prime number   x = odd prime number * 11p   Least value of x = Lowest odd prime number * 11 * Lowest value of p   = 3 * 11* 2= 
3 * 11* 2 = 66
66   Answer 66
Answer: D
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to: Select the correct option.
A) 2.2
B) 8.2
C) 2.9
D) 2.1
E) 2.6

Solution: xz = y2 10(0.48z) = 10(2 x 0.70) = 101.40   0.48z = 1.40   z =	140	=	35	= 2.9 (approx.)   48	12   Answer: 2.9
Answer: C
The sum of two numbers is 65. Their difference is 5. The bigger number is  Choose the correct answer:  A) 20  B) 25  C) 30  D) 35  E) 45

Solution: X + Y = 65   X - Y = 5   Adding 2X = 70 ==> X = 35 and Y = 65 - 35= 
65 - 35 = 30
30   Bigger number is X= 35   Answer 35.
Answer: D
40 is subtracted from 60% of a number, the result is 50. Find the number?	Choose the correct choice
A) 150
B) 189
C) 177
D) 167
E) 190

Solution: (60/100) * X – 40 = 50   6X = 900   X = 150   150nswer: 150
Answer: A
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
Options:
A) 3/41
B) 2/41
C) 9/42
D) 3/37
E) 4/49

Solution: The probability that first toy shows the even number,   =1021=1021   Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.   Hence, probability that second toy shows the even number,   =920=920   Required probability,   =(1021)×(920)=(1021)×(920)   =9/42   9/42
Answer: C
A 600 m long train crosses a tree in 60sec, how much time will It take to pass a platform 450 m long?  Choose the correct choice from the following.
A) 288 B) 190 C) 188 D) 188 E) 105

Solution: L = S*T   S= 600/60= 
600/60 = 10
10 m/Sec.   Total length (D)= 1050 m   T = D/S   T = 1050/10= 
1050/10 = 105
105 Sec   Answer:105
Answer: E
√4 percent of 4√4 = Choices.
A) 0.16  B) 0.17  C) 0.18  D) 0.2  E) 0.19

Solution: √4 = 2   So, √4 percent of 4√4 = 2 percent of (4)(2)   = (2/100)(8)   = 16/100= 
16/100 = 4/25 = around 0.16
0.16   0.16nswer:   0.16
Answer: A
Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 11 even numbers. His mother immediately worked out the answer. How much had he scored in Math? Pick one
A) 80
B) 190
C) 132
D) 170
E) 60

Solution: 132   132   Sum = (n x n) + n   Hence,11 x 11 = 121 + 11= 
121 + 11 = 132
132
Answer: C
The length of a rectangle is 2 times its width. If the width of the rectangle is 5 inches, what is the rectangle's area, in square inches?  Pick one
A) 50 square inches B) 75 square inches C) 68 square inches D) 89 square inches E) 92 square inches

Solution: If the width is 5 in and the length is 2 times the width, then the length is    2 * 5= 
 2 * 5 = 10
10 in   The area is given by     5 * 10= 
  5 * 10 = 50
50 square inches   correct answer 50 square inches
Answer: A
Nicky and Cristina are running a 500 meter race. Since Cristina is faster than Nicky, she gives him a 12 second head start. If Cristina runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him? Options.
A) 50  B) 45  C) 40  D) 35  E) 30

Solution: The distance traveled by both of them is the same at the time of overtaking.   3(t+12) = 5t   t=18.   Cristina will catch up Nicky in 18 seconds.   So in 18 seconds Cristina would cover = 18*5= 
18*5 = 90
90 meter.   Now Time taken my Nicky to cover 90 meter= 90/3= 
90/3 = 30
30 Seconds.   30
Answer: E
The average weight of 8 persons increases by 2.5 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 one.
A) 70 kg	B) 75 kg	C) 80 kg	D) 85 kg	E) 95 kg

Solution: Explanation:   Total weight increased = (8 x 2.5) kg = 20 kg.   Weight of new person = (65 + 20)= 
(65 + 20) = 85
85 kg. Answer: 85 kg
Answer: D
If (a – b) is 11 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
Select the correct option:
A) 6	B) 2	C) 3	D) 4	E) 5

Solution: (a – b) – (c + d) = 11 and (c – d) – (a + b) = 3   => (a – c) – (b + d) = 11 and (c – a) – (b + d) = 3   => (b + d) = (a – c) – 11 and (b + d) = (c – a) – 3   => (a – c) – 11 = (c – a) – 3 => 2(a – c) = 8 => (a – c) = 4   ANSWER:4
Answer: D
If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a40 is equal to ?	Choose the most appropriate option:  A) a. 5*2^99-6  B) b. 5*2^99+6  C) c. 6*2^99+5  D) d. 6*2^39- 5  E) e. 6*2^99-6

Solution: Here is my solution:   an+1=2an+5............(1)   lets ADD 5 to both sides....   so (an+1) + 5= 2 (an+5)....................taking 2 as common factor   now a1=1. so for n=1, an+5=6.......   putting n=1. we get both sides as,   a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)   a2= 2 *6 - 5   a2= 2 * 2 *3 - 5   a2= 2^2 *3 - 5................. so with same progression   a40= 2^40 * 3 - 5   a40=2 * 2^39 * 3 - 5   a40= 6 * 2^39 - 5   d. 6*2^39- 5
Answer: D
The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is:	Choose the correct choice from the following:
A) 36.5 B) 21.4 C) 19.5 D) 18.2 E) 17.9

Solution: Explanation:   Correct sum = (36 * 50 + 48 - 23)= 
(36 * 50 + 48 - 23) = 1_825
1825.   Correct mean= 1825/50= 
1825/50 = 73/2 = around 36.5
36.5   Option 36.5
Answer: A
he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4. What is the capacity of the tank?	Choose the correct choice from the following answers:	A) 360 liters	B) 256	C) 48	D) 525	E) 425

Solution: 4x=3(x+4),where x may be number of times 4l bucket is used.   4x=3(x+4)-->1.   x=12,   substitute x to lhs or rhs of 1,which   gets you the capacity,and it is 48.   ANSWER:48
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? Answers
A) 5:15  B) 5:19  C) 5:13  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
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
Choose the most appropriate option:
A) 1
B) 3
C) 5
D) 2
E) 0

Solution: Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.   Thus, when 2n is divided by 4, the remainder is 2.   ANSWER 2
Answer: D
A bicyclist's wheel has a circumference of 8 meters. if the bicyclist covers 160 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?	Choose the correct option.
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.   To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt. =160/8*5 =4   Answer (4)
Answer: C
What is the tens digit of 36^30?	Choices.
A) 1
B) 7
C) 5
D) 3
E) 9

Solution: 36^10 = 6^20   (6^2)=6*6= 
6*6 = 36
36   (6^3)= 36*6 = .16   (6^4)= .16*6 = ..96   (6^5) = ..96*6 = ..76   (6^6) = ..76*6 = ...56   (6^7) = ....56*6 = ....36   If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...   Continue the pattern up to 6^30 ( dont actually calculate full values) and answer is 7: 7
Answer: B
. If A is 35% greater than B then how much percentage is B smaller than A? Choose the correct option
A) 16 2/3% B) 18 2/3% C) 16% D) 17% E) None of these

Solution: Explanation:   16 2/3% = 120   B = 100   16 2/3%-B/16 2/3% * 100 = 20/120 * 100 = 2000/120 % = 200/12 % = 16 2/3%   Smaller than 16 2/3%   16 2/3%nswer: Option 16 2/3%
Answer: A
Which of the following could be the sides of an obtuse angled triangle?
I. 51, 29, 100
II. 10,110, 60
III. 40 ,20 70	Select.
A) I and III only B) II only C) III only D) I and II only E) I, II and III

Solution: obtuse angled triangle means one angle more than 90 deg and total 180 deg.. I and II only   HENCE, (I and II only)
Answer: D
k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?	Choose one
A) Rs. 1640  B) Rs. 2500  C) Rs. 2160  D) Rs. 3000  E) None of these

Solution: Explanation:   => 60x5 : 36x6 : 75x3   => 100 : 72 : 75   => 72/247 x 7410 = Rs. 2160   ANSWER IS Rs. 2160
Answer: C
5 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
Choose one
A) 4  B) 6  C) 16  D) 24  E) 256

Solution: it is like a circular arrangement.   total ways for n people to arrange in a circle is = factorial (n-1)   in this case n= 5   hence ans = 4 factorial = 24   hence 24
Answer: D
The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.430 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
Choose one:
A) 400 B) 465 C) 430 D) 450 E) 510

Solution: Let no. of non- officers be x   15 * 430 + x * 110 = (x + 15) 120   x = 465   465
Answer: B
One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,80,000 as total savings, how much has he saved in Public Provident Fund ?  Answers.
A) 80000
B) 60000
C) 50000
D) 72000
E) 90000

Solution: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (180000 - x) respectively. Then,   =1/3 x = 1/2 (180000 - x)   =x/3 + x/2 = 90000   =5x/6 = 90000   =x = 90000 x 6 /5	= 108000   Savings in Public Provident Fund = Rs. (180000 - 108000) = Rs. 72000   Answer is 72000.
Answer: D
A rectangular field is to be fenced on three sides leaving a side of 40 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?  Select the correct option:
A) 44ft  B) 88ft  C) 74ft  D) 11ft  E) 66ft

Solution: Given that length and area, so we can find the breadth.   Length x Breadth = Area   40 x Breadth = 680   Breadth = 17 feet   Area to be fenced = 2B + L = 2 (17) + 40 = 74 feet   Answer: 74ft) 74ft
Answer: C
In Township K each property is taxed at 10 percent of its assessed value. If the assessed value of a property in Township K is increased from $20,000 to $28,000, by how much will the property tax increase?  Choose the correct answer:  A) $800  B) $1000  C) $600  D) $400  E) $500

Solution: Increase in house value = $28,000 - $20,000 =$8000   So, tax increase = 10% of$8000=$800   $800nswer: $800
Answer: A
a natural numbr has exactly 10 divisors including 1 and itself.how many distint prime factors this natural numbr will have? Choices:	A) 1 or2	B) 1 or3	C) 1 or 2or 3	D) 2 or 3	E) 2 or 5

Solution: Here it is given that the number has exactly 10 divisor including 1 and itself.   So the number may be (any one prime factors)power 9 .....I.e (2)pow 9, (3)pow 9....etc.total 10 factor=(9+1)= 
(9+1) = 10
10.   Also the number may be as (any one prime factors)pow 1*(any one prime factors)pow 4........I.e...(2)pow 1*(3)pow 4...etc= total 10 factor ((1+1)*(4+1))= 
 ((1+1)*(4+1)) = 10
10.   Hence either 1 or 2 is correct   1 or2NSWER:1 or2
Answer: A
If c is a positive integer, which of the following could NOT be the square of c?  Choose the correct option.
A) 5,008,644 B) 5,004,169 C) 4,999,696 D) 4,995,225 E) 4,990,752

Solution: A number ending with 2 can never be a perfect square.   Units digit of a perfect square must be:   1,4,9,6,5   Answer 4,990,752)
Answer: E
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 6720 votes were polled, then how many valid votes did B get? Options.
A) 1888  B) 2999  C) 2834  D) 2777  E) 2184

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 6720   32.5k = 32.5k/100k * 6720 = 2184   The number of valid votes polled in favour of B is 2184.   Answer: 218432.5 /100  * 6720= 
32.5 /100  * 6720 = 2_184
2184   The number of valid votes polled in favour of B is 2184.   Answer: 2184
Answer: E
Of 70 players on a football team, 40 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?
Choose the correct choice from the following choices.
A) 60 B) 59 C) 63 D) 71 E) 92

Solution: Total = 70   Thrower = 40   Rest = 70 - 40= 
70 - 40 = 30
30   Left Handed= 30/3= 
30/3 = 10
10   Right handed= 20   If all Thrower are right handed then total right handed is   40 + 20= 
  40 + 20 = 60
60   so A. 60 is the right answer
Answer: A
It takes Joey the postman 1 hours to run a 1 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?  Choose the correct choice from the following answers:
A) 1.67
B) 12
C) 13
D) 14
E) 15

Solution: let his speed for one half of the journey be 3 miles an hour   let the other half be x miles an hour   now,   avg speed =5 mile an hour   2*1*x/1+x=5   2x=5x+5=>3x=5=5/3=1.67   1.67
Answer: A
what is the angle between the hands of a clock when time is 10:30?	Choose the most appropriate option
A) 65deg	B) 75deg	C) 45deg	D) 15deg	E) 135deg

Solution: Angle between two hands =   30h - 11/2 m = 30*10 - 30*11/2 = 300 - 165= 
300 - 165 = 135
135deg   ANSW135degR:135deg
Answer: E
A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man?  Choose the correct choice
A) 87 B) 29 C) 40 D) 77 E) 101

Solution: Explanation:   The average speed ‘v’, when a man travels two same distance with different speeds ‘v1’ and ‘v2’ is:   v = (2*v1*v2) / (v1 + v2)   In the above problem, v1 = 30 and v2 = 60   Therefore, v = (2*30*60)/(30 + 60) = 3600/90= 
3600/90 = 40
40   ANSWER:40
Answer: C
Find the remainder of the division (3^14)/4.	Select.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: Find the pattern of the remainders after each power:   (3^1)/4 remainder 3   (3^2)/4 remainder 1 -->this is where the cycle ends   (3^3)/4 remainder 3 -->this is where the cycle begins again   (3^4)/4 remainder 1   Continuing the pattern to (3^14)/4 gives us a remainder of 1   Final 1nswer:   1) 1
Answer: A