MU-NLPC/Calc-aqua_rat huggingface dataset:
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. yz is even
2. (z-x)(y-x+1) = 4
3. xy is odd  Select:
A) I only	B) I , II only	C) III only	D) I and II only	E) I, II, and III

Solution: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1   Statement 1 yz =y*(y+1) ..if one is odd then other will be even and vice versa ..true   Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2= 
2*2 = 4
4 So, always true   Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.   So, I and II are always true and hence answer is   I , II only
Answer: B
A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 26 per kg, then his gain percent is	Pick one:
A) 12%  B) 39%  C) 14%  D) 15%  E) 16%

Solution: Explanation:   Suppose he bought 5 kg and 3 kg of tea.   Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.   Selling price = Rs. (8 x 26) = Rs. 208.   Profit = 208 - 150= 
208 - 150 = 58
58   So, Profit %= (58/150) * 100 = 39%   Option 39%
Answer: B
The ratio of the volumes of two cubes is 125 : 512. What is the ratio of their total surface areas?	Select the correct option:
A) 81 : 121
B) 25 : 64
C) 729 : 1331
D) 27 : 121
E) None of these

Solution: Ratio of the sides = Â³âˆš125 : Â³âˆš512 = 5 : 8   Ratio of surface areas = 5^2 : 8^2 = 25 : 64   ANSWER: 25 : 64
Answer: B
If â€˜MADURAIâ€™ is coded as â€˜DADCIAIâ€™, then â€˜DELHIâ€™ is coded as  Choose the correct choice from the following answers
A) DEHIE	B) DDEHI	C) EDDIH	D) DECHI	E) CHIDE

Solution: M=13,1+3=4=DECHI   A=1=A   SIMILARLY,   M=13=1+3= 
1+3 = 4
4=DECHI   DECHI=4=DECHI   E=5=E   L=12=1+2=C   H=8=H   I=9=I   SO ANS IS   DECHIECHI   ANSWER:DECHI
Answer: D
Find the circumference and area of radius 7 cm. Pick one:
A) 124 cm²
B) 144 cm²
C) 154 cm²
D) 184 cm²
E) 194 cm²

Solution: Area of circle = πr²   = 22/7 × 7 × 7 cm²   = 154 cm²   ANSWER:154 cm²
Answer: C
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is? Options:
A) 22
B) 88
C) 36
D) 77
E) 81

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer:36
Answer: C
How many integers between 2000 and 3000 that have distinct digits and increase from left to right ?
Choose the correct choice from the following answers
A) 10  B) 20  C) 60  D) 120  E) 600

Solution: Since the numbers must be distinct and increasing from left to right,   The only arrangements we could come-up with are:   245_ --> 4   246_ --> 3   247_ --> 2   248_ --> 1   256_ --> 3   257_ --> 2   258_ --> 1   267_ --> 2   268_ --> 1   Number of integers =20   20
Answer: B
How many positive integers less than 600 can be formed using the numbers 1, 2, 3, 5 and 6 for the digits?	Choose the correct choice from the following options:
A) 48  B) 130  C) 66  D) 68  E) 84

Solution: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:   0 1 1   1 2 2   2 3 3   3 5 5   5 6 6   Number of possibilities = 5*5*5= 
5*5*5 = 125
125.   Then, just add up the number of 1 digits numbers= 5, so total is  125+5= 
 125+5 = 130
130.   Answer: 130
Answer: B
After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.25 cubic inches, what is the original volume of the cubic ice, in cubic inches?
Select the correct option:
A) 2.5 B) 3.0 C) 4.0 D) 6.5 E) 8.0

Solution: Let initial volume of ice be = x   Ice Remaining after 1 hour = x - 0.75x = 0.25x   Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x   (1/16)x = 0.25   x = 4   Alternate solution: Try to backsolve.   Initial volume = 4   After one hour --> (1/4)4 = 1   After two hours --> (1/4)1 = 0.25   Answer: 4.0
Answer: C
The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream? Pick:  A) 80,70 kmph  B) 80,40 kmph  C) 75,35 kmph  D) 80,80 kmph  E) 84,40 kmph

Solution: Speed downstream = 55 + 20= 
55 + 20 = 75
75 kmph   Speed upstream= 55 - 20= 
55 - 20 = 35
35 kmph   Answer: 75,35 kmph
Answer: C
If y ≠ 3 and 2r/y is a prime integer greater than 2, which of the following must be true?
I. r = y
II. y = 1
III. r and y are prime integers.  Select the correct option
A) None B) I only C) II only D) III only E) I and II

Solution: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   So we should try to make the listed statements not true for some r and y (which satisfy y≠3 and 2r/y=prime>2).   I. r = y --> not necessarily true: r=3 and y=2 (2r/y=3=prime>2);   II. y=1 --> not necessarily true: r=3 and y=2 (2r/y=3=prime>2);   III. r and y are prime integers --> not necessarily true: r=10 and y=4 (2r/y=5=prime>2).   Nonenswer: None.
Answer: A
ABCD is a square. E,F,G,H is the midpoint of the sides of square. J and K is the midpoint of the sides HG and FG . L is a point on sides EF such that LF= 1/3 EF. Find the ratio of area of triangle JKL to the area of square ABCD.  Choose the correct option:
A) 5: 46
B) 5: 44
C) 4: 48
D) 5: 48
E) 5: 4

Solution: ratio = 5: 48   ANSWER:5: 48
Answer: D
sowdharya had 90 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 45?
Choose the correct choice from the following choices:	A) 75	B) 72	C) 71	D) 76	E) 73

Solution: Let the number of 45-rupee notes = x   Then, the number of 95-rupee notes = (90 – x)   45x + 95(90 – x) = 5000 : x = 71   ANSWER:71
Answer: C
Find the constant b so that the three points A(2 , 3), B(4 , 7) and C(8 , b) are collinear (i.e. on the same line).  Pick:
A) 5	B) 10	C) 15	D) 20	E) 25

Solution: The slope of the line through A and B must be equal to the slope of the line through B and C.   (7 - 3)/(4- 2) = (b - 7)/(8 - 4)   solve the above for b to find b = 15.   correct answer 15)15
Answer: C
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is?	Choices.
A) 7/19	B) 7/12	C) 7/97	D) 7/29	E) 7/15

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂   = 7/15   Answer: 7/15
Answer: E
The music class consists of 5 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
Select the correct option.
A) 155	B) 158	C) 161	D) 165	E) 210

Solution: Reverse combinatorics approach is preferred method on this one   Note that at least 1 boy gives clue to using this method   All combinations - five girls = answer   All combinations is 12C3 = 220   All girls 5C3 = 10   So our answer is   220-10= 
  220-10 = 210
210   Hence, answer is (210)
Answer: E
If x^6 > x^9 > x^11, which of the following could be the value of x?  Pick
A) -1/5	B) 52	C) 6	D) 3	E) -4.7

Solution: x^6 > x^9 > x^11   1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.   This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.   2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.   With this information, we know that x is a negative number less than -1; therefore, -4.7 (-4.7) is the only option.
Answer: E
A feed store sells two varieties of birdseed: Brand A, which is 60% millet and 40% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?  Choose one
A) 40%
B) 60%
C) 50 %
D) 45 %
E) 55 %

Solution: Yes there is a simple method :   Consider the following method   Brand A : 60% millet and 40% sunflower   Brand B : 65% millet and 35% safflower   Mix : 50% millet   Here the weighted average is 50%,   Now Brand A has 60% millet, which is 10% more than the weighted average of mix = + 0.10 A --------------- I   Similarly, Brand B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II   Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II   implies, 0.10 A = 0.15 B   Therefore A/B = 0.15/0.10 = 3/2   A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5   We have to find, percent of the mix is Brand A i.e. A : (A + 60%) = 3 : 5 = (3 / 5) * 100= 
(3 / 5) * 100 = 60
60 %   Here is a pictorial representation :   60%rand A= 60%------------------------10% or 0.10 above average, A times-----------------Total above = + 0.10 A   ----------------------------------------------------------------------------------------Average = 50% or 0.50   60%rand 60% = 65 %--------------------------15% or 0.15 above average, 60% times-----------------Total above = + 0.15 60%   Since the amount below the average has to equal the average above the average; therefore,   0.10 A = 0.15 60%   A/60% = 3/2   A:60%: Total = 3:2:5   Therefore   A/Total = 3:5 = 60 %   Answer: 60%
Answer: B
In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?
Choose the correct choice from the following:
A) 360
B) 280
C) 320
D) 330
E) 350

Solution: Solution: Let us assume there are 100 students in the institute.   Then, number of boys = 60   And, number of girls = 40   Further, 15% of boys get fee waiver = 9 boys   7.5 % of girls get fee waiver = 3 girls   Total = 12 students who gets fee waiver   But, here given 90 students are getting fee waiver. So we compare   12 = 90   So, 1 = 90/12= 
90/12 = 15/2 = around 7.5
7.5   Now number of students who are not getting fee waiver= 51 boys and 37 girls.   50% concession = 25.5 boys and 18.5 girls (i.e. total 44).   Hence, required students = 44*7.5= 
44*7.5 = 330
330.   Answer: Option 330
Answer: D
The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.	Choose the correct choice.
A) 200	B) 345	C) 255	D) Cannot be determined	E) 342

Solution: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.   4a = 2(l + b)   2a = l + b   l . b = 480   We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .   Area of the square cannot be found.   Answer: Option Cannot be determined
Answer: D
Find the area of trapezium whose parallel sides are 30 cm and 12 cm long, and the distance between them is 16 cm?
Choose the most appropriate option:  A) 288 cm2  B) 277 cm2  C) 285 cm2  D) 336 cm2  E) 340 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (30 + 12) * (16)   = 336 cm2   Answer: 336 cm2
Answer: D
A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested? Choose the correct choice from the following answers:
A) 25
B) 37
C) 36
D) 29
E) 21

Solution: Explanation:   From the information provided we know that,   Principal + 8% p.a. interest on principal for n years = 180 …….. (1)   Principal + 4% p.a. interest on principal for n years = 120 ……… (2)   Subtracting equation (2) from equation (1), we get   4% p.a. interest on principal for n years = Rs.60.   Now, we can substitute this value in equation (2),   i.e Principal + 60 = 120   = Principal = Rs.60.   We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.   In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.   Therefore, 60 =(60*n*4)/100   => n = 100/4= 
100/4 = 25
25 years.   25nswer: 25) 25years
Answer: A
The first term of an arithmetic progression is 3 and the 10 th term is 21. Find 15 th and 22 nd terms.  Choose the most appropriate option:	A) 21,35	B) 31,45	C) 30,46	D) 29,40	E) 39,40

Solution: Exp. a = 3, T 10 = a +9d =21, 3 +9d = 21, d =18/9= 
18/9 = 2
2   T 15= a + 14d =3 +14*2= 
3 +14*2 = 31
31, T22= a + 21d = 3+ 21*2= 
3+ 21*2 = 45
45   ANSWER:31,45
Answer: B
Look at this series: 1.25, 7.5, ____, 270, 1620, ... What number should fill the blank?  Choose the correct choice from the following:
A) 50	B) 65	C) 45	D) 55	E) 40

Solution: This is a simple multiplication series. Each number is 6 times greater than the previous number.   Answer: 45
Answer: C
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?	Choose the correct answer:
A) 4 B) 10 C) 15 D) 16 E) 17

Solution: L.C.M of 2,4,6,8,10,12 is 120. i.e after each 2 min they will toll together.So in 30 min they will toll 15 times.As they have initially tolled once,The answer will be  15+1= 
 15+1 = 16
16.   ANSWER:16
Answer: D
If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 9000 ? Choose the correct answer:
A) 11	B) 13	C) 15	D) 18	E) 10

Solution: Required difference = [3 ½ % of Rs.9000] – [3 1/3 % of Rs.9000]   = [(7/20-(10/3)]% of Rs.9000 =1/6 % of Rs.9000   = Rs. [(1/6)8(1/100)*9000] = Rs. 15.   Answer is 15.
Answer: C
Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?  Pick
A) four (4)	B) 2	C) 5	D) 7	E) 8

Solution: four (4)   4   No Of circles in the number.
Answer: A
A fish can go upstream at 35 kmph and downstream at 55 kmph, and then find the speed of the fish in still water?  Choose one.
A) 45	B) 55	C) 35	D) 65	E) 70

Solution: US = 35   DS = 55   M = (35 + 55)/2= 
(35 + 55)/2 = 45
45   45nswer:45
Answer: A
The average age of a committee of 10 members is 30 years. A member aged 60 years retired and his place was taken by another member aged 40 years . The average age of
present committee is;	Options:
A) 39 years
B) 28 years
C) 36 years
D) 35 years
E) 37 years

Solution: Total age of the committee = 30*10= 
30*10 = 300
300,   Total age when a member is retired   and a new one was joined= 300-60 +40, =280   Average age of present committee = 280/10= 
280/10 = 28
28.   ANSWER:28 years
Answer: B
The function f is defined for all the positive integers s by the following rule: f(s) is the number of positive integers each of which is less than s and has no positive factor in common with s other than 1 . if p is a prime number then f(p)?
Select:	A) p-1	B) p-2	C) (p+1)/2	D) (p-1)/2	E) 2

Solution: The moment you put a prime number in the function f(s), notice that all the numbers lesser than s have no divisor clashing with divisor of s since s is prime!!.   For instance f(7)= {6, 5, 4, 3, 2, 1}   Thus for f(p) number of integers falling under this set will be p-1   p-1nswer :- p-1
Answer: A
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is: Choose the correct choice from the following answers:
A) 28
B) 19
C) 22
D) 20
E) 21

Solution: Let the total number of workers be x. Then,   8000x = (14000 * 7) + 6000(x - 7)   = 2000x = 56000   = x = 28.   28NSWER:28
Answer: A
Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion? Answers:
A) 3 to 2	B) 5 to 2	C) 6 to 1	D) 33 to 7	E) 3 to 8

Solution: Explanation :   Odds of winning Arrogant is 5/3, then their probability of winning is 5/ (5+3) i.e 5/8.   Similarly,   Odds of winning Overconfident is 1/4, then their probability of winning is 1/ (1+4) i.e 1/5.   Therefore, the probability of winning of Arrogant or Overconfident is :-   =>(5/8) + (1/5).   =>33/40.   Thus, the required odds will be 33/(40-33) i.e 33/7.   Answer : 33 to 7
Answer: D
The smallest number which when diminished by 3, is divisible by 12, 16, 18, 21 and 28 is	Pick one:
A) 1008 B) 1011 C) 1022 D) 1032 E) 1043

Solution: Required Number = (L.C.M of 12, 16, 18,21,28)+3   = 1008 + 3= 
1008 + 3 = 1_011
1011   Answer: 1011
Answer: B
Of the 150 people at a party, 70 were women, and 40 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?  Choose the correct choice from the following answers
A) 40  B) 50  C) 60  D) 70  E) 80

Solution: Total people at party=150   Women=70   so Men  150-70= 
 150-70 = 80
80   No. of pple who tried appetizer=150-50 (given info)=100   No of women who tried appetizer=40   So Remaining ppl(men) who tried the appetizer =100-40= 
100-40 = 60
60   60orrect Option 60
Answer: C
A and B together have Sterling 1230. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?  Choices.
A) Sterling 460	B) Sterling 484	C) Sterling 550	D) Sterling 492	E) None

Solution: Explanation: 4/15A = 2/5B   A = (2/5 x 15/4)B   A = 3/2 B   A/B = 3/2   A : B = 3 : 2.   B's share = Sterling (1230 x 2/5) = Sterling 492.   Answer: Option Sterling 492
Answer: D
Tom opened a shop investing Rs.20000. Jose joined him 8 months later, investing Rs.35000.What will be Tom's and Jose's share of profit ratio after two years? Pick:
A) 4:9  B) 6:7  C) 7:6  D) 5:8  E) 8:5

Solution: SoL = ~s- So Tom's and Jose's share of profit ratio= 20*24:35*16 = 6:7   Answer: 6:7
Answer: B
In how many ways, a committee of 7 members can be selected from 6 men and 5 ladies, consisting of 4 men and 3 ladies?  Options
A) 180 B) 150 C) 200 D) 310 E) 250

Solution: (4 men out 6) and (3 ladies out of 5) are to be chosen   Required number of ways = 6C4*5C3 = 150   Answer is 150
Answer: B
If each of 3 digit code is formed of integers from 1 to 20, inclusively, and each of the digits are different, how many possible codes are there?  Choose the correct choice from the following.
A) 6,040
B) 6,840
C) 6,240
D) 6,340
E) 8,440

Solution: Code consists of 3 digits and no digit is repeated.   First digit of the code can have 20 possibilities   Second digit can have 19 possibilities   Third digit can have 18 possibilities   Total number of possible codes = 20*19*18= 
20*19*18 = 6_840
6840   Answer: 6,840
Answer: B
The sum of the first 60 positive even integers is 3,660. What is the sum of the first 60 odd integers? Select:  A) 3600  B) 3400  C) 3300  D) 3200  E) 3100

Solution: Sum of first n even numbers = n(n+1) =3660   Sum of first n odd numbers = n^2 = 60*60= 
60*60 = 3_600
3600 (here n=60)   3600nswer : 3600
Answer: A
A trolley which travels at a constant speed and can cover the platform of length 300m in two minute. How long it will take a train of length 200m and having a speed 60kph to pass the trolley?
Choose the correct choice from the following answers:
A) 11.21
B) 14.11
C) 16.32
D) 18.35
E) 20.45

Solution: Speed of the trolley= 300/120= 
300/120 = 5/2 = around 2.5
2.5m/s   Speed of the train= 60kph = 16.67m/s   Relative speed of train with respect to trolley=16.67-2.5= 
16.67-2.5 = 14.17
14.17m/s   Time taken by the train to pass the trolley= 200/14.17=14.11s   Answer: 14.11
Answer: B
The sector of a circle has radius of 21 cm and central angle 270o. Find its perimeter?	Choose the correct answer.
A) 91.5 B) 92 C) 93 D) 141 E) 95

Solution: Perimeter of the sector = length of the arc + 2(radius)   = (270/360 * 2 * 22/7 * 21) + 2(21)   = 141 cm   Answer: Option 141
Answer: D
A sum of Rs.100 is lent at simple interest of 3% p.a. for the first month, 9% p.a. for the second month, 27% p.a. for the third month and so on. What is the total amount of interest earned at the end of the year approximately Choose the most appropriate option
A) Rs.797160
B) Rs.791160
C) Rs.65930
D) Rs.66430
E) Rs.67430

Solution: Total amount of Interest is   I = P/100 * 1[3/12 + 9/12 +27/12…. 312/12   Where P = 100; I = 1/12 (3+9+…..312)   I = 1/12(3(312-1))/3-1   = 531440* 3/12*2 =Rs.66430   ANSWER:Rs.66430
Answer: D
A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?
Choose one
A) 91/9%
B) 100/9%
C) 11
D) 92/9%
E) None of these

Solution: Explanation :   Let the amount = Rs.100   Then 100/9%D = Rs.10 (∵ banker's discount, 100/9%D is the simple Interest on the face value of the bill for unexpired time and bill is discounted at 10% per annum)   Proceeds = Rs.100 – Rs.10 = Rs.90   Hence we should get Rs.10 as the interest of Rs.90 for 1 year so that nothing will be lost   ⇒ 10 = (90 × 1 × R)/100   ⇒ R = (10 × 100)/90 = 100/9 Answer : Option 100/9%
Answer: B
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + 4a = 3, which of the following best approximates the circumference of circle O? Choose the correct choice from the following answers
A) 28	B) 22	C) 20	D) 16	E) 12

Solution: Given that (1/a)+a =3   Square both sides of the equation:   We get,   [(1/a)^2 + a^2 + 2*(1/a)*a] = 9   => (1/a)^2 + a^2 + 2 = 9   => (1/a)^2 + a^2 = 7 ----------------- (1)   Diameter D = (1/a)^2 + a^2   = 7 (From (1))   So Radius = D/2 = 7/2   Circumference = 2*Pi*r   = 2*(22/7)*(7/2)   =12   So the answer should be 12.
Answer: E
A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 300. The dividend from the stock is :  Answers:
A) 7.5 % B) 18.75 % C) 9.75 % D) None of these E) Cannot be determined

Solution: Solution   By investing Rs. 1552,income = Rs. 128.   By investing Rs. 97, income = Rs. (300/1552x97)= Rs 18.75   âˆ´ Dividend =1 8.75%.   Answer 18.75 %
Answer: B
A person travelled from his house to office at 10km/hr and office to house at 90km/hr. Then find the average speed?	Choose the correct choice from the following
A) 15km/hr	B) 18km/hr	C) 25km/hr	D) 28km/hr	E) 33km/hr

Solution: Average speed = (2*10*90)/(10+90)= 
(2*10*90)/(10+90) = 18
18km/hrAnswer is 18km/hr
Answer: B
Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the
rest at 5 kmph. Find the total distance. Select the correct option:	A) 4 km	B) 5 km	C) 6 km	D) 7 km	E) 8 km

Solution: time=distance/speed   let total distance travelled be x in 84/60 hrs   2/3 rd of x travelled in 4 km/hr   1/3 rd of distance travelled in 5 km/hr   2x/(3*4)+x/(3*5)=84/60   x=6 km   ANSWER:6 km
Answer: C
A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train?  Choose the correct choice:	A) 230 m	B) 250m	C) 643m	D) 832m	E) 270m

Solution: Speed =	(72 x	5/18)m/sec	= 20 m/sec.   Time = 26 sec.   Let the length of the train be x metres.   Then,	x + 270/26	= 20   x + 270 = 520   x = 250.   Answer:250m
Answer: B
A straight line in the xy- plane has y-intercept of 10 . On this line the x-coordinate of the point is 100 and y-coordinate is 1000 then what is the slope of the line?  Choose the correct choice: A) 2 B) 5.5 C) 6.5 D) 3.2 E) 9.9

Solution: Eq of line = Y = MX +C   C= 10   X=100   Y=100M + 10,   Substitute Y by 1000 as given in question.   1000=100M+10 , M =9.9.   correct option is 9.9
Answer: E