MU-NLPC/Calc-aqua_rat huggingface dataset:
If n is a positive integer, which of the following is a possible value of |46 - 5n| ?
Options
A) 7 B) 2 C) 11 D) 15 E) 20

Solution: When 46>5n, then |46- 5n| = 46- 5n = (45-5n) + 1 = {multiple of 5} + 1   When 46<=5n, then |46- 5n| = -(46- 5n) = (5n-45) - 1 = {multiple of 5} - 1   So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only C fits.   Answer: 11
Answer: C
The length of a train and that of a platform are equal. If with a speed of 54 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Choose the most appropriate option:  A) 227  B) 299  C) 450  D) 750  E) 211

Solution: Speed = [54 * 5/18] m/sec = 15 m/sec; Time = 1 min. = 60 sec.   Let the length of the train and that of the platform be x meters.   Then, 2x/60 = 15 è x = 15 * 60 / 2= 
15 * 60 / 2 = 450
450   Answer: 450
Answer: C
Sum of three numbers 286, If the first number be twice then second and third number be one third of the first, then the second number is	Choose one
A) A)70  B) B)71  C) C)78  D) D)73  E) E)74

Solution: Explanation:   Let the second number is x, then first is 2x, and third is 1/3(2x)   =>2x+x+2x/3=286   <=>11x/3=286   =>x=78   Answer: Option 78
Answer: C
Rony walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:20. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 35 meters. What is Rony's speed in meters per minute? Select.
A) 108 B) 175 C) 198 D) 216 E) 252

Solution: Total distance from 10 to 90 =80 + from 90 to 70 =20   So the dist is 100×35(per block dist)   Speed = 3500mts/20min =175m/min   175 is the answer
Answer: B
Rs.1200 is divided so that 5 times the first share, 10 times the 2nd share and fifteen times third share amount to the same. What is the value of the second share?	Pick: A) s525 B) s527 C) s598 D) s400 E) s500

Solution: A+B+C = 1200   5A = 10B = 15C = x   A:B:C = 1/5:1/10:1/15 =3:2:1   2/6 * 1200= 
2/6 * 1200 = 400
Rs 400   Answer:s400
Answer: D
Mohit sold an article for $12000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?	Answers:
A) 16000	B) 25000	C) 10000	D) 18000	E) 17000

Solution: Let the CP be $x.   Had he offered 10% discount, profit = 8%   Profit = 8/100 x and hence his SP = x + 8/100 x = $1.08x = 12000 - 10/100(12000) = 12000 - 1200= 
12000 - 1200 = 10_800
$10800=> 1.08x = 10800   => x = 10000   10000
Answer: C
A cab driver 5 days income was $250, $400, $750, $400 , $500. Then his average income is?
Select
A) $440
B) $450
C) $460
D) $470
E) $480

Solution: avg = sum of observations/number of observations   avg income=(250+400+750+400+500)/5= 
(250+400+750+400+500)/5 = 460
460   Answer is $460
Answer: C
The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?  Pick
A) 175
B) 116
C) 197
D) 176
E) 267

Solution: 25x + 46   = 26(x – 5)   x = 176   Answer:176
Answer: D
What is the next number of the following sequence.
3, 10, 13, 20, 23, 30,  Select:
A) 28  B) 29  C) 30  D) 33  E) 36

Solution: 3   3+7= 
3+7 = 10
10   10+3= 
10+3 = 13
13   13+7= 
13+7 = 20
20   20+3= 
20+3 = 23
23   23+7= 
23+7 = 30
30   30+3= 
30+3 = 33
33   ANSWER:33
Answer: D
A regular square is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ? Choose the most appropriate option:
A) 45 degrees
B) 54 degrees
C) 72 degrees
D) 84 degrees
E) 108 degrees

Solution: its a regular square so divide the globe by 4.   = 360/4= 
360/4 = 90
90   90 would be the angle at O.   Angles at A and B are equivalent, so   90 + 2x= 180   2x = 90   x =45   Angles OAB and OBA will be 45 degrees each.   45 degrees
Answer: A
5 noun, 4 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
Pick.
A) 360  B) 430  C) 510  D) 540  E) 630

Solution: we have to choose one from each set. 1 from 5 nouns and 1 from 4 verbs and 1 from 3 adjectives.   then we have to arrange 3 different sets in 3! ways.   so,   5c1*4c1*3c1*3!=360   360NSWER:360
Answer: A
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his first child?	Choose the correct option:
A) 12
B) 24
C) 30
D) 48
E) 120

Solution: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and C1 are always together.   Consider F and C1 to be one unit, then we would have total of four units: {FC1}, {M}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and C1 within their unit can be arranged in 2 ways: {FC1} or {C1F}, so total number of arrangements is 4!*2=48.   Answer: 48.
Answer: D
If x < y < z and y-x > 1, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?  Choose the most appropriate option
A) 6  B) 3  C) 8  D) 9  E) 10

Solution: We have:   1) x<y<z 2)="" y-x="">1   3) x</y<z>=2k (x is an even number)   4) y=2n+1 (y is an odd number)   5) z=2p+1 (z is an odd number)   6) z-x=? least value   z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.   we are asked to find the least value, so we have to pick the least numbers   since y is odd and x is even, y-x must be odd. since y-x>1, the least value for y-x must be 3, the least value for x must be 2, and, thus, the least possible value for y must be 3 (y-2=1, y=3)   2<3<z, since z is odd, the least possible value for z is 5   z-x=5-2= 
5-2 = 3
3   Answer 3
Answer: B
A certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?	Choose one:
A) a) 10,700	B) b) 10,800	C) c) 10,900	D) d) 12,000	E) e) 11,100

Solution: Let x = number of people in smallest district   x*1.1 = number of people in largest district   x will be minimised when the number of people in largest district is maximised   10*x*1.1 = 11x = total number of people in other districts   So we have 11x + x = 142k   x = 12,000   Answer : d) 12,000
Answer: D
2, 6, 12, 20, 30, 42, 56, (...) Choose the correct option.
A) 62 B) 74 C) 72 D) 81 E) 58

Solution: The pattern is 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8.   Hence, next number is 8×9 = 72   Answer is 72
Answer: C
In what ratio must water be mixed with milk to gain 1623% on selling the mixture at cost price?  Select the correct option:
A) 6 : 1
B) 1 : 6
C) 1 : 4
D) 4 : 1
E) None of these

Solution: Explanation :   Let CP of 1 litre milk = Rs.1SP of 1 litre mixture = CP of 1 litre milk = Rs.1Gain=1623%=503%CP of 1 litre   mixture = 100(100+Gain%)×SP=100(100+503)×1=100(3503)=300350=67 1 : 6y the rule of alligation, we   have   CP of 1 litre water CP of 1 litre milk   0 1   CP of 1 litre mixture   6/7   1 - 6/7 = 1/7 6/7 - 0 = 6/7   Quantity of water : Quantity of milk = 1/7 : 6/7 = 1 : 6   Answer : Option 1 : 6
Answer: B
Two mixers and one T.V. cost Rs. 7000, while two T.V.s and a mixer cost Rs, 9800. The value of one T.V. is:  Select
A) Rs.4000	B) Rs.4500	C) Rs.4300	D) Rs.4200	E) None of these

Solution: Explanation :   Let C.P. of a mixer be Rs. x and that of a T.V. be Rs. y.   Then,   2x + y = 7000 and 2y + x = 9800.   Multiplying 2nd equatien by 2 and subtracting first from it, we get   3y = 19600 - 7000= 
19600 - 7000 = 12_600
12600   or   y= 4200 C.P. of a T.V. = Rs. 4200   Answer : Rs.4200
Answer: D
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 40 percent of the pollutant?  Choose the correct choice:
A) $500,000
B) $100,000
C) $50,000
D) $10,000
E) $5,000

Solution: To remove 90% of pollutant   C= 100,000(90)/(100-90) = 900,000   To remove 40% of pollutant   C' = 100,000(40)/(100-40) = 400,000   Difference = C - C' = 500,000   $500,000nswer - $500,000
Answer: A
The average age of a class of 12 students is 8 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher Choices:
A) 30 Years
B) 31 Years
C) 21 Years
D) 34 Years
E) 49 Years

Solution: Total age of students is 12X8 = 96 Years   Total age inclusive of teacher = 13X (8+1) = 117   So, Teacher's age is 117-96= 
117-96 = 21
21 Yrs   There is a shortcut for these type of problems   Teacher's age is 8+(13X1)= 21 Years   21 Years
Answer: C
A man counted his animals, 80 heads and 280 legs (ducks and goats). how many goats are there?
Select:	A) 30	B) 40	C) 50	D) 60	E) 70

Solution: let no of ducks=d and no of goat=g   d+g=80(heads)----------> eq 1   each duck has 2 legs and goat has 4 legs   2d+4g=240 and divide 2d+4g=240 by 2 we get d+2g=140 -----------> eq2   subtract eq1 from eq2   we get no of goats=60   ANSWER:60
Answer: D
A fisherman sells 300 fish for Rs. 9000 at a profit of Rs. 6 per fish. Find his cost price for one metre of cloth?	Choose the correct choice from the following answers
A) 24	B) 36	C) 30	D) 18	E) 20

Solution: SP per fish = 9000/300 = Rs. 30 Profit per fish = Rs. 6 CP per metre = 30 - 6= Rs. 2424nswer: 24
Answer: A
Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?	Choices.
A) 2.5  B) 3  C) 3.5  D) 4  E) 4.5

Solution: The part filled by A + B + C in 1 hour   = 1/6 + 1/8 + 1/24   = 8/24 = 1/3   All the three pipes together will fill the tank in 3 hours.   The answer is 3.
Answer: B
If x is the reciprocal of a positive integer, then the maximum value of x^y, where y = –x^2, is achieved when x is the reciprocal of Choose the correct choice from the following:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Let's take answer C and try to substitute it in the task:   x=13   y=−(13)^2=−1/9   x^y=1/3−1/9   So x will be equal to ninth square root from 33.   1nd we can infer that maximum value will be when we take x=1 because then x^y will be equal to 1   1nswer is 1
Answer: A
The area of an isosceles trapezoid with sides of length 5 and bases of length 9 and 15 is?
Choose the correct choice from the following answers:
A) 44
B) 48
C) 46
D) 47
E) 50

Solution: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 15 will be divided into 3 parts= 9, 3 and 3 (Making one square and two right triangles)   For the right triangle, height will be= (5^2-3^2)^1/2= 4   And the area of trapezoid = 1/2 (481+482)H= 1/2*24*4= 
1/2*24*4 = 48
48   48
Answer: B
In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
Choose the correct choice: A) 5.0 sec B) 2.9 sec C) 1.3 sec D) 2.9 sec E) 1.8 sec

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 200/40= 
200/40 = 5
5.0 sec.   5.0 secnswer:5.0 sec
Answer: A
The price of rice falls by 10%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously? Choose one:
A) 5 kg
B) 15 kg
C) 25 kg
D) 30 kg
E) None

Solution: Solution: Let Rs. 100 be spend on rice initially for 20 kg.   As the price falls by 10%, new price for 20 kg rice,   = (100 -10% of 100) = 90   New price of rice = 90/20 = Rs. 4,5 per kg.   Rice can bought now at = 100/4,5 = 22,22 kg.   Answer: Option None
Answer: E
The total marks obtained by a student in Mathematics and Physics is 40 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. Options.
A) 40
B) 26
C) 27
D) 28
E) 30

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 40 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (40 + 20) / 2= 
(40 + 20) / 2 = 30
30.Answer:30
Answer: E
Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6, then the resultant number contains same all digits (of course in a different place)
Answers.
A) 143258  B) 142876  C) 142881  D) 142852  E) 142857

Solution: 142857   142857   142857xplanation:     142857 * 1= 
  142857 * 1 = 142_857
142857   142857 * 2= 
142857 * 2 = 285_714
285714   142857 * 3= 
142857 * 3 = 428_571
428571   142857 * 4= 
142857 * 4 = 571_428
571428   142857 * 5= 
142857 * 5 = 714_285
714285   142857 * 6= 
142857 * 6 = 857_142
857142   Note: Such numbers are called cyclic numbers.
Answer: E
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction E of the total distance did he cover while the sun was shining on him?  Choose the correct choice from the following choices:	A) 1/4	B) 4/5	C) 1/5	D) 1/6	E) 1/7

Solution: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is E=2/14 = 1/7. Answer: 1/7
Answer: E
There are between 90 and 100 cards in a collection of cards. If they are counted out 3 at a time, there is 1 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?  Answers: A) 91 B) 93 C) 95 D) 97 E) 99

Solution: The numbers with the form 4n+1 are 93 and 97.   Only 97 has the form 3k+1.   The answer is 97.
Answer: D
A man can row a boat at 25 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 50 km downstream?	Select the correct option:  A) 1/2  B) 4/3  C) 2/3  D) 5/3  E) 1/3

Solution: Speed downstream = 25 + 5= 
25 + 5 = 30
30 kmph.   Time required to cover 50 km downstream= d/s = 50/30   = 5/3 hours.   Answer: 5/3
Answer: D
The Salary of an employee increase consistently by 15% per year. If his present salary is Rs. 24000 then what will his salary be after 3 years ?
Choose the correct choice from the following:	A) Rs. 32497	B) Rs. 34384	C) Rs. 35065	D) Rs. 36501	E) Rs. 37650

Solution: Explanation :   Salary = 24000 x 1.15 x 1.15 x 1.15 = 36501   Answer : Option Rs. 36501
Answer: D
From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is
Pick one:
A) 1/26 B) 1/25 C) 1/20 D) 1/21 E) 1/22

Solution: Let E1 be the event of drawing a red card.   Let E2 be the event of drawing a king .   P(E1 ∩ E2) = P(E1) . P(E2)   (As E1 and E2 are independent)   = 1/2 * 1/13 = 1/26.   1/26nswer: 1/26
Answer: A
In how many ways can two members be selected from a group of ten members?
Select the correct option.
A) 10C2
B) 10C8
C) 10C4
D) 10C3
E) 10C1

Solution: two members can be selected from ten members in   10C6   = 10C2 ways.   10C2nswer: 10C2
Answer: A
In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 7 people read all three newspapers. Find the minimum number of people who read both A and B but not C.
Choose the correct choice from the following answers.
A) A)1 B) B)2 C) C)3 D) D)0 E) E)5

Solution: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.   A and B and C is 7 - that means A and B is at least 7. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C   A and B but not C = |A|-|B| - 7   So i would pick A=35 and B =50 to minimize the value to a 1. (1NS 1)
Answer: A
A is 1.5 times as fast as B. A alone can do the work in 30 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed? Choose the correct choice
A) 23
B) 22
C) 21
D) 36
E) 25

Solution: A can finish 1 work in 30 days   B can finish 1/1.5 work in 30 days - since A is 1.5 faster than B   This means   B can finish 1 work in 30*1.5= 
30*1.5 = 45
45 days   Now using the awesome GMAT formula when two machines work together they can finish the job in= AB/ (A+B) = 45*30/(45+30) = 20*30/50 = 18 days   Since they alternate on days, it will take them double this time so total time = 18 * 2= 
18 * 2 = 36
36 days   So answer is 36
Answer: D
An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested?	Choose one
A) 99	B) 112	C) 118	D) 124	E) 130

Solution: Let x be the number of green apples.   There were 496 total apples; there are three times as many red apples as green apples. Therefore,   x + 3x = 496   4x = 496   x = 124   Answer: 124
Answer: D
If A's height is 45% less than that of B, how much percent B's height is more than that of A?  Choose the correct choice from the following:
A) 66.66% B) 81.81% C) 66.766% D) 86.66% E) 66.65%

Solution: Excess of 81.81%'s height over A's = [(45/(100 - 45)] x 100%   = 81.81%   Answer: 81.81%)
Answer: B
A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Choose the correct choice from the following: A) Rs.500 B) Rs.750 C) Rs.1250 D) Rs.1500 E) Rs.1800

Solution: (5/100) A = (15/100) B   A = 3B   A + B = 2000   4B = 2000 => B = 500   A = 1500   ANSWER:Rs.1500
Answer: D
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $12,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?  Choose the correct choice from the following answers:  A) 62,000  B) 85,500  C) 95,500  D) 100,500  E) 100,000

Solution: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).   62,000nswer: 62,000.
Answer: A
The value of ((x – y)³ + (y - z)³ + (z – x)³)/(18 (x – y) (y – z) (z – x))
is equal to :
Choose the correct choice from the following choices:
A) 0 B) 1/6 C) 1 D) 1/4 E) 1/3

Solution: Since (x – y) + (y – z) + (z – x) = 0,   so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).   (3 (x – y) (y – z) (z – x))/(18(x – y) (y – z) (z – x)) = 1/6.   ANSWER:1/6
Answer: B
If mn > 0, which of the following must be negative?
Choose the correct choice from the following choices:	A) 2m+n	B) 2m/n	C) m/n	D) -2mn	E) -m/-n

Solution: - * + = -   Answer : -2mn
Answer: D
There are 2 sections A and B in a class, consisting of 50 and 40 students respectively. If the average weight of section A is 50kg and that of section B is 70kg, Find the average of the whole class? Choose the correct choice from the following answers:	A) 50.78kg	B) 49.32kg	C) 61.67kg	D) 58.88kg	E) 70.89kg

Solution: Total weight of 50+40 students = 50*50 + 40*70 = 2500+2800= 
2500+2800 = 5_300
5300/90= 58.88 kg   Answer is 58.88kg
Answer: D
The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC? Options.
A) –3/4	B) >–4/3	C) –5	D) –5/2	E) –9/4

Solution: First to find the midpoint of B & C — average the x-coordinates: (–1+ 5)/2 = 2; and average the y-coordinates: (–1 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 – 5 = -9/2. The run is the change in the x-coordinates: 2 – 0 = 2. Slope = rise/run = [–9/2]/2 = –9/4. Answer = (–9/4)
Answer: E
A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 3 books from the list, including at most 2 novels. How many selections of 3 books satisfy the requirements? Pick one:	A) 40	B) 115	C) 130	D) 144	E) 195

Solution: 40ns: B   Solution: Selection requires at most 2 novels, means=   0N4P + 1N3P + 2N2P   6c0*4c3+ 6c1*4c2   = 4+ 36= 
4+ 36 = 40
40   40ns: 40
Answer: A
In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled. Choose the correct choice:	A) 1 hour and 59 minutes	B) 2 hour and 59 minutes	C) 4 hour and 59 minutes	D) 4 hour and 59 minutes	E) 5 hour and 59 minutes

Solution: Solution:   The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half.   So, it will take 1 hour and 59 minutes for it to be filled half.   1 hour and 59 minutesnswer 1 hour and 59 minutes
Answer: A
A string of 13 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.02, what is the probability that the string of light bulbs will fail during the time period T?
Choose the correct choice from the following answers:	A) 0.02	B) (0.02)^13	C) 1 - (0.02)^13	D) (0.98)^13	E) 1 - (0.98)^13

Solution: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.   The opposite event is when none of the 13 light bulbs fails, since the probability of each light bulb not to fail is 1-0.02= 
1-0.02 = 0.98
0.98 the the probability that none of the 13 light bulbs fails is 0.98^13.   Hence, the probability that at least one light bulb fails is 1-0.98^13.   Answer: E.   Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 13, then according to your logic the probability that the string of light bulbs will fail would be 100*0.02= 
100*0.02 = 2
2, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: E
R is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can R be?
Select:
A) 300,000  B) 349,999  C) 350,000  D) 399,999  E) 400,000

Solution: R 1,000,000-300,000=700,000 integers   700,000/2= 350,000 even integers.   350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.   350,001-2=349,999   349,999
Answer: B
Four different children have jelly beans: Aaron has 5, Bianca has 7, Callie has 8, and Dante has 13. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?  Choose the correct choice from the following options:
A) 2	B) 3	C) 4	D) 5	E) 6

Solution: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 13 jelly beans so each child has no more than 1 fewer jelly bean than any other child.   Dante + Aaron = 13+5= 
13+5 = 18
18/2= 
18/2 = 9
9   13-8= 
13-8 = 5
5 so Dante must provide 5 jelly beans to Aaron.   Answer (5)
Answer: D