MU-NLPC/Calc-aqua_rat huggingface dataset:
UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 9:1. If 90% of the Toyota bought and 10% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?  Choices
A) 82%  B) 64%  C) 28%  D) 69%  E) 80%

Solution: let total no of Vehicles bought be 100, Toyota 90 and Honda 10, so total number of SUV's bought for Toyota and Honda respectively  90* 90/100= 
 90* 90/100 = 81
81 and   10* 10/100= 
  10* 10/100 = 1
1   so total 82 SUV's were bought out of 100 Vehicles bought..so required % is 82%   82%NSWER:82%
Answer: A
How many factors of 220 are odd numbers greater than 1?
Options.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: When factorized, 220 has 4 prime factors. Of these prime factors 2 are odd and 2 are even. Hence total number of odd factors is 2*2(4), which includes 1. The total number of odd factors greater than 1 are 3.(option 3)
Answer: A
What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
Choices.
A) 1200 B) 1256 C) 1349 D) 1456 E) 1590

Solution: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.   First + second = third => we can eliminate 3 & 9 since  3 + 9= 
 3 + 9 = 12
12.   Last is 3 times the second=> we can eliminate option 2 & 6 since  3 * 6= 
 3 * 6 = 18
18.   Hence the number is 1349   1349
Answer: C
W(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point W?
Choose one
A) (1, 2). B) (2, 0). C) (0, -2). D) (-2, 0). E) (2, 2).

Solution: A quick glance at the options,W(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=(-2, 0).
Answer: D
If –3 < x < 3 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2
Choose the most appropriate option:
A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III

Solution: Answer is D. Let's look at the statements one by one   Stmt I. x^3 < x   if 0<x<1 -1<x<0="" but="" if="" then="" x="" x^3="" x^3<="">x   So this statement is not always true   Stmt II. x^2 < |x|   Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.   Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x </x<1>= 1/2, then x^2 = 1/4 and 1/4<1/2   So Stmt II is always true   Stmt III. x^4 – x^5 > x^3 – x^2   This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).   Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 (1-x)="" means="" that="" which="">0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.   So Stmt III is always true   I, II, and III</x<1>
Answer: E
A cylindrical can has a radius of 4 centimeters and a height of 24 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
Choose the most appropriate option:
A) 16 pi
B) 64 pi
C) 96 pi
D) 192 pi
E) 576 pi

Solution: They are asking the lateral surface area of the cylinder.   the Lateral surface area = 2* pi * r *h   = 2*pi*4*24=192 pi   Answer is 192 pi.
Answer: D
A train running at the speed of 90 km/hr crosses a pole in 9 seconds. Find the length of the train. Pick
A) 225 meter
B) 200 meter
C) 250 meter
D) 210 meter
E) 230 meter

Solution: Speed = 90*(5/18) m/sec = 25 m/sec   Length of Train (Distance) = Speed * Time     (25) * 9= 
  (25) * 9 = 225
225 meter   225 meternswer:225 meter
Answer: A
Josh spends a total of $5.5 buying S items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then S may be which of the following?
Choose the correct choice from the following answers.
A) 99
B) 100
C) 101
D) 112
E) 113

Solution: S items in the convenience store$5.5 = 550 cents   550 = 50a + 5b   =>110 = 10a + b   b = 110 - 10a = 10(11-a)   Hence b is even and multiple of 10.   Possible values of b:   b = 10,20,30,40,50,60,70,80,90,100   a = 11,9,8,7,6,5,4,3,2,1   The total (a+b) is 21,29,38,47,56,65,74,83,92,101   The only option is 101. Hence 101.
Answer: C
There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?	Choose the correct choice from the following options:
A) 25 B) 66 C) 88 D) 89 E) 53

Solution: Let the two positive numbers be 5x and 8x respectively.   8x - 5x = 15   3x = 15 => x = 5   => Smaller number = 5x = 25.   25nswer: 25
Answer: A
Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 45? Pick one.
A) 1/16 B) 5/42 C) 1/8 D) 3/16 E) 1/4

Solution: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);   42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;   So, the probability is 2/16=5/42.   Answer: 5/42.
Answer: B
At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten? Choose the correct choice from the following choices:
A) 12 greater
B) 12 fewer
C) 28 fewer
D) 36 fewer
E) 44 fewer

Solution: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students   KG= 1/6 * 480= 
1/6 * 480 = 80
80   5th and 6th graders= 1/3 * 384= 
1/3 * 384 = 128
128 (1/3 of remainder)   1st and 2nd grade= 1/4 * 480= 
1/4 * 480 = 120
120 ( 1/4 of all students)   equal number of students in 3rd and 4th=> 480 - 344= 
480 - 344 = 136
136 and   136/2= 
  136/2 = 68
68 each since equal number   (344 is the sum of remaining students)   thus   80-68= 
  80-68 = 12
12>>> therfore answer is 28 fewer   12 fewer
Answer: B
If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. If x is positive, y must be positive
III.Both x and y are positive
Choose the correct choice from the following choices
A) I only	B) II only	C) III only	D) I and II	E) II and III

Solution: If x-y=8, which of the following must be true?   I. Both x and y are positive   II. If x is positive, y must be positive   III. If x is negative, y must be negative   1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D   2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E   I only) I only   B) II only   C) III only   D) I and II   E) II and III   I onlynswer I only
Answer: A
Runner A passed a post running at a constant speed of 50 miles per hour. Then, 15 minutes later, Runner B passed the same post at a constant speed of 60 miles per hour. If both runners maintained their speeds and both remained on the highway for at least 2 hours, how long after Runner B passed the gas station did he catch up with Runner A?	Choose the correct choice from the following answers
A) 30 min B) 45 min C) 1 hr D) 1 hr 15 min E) 1 hr 30 min

Solution: When Runner B is at the post, Runner A is 50/4 miles ahead on the highway. (the distance covered in 15 min)   every hour, Runner B runs 10miles more than Mary. how many hours will it takes him to run 50/4 miles more? the answer is (50/4)/10 = 25/20=1h15min.   Answer 1 hr 15 min
Answer: D
At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.70. What is the price of 2 doughnuts?	Select the correct option
A) $ 0.55  B) $ 1.00  C) $ 1.10  D) $ 1.30  E) $ 1.80

Solution: Joe ordered 3 Dougnuts and Cup of Coffee. Stella ordered 2 Doughnuts and cup of coffee which means Joe ordered 1 doughnut more than stella only. So 1 doughnut must be 2.25 - 1.7= 
2.25 - 1.7 = 0.55
0.55   Price of 1 Doughnut= 0.55   Price of 2 Doughnut = 0.55*2= 
0.55*2 = 1.1
1.1   ANSWER:$ 1.10
Answer: C
Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.45, b = 2.95, and c = 3.75, what is y – x?
Choose the correct choice from the following answers:
A) -0.1
B) 0
C) 0.2
D) 0.1
E) 0.3

Solution: To find x, we first sum a, b, and c, then round to the tenths place. 5.45 + 2.95 + 3.75 = 12.15, which rounds to 12.2.   To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 2.9 + 3.7 = 12.0.   We are looking for y - x, which gives us 12.3 - 12.2 = 0.2, or answer choice C.   0.2
Answer: C
In track last week, the boys ran 34 laps. The girls ran 20 more
laps. Each lap is a 1/6th of a mile. How many miles did the girls run?	Select the correct option
A) 9 miles B) 10 miles C) 11 miles D) 12 miles E) 13 miles

Solution: The girls ran 34 + 20= 
34 + 20 = 54
54 laps. 54 x 1/6= 54/6, which reduces to 9.   The girls ran 9 miles   correct answer 9 miles
Answer: A
A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?	Choices:
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence 2
Answer: A
A and B invests Rs.3000 and Rs.10000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Choose the most appropriate option:  A) 9:6  B) 9:8  C) 9:20  D) 9:9  E) 9:5

Solution: (3*6 + 6*6): (10*12)   54:120 => 9:20.Answer:9:20
Answer: C
Which of the following fractions T has a decimal equivalent that is a terminating decimal? Choose the correct choice:
A) 10/189 B) 15/196 C) 16/225 D) 25/144 E) 39/128

Solution: The fraction T will terminate if and only if the denominator has prime divisors only 2 and 5 or both.   A. 10/189 = 10/(3*3*3*7) Non-term.   B. 15/196 = 15/(2*2*7*7) Non-term.   C. 16/225 = 16/(5*5*3*3) Non-term.   D. 25/144 = 25/(2*2*2*7) Non-term.   E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
In a simultaneous throw of a pair of dice, find the probability of getting a total more than 5 Choose the correct choice from the following answers.
A) 1/2
B) 7/12
C) 5/13
D) 5/12
E) 3/8

Solution: Total number of cases = 4*4= 
4*4 = 16
16   Favourable cases= [(2,4),(3,3),(3,4),(4,2),(4,3),(4,4)] = 6   So Probability = 6/16 = 3/8   Answer is 3/8
Answer: E
Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is	Pick:  A) 5/17  B) 5/12  C) 5/19  D) 5/29  E) 5/13

Solution: Using question number 11 and 12, we get the probability as   1 - (1/36 + 5/9)   = 5/12   Answer:5/12
Answer: B
In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?	Select the correct option.
A) 69	B) 70	C) 71	D) 72	E) 73

Solution: number of ways = 2*3!*3! = 72   Answer is 72
Answer: D
If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively:
Choose one
A) Rs.260	B) Rs.360	C) Rs.350	D) Rs.364	E) Rs.362

Solution: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4   A:B = 2:3 and B:C = 1:4 = 3:12   A:B:C = 2:3:12   A;s share = 510 * 2/17 = Rs. 60   B's share = 510 * 3/17 = Rs. 90   C's share = 510 * 12/17 = Rs.360.   Answer: Rs.360
Answer: B
How many different ways can 2 students be seated in a row of 4 desks, so that there is always at least one empty desk between the students?	Options
A) 2  B) 3  C) 4  D) 6  E) 12

Solution: Total cases : 12 ( student one has 4 options and student two has three options, 4x3=12)   Non-favourable cases : 6 (when two students sit together. students in desk 1 and desk 2 , in desk 2 and desk 3, in desk 3 and desk 4) for each of these cases there are two possibilities because the positions can be interchanged. hence 2x3=6.   SO favourable cases :  12-6= 
 12-6 = 6
6. ANSWER:6
Answer: D
A women in her conversation said " if u reverse my own age, in figures represent my husbands age. he is of course senior to me and difference between our age is one 0ne-eleventh of their sum. what is the woman's and her husbands age?	Answers:
A) 45,54
B) 46,57
C) 84,57
D) 34,58
E) 52,54

Solution: let man,s age be xy   the woman's age is yx   then 10x+y-10y-x=1/11(10x+y+10y+x)   9x-9y=x+y   8x=10y   x/y=10/8=5/4   so xy=54 and yx=45   45,54NSWER:45,54
Answer: A
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?  Choices
A) 150	B) 88	C) 77	D) 62	E) 52

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150nswer: 150
Answer: A
A certain barrel, which is a right circular cylinder, is filled to capacity with 200 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel? Choose the correct choice from the following.
A) There is no empty capacity B) 1100 gallons C) 1300 gallons D) 1400 gallons E) 1800 gallons

Solution: Radius of first cylinder=r, diameter=2r, height=h   Radius of second cylinder=2r, diameter=2d and height=2h   Volume of first cylinder=pie (r^2)*h=200   Volume of second cylinder=pie(2r^2)2h   Put the value of pie (r^2)*h=200 in the second cylinder,volume= pie (r^2)*4*2=200*8= 
200*8 = 1_600
1600 gallons   Empty capacity=1400   1400 gallons
Answer: D
Gautami went to the stationers and bought things worth Rs. 100, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 5%. then what was the cost of the tax free items?  Select the correct option
A) Rs. 99.50  B) Rs. 70.50  C) Rs. 89.50  D) Rs. 69.50  E) Rs. 80.50

Solution: Solution   Let the amount of taxable purchases be Rs.x.   Then, 5% of x	= 50/100   x ‹=› (50/100×100/5)   = 10   Cost of tax free items	= Rs.[100 - (10 + 0.50)]   = Rs. 89.50   Answer Rs. 89.50
Answer: C
When a student Joe, weighing 40 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe? Select:
A) 5 kg
B) 11 kg
C) 30 kg
D) 36.5 kg
E) 71 kg

Solution: After two persons leave the group the average remains the same. That means the weight of the two persons = 40+30= 
40+30 = 70
70   So, the average the two persons= 35   That gives the answer  40-35= 
 40-35 = 5
5   5 kgnswer 5 kg
Answer: A
Three men A, B and C working together can do a work in 17 days. They start the work together and A works for 5 days and takes rest on the sixth day, B works for 5 days and takes rest on the next two days and C works for 8 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)  Choose the correct choice from the following choices
A) 24 days  B) 23 days  C) 22 days  D) 21 days  E) 20 days

Solution: Total work is 3*17= 
3*17 = 51
51 units.   A does 5 days of work every 6 days.   B does 5 days of work every 7 days.   C does 8 days of work every 11 days.   Test the options.   In 20 days:   A will do  5*3 + 2= 
 5*3 + 2 = 17
17 units (3 complete cycles and 2 days of work).   B will do  5*2+ 5= 
 5*2+ 5 = 15
15 units (2 complete cycles, 5 days of work, and 1 day of rest).   C will do  8*1 + 8= 
 8*1 + 8 = 16
16 units (1 complete cycle, 8 days of work, and 1 day of rest).   Total= 17 + 15 + 16= 
17 + 15 + 16 = 48
48 units.   In 21 days:   A will do  5*3 + 3= 
 5*3 + 3 = 18
18 units (3 complete cycles and 3 days of work).   B will do  5*3= 
 5*3 = 15
15 units (3 complete cycles).   C will do  8*1 + 8= 
 8*1 + 8 = 16
16 units (1 complete cycle, 8 days of work, and 2 days of rest).   Total= 18 + 15 + 16= 
18 + 15 + 16 = 49
49 units.   In 22 days:   A will do  5*3 + 4= 
 5*3 + 4 = 19
19 units (3 complete cycles and 4 days of work).   B will do  5*3 + 1= 
 5*3 + 1 = 16
16 units (3 complete cycles and 1 day of work).   C will do  8*1 + 8= 
 8*1 + 8 = 16
16 units (1 complete cycle, 8 days of work, and 3 days of rest).   Total= 19 + 16 + 16= 
19 + 16 + 16 = 51
51 units.   Answer: 22 days.
Answer: C
A double decked bus can accomodate 100 passengers,40 in the upper deck and 60 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck? Pick
A) 1. 85!50!60!/40!45! B) 2. 75!/30!45! C) 3. 110!/50!60! D) 4. 110!50!60!/40!45! E) 5. 110!/40!45!

Solution: 100 passengers,40 in the upper deck and 60 in the lower deck.   25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck   So those 15 will be put in lower deck and 10 will be in upper deck   So from the rest 75 passengers(100-25), we need to find 30 people to put into upper deck and the rest go to lower deck   So the ways are: C(75,30) = 75!/30!45! . Answer 2. 75!/30!45!
Answer: B
In a certain supermarket, a triangular display of cans is arranged in 9 rows, numbered 1 through 9 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 120 cans in the entire display, how many cans are in the six row?
Choose the correct answer
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: Let x be the number of cans in row 1.   The total number of cans is x + (x+3) + ... + (x+24) =   9x + 3(1+2+...+8) =   9x + 3(8)(9)/2 =   9x + 108   Since the total is less than 120, x must equal 1.   The number of cans in the 6th row is 1 + 3(5) = 16   The answer is 16.
Answer: C
If the height of a cone is increased by 100% then its volume is increased by?
Choose the correct option
A) 200% B) 300% C) 100% D) 500% E) 350%

Solution: Height of=>100%   so increased by 100%   ANSWER 100%
Answer: C
A number is doubled and 5 is added. If the resultant is trebled, it becomes 135. What is that number?
Pick one.
A) 12  B) 29  C) 20  D) 15  E) 99

Solution: Explanation:   Let the number be x.   Therefore,   3(2x + 5) = 135   6x + 15 = 135   6x = 120   x = 20   ANSWER:20
Answer: C
If M = s% of t and N = t% of s, then which of the following is true? Choose the correct choice from the following
A) M is equal to N	B) M is smaller than N	C) M is greater than N	D) none of these	E) Cannot be determined

Solution: Explanation :   Solution: s% of t = (s/100 * t)   => (t/100 * s) = t% of s   => M = N   M is equal to Nnswer : M is equal to N
Answer: A
The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is? Choose the correct choice
A) 8	B) 7	C) 6	D) 5	E) 2

Solution: 2x * x = 128 => x= 8   8nswer: 8
Answer: A
Distance between 2 places A and B is given. A man P starts from place A at 9 pm and another man Q goes from B at 10pm . Speed of Q is double of that of P. Both cover 1/4 dist in the same time interval. then A travels the entire dist in time Select
A) 8hrs B) 9hrs C) 10hrs D) 11hrs E) 12hrs

Solution: let speed of p and q are x, 2x   time taken by 8hrs to cover 1/4 distance =t   x*t = 2x*(t-1)   t=2 for 1/4 of total distance   8hrs travels the entire dist in time 2*4= 
2*4 = 8
8hrs   8hrsNSWER:8hrs
Answer: A
The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Choose the most appropriate option
A) 1:96	B) 1:99	C) 1:95	D) 1:12	E) 1:11

Solution: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.   (4x)(3x) = 6912   12x2 = 6912   x2 = 576 = 4 * 144 = 22 * 122 (x > 0)   => x = 2 * 12= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x   =1:96.   1:96nswer:1:96
Answer: A
In the game of Dubblefud, red chips, blue chips and green chips are each worth 1,2 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 15, 000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection? Choose one
A) 10	B) 20	C) 30	D) 40	E) 50

Solution: this is equivalent to :-   x * 2y * 5z = 15000   y   = z (given)   x * 2y * 5y = 15000   x * y^2 = 15000/10   2x * y^2 = 1500   now from options given we will figure out which number will divide 800 and gives us a perfect square :-   which gives us x = 30 as   2* 30 * y^2 =1500   y^2 = 25   y =5   Number of red chips = 30 hence 30
Answer: C
Zinc and copper are melted together in the ratio 9 : 11. What is the weight of melted mixture, if 28.8 kg of zinc has been consumed in it?
Choices:
A) 58 kg	B) 60 kg	C) 64 kg	D) 70 kg	E) None

Solution: Sol.   For 9 kg Zinc, mixture melted = (9+11) kg.   For 28.8 kg Zinc, mixture, melted = [20/9 x 28.8] kg   = 64 kg.   Answer 64 kg
Answer: C
If x+y=10, x-y=18, for integers of x and y, x=?  Answers.
A) 14 B) 15 C) 25 D) 13 E) 42

Solution: x+y =10   x-y = 18   2x = 28   x = 14   14nswer is 14
Answer: A
(1^2+2^2+3^2+.....+7^2)=? Select
A) 330  B) 345  C) 365  D) 140  E) None of them

Solution: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)   n=7   =(1/6x7x8x15)   =140   Answer is 140.
Answer: D
What is the area of an equilateral triangle whose one side length is 50?
Choose the correct choice from the following.
A) 225√3  B) 325√3  C) 425√3  D) 525√3  E) 625√3

Solution: -> -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(50^2)/4=625√3 and the answer is 625√3.
Answer: E
Two thirds of the roads from A to B are at least 5 miles long, and 3/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?	Choose the correct choice from the following options.
A) 1/6 B) 1/4 C) 2/3 D) 3/4 E) 11/12

Solution: So please:   Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-1/3*1/4=11/12.   Answer: 11/12.
Answer: E
If a - b = 3 and a2 + b2 = 29, find the value of ab?	Select
A) 10	B) 12	C) 14	D) 17	E) 18

Solution: 2ab = (a2 + b2) - (a - b)2   = 29 - 9= 
29 - 9 = 20
20   ab= 10   10)
Answer: A
5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.210 only. Menâ€™s wages are?  Choose one:
A) 6Rs  B) 2Rs  C) 4Rs  D) 9Rs  E) 14Rs

Solution: 5M = xW = 8B   5M + xW + 8B ----- 210 Rs.   5M + 5M + 5M ----- 210 Rs.   15M ------ 210 Rs. => 1M = 14Rs.   Answer: 14Rs
Answer: E
a man can row 20 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream  Choose the correct answer:  A) 13 km/hr.  B) 6 km/hr.  C) 9 km/hr.  D) 15 km/hr.  E) 10 km/hr.

Solution: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.   So,2x=20 or x=10.   Rate upstream=10 km/hr,rate downstream=30 km/hr.   Hence,rate of stream=1/2(30-10)km/hr=10 km/hr.   Answer is 10 km/hr..
Answer: E