MU-NLPC/Calc-aqua_rat huggingface dataset:
There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set E, which cannot be the range of the set E?
Choose the correct option:
A) 8
B) B.11
C) C.14
D) D.17
E) E.21

Solution: Let Set A has 1,8 as elements   B has 1,14 as elements.. So Range for Combined set E becomes  14-1= 
 14-1 = 13
13   For range to be 14,   A= 1,8   B= 2,15 (Range=14)   For range to be 17   A=1,8   B= 5,18   For range to be 21:   A=1,8   B= 9 ,22   So we are left with A and B.   Now consider A has elements A= -1,-8 and Thus Range =-1-(-8)= 
-1-(-8) = 7
7   So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...   Consider Option A   A=-1,-8   B= y,x where y and x are smallest and largest element in Set B   Elements of Combined Set: -8,-1,y and x   Now x-(-8)= 
-(-8) = 8
8 or x=0, then x-y=13 or y=-13...   Range of Combined Set: 0-(-13)= 13...   I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B.11
Answer: B
A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares? Select
A) 400  B) 365  C) 385  D) 315  E) 325

Solution: Explanation:   Average of the two areas =7002=350   one-fifth of the average of the two areas=3505=70   ⇒ Difference of the two areas =70   Let area of the smaller part =x hectares.   Then, area of the larger part =x+70 hectares.   x+(x+70)=700   ⇒2x=630   ⇒x=315   Answer: Option 315
Answer: D
If n is an integer and 101n^2 is less than or equal to 8100, what is the greatest possible value of n?  Answers
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: 101 * n^2 <=8100   n^2 <=8100/101 which will be less than 81 since  8100/100= 
 8100/100 = 81
81 which is the square of 9   Next closest value of n where n^2<=81 is 8   Ans 8
Answer: B
A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?	Choices.
A) 20%	B) 28%	C) 33 1/3 %	D) 35 2/7 %	E) 25%

Solution: The total number of mangoes bought by the shopkeeper be 12.   If he buys 4 a rupee, his 33 1/3 %P = 3   He selling at 3 a rupee, his SP = 4   Profit = SP - 33 1/3 %P = 4 - 3= 
4 - 3 = 1
1   Profit Percent= 1/3 * 100 = 33 1/3 %   ANSWER:33 1/3 %
Answer: C
How many terms are there in 2,4,8,16……1024?  Choices:
A) 10	B) 14	C) 16	D) 18	E) 20

Solution: Clearly 2,4,8,16……..1024 form a GP. With a=2 and r = 4/2= 
4/2 = 2
2.   Let the number of terms be n . Then   2 x 2n-1=1024 or 2n-1 =512 = 29.   n-1=9 or n=10.   10NSWER 10 10
Answer: A
What is the smallest integer k for which 64^k > 4^20? Choose the correct option
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: 64^k > 4^20   4^(3k) > 4^20   3k > 20   k = 7   The answer is 7.
Answer: D
Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "Z", and assuming that there are only 14 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?	Options:  A) A)1/12  B) B)9/100  C) C)1/8  D) D)4/5  E) E)9/10

Solution: Total letters 14,out of which the first letter is anything of 10 but N or X...   So there are 12possible letters for first place..   And only one of them is correct..   So 1/12   1/12nswer: 1/12
Answer: A
Working alone at its constant rate, machine K took 3 hours to produce 1/5 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
Choose the correct choice from the following:
A) 10 B) 12 C) 15 D) 25 E) 30

Solution: Machine K works at a rate of 1/15 of the units per hour.   The rate of K + M together is 4/5 * 1/6 = 2/15 of the units per hour.   The rate of machine M is 2/15 - 1/15 = 1/15.   It would have taken machine M a total time of 15 hours.   The answer is 15.
Answer: C
Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/7, 1/2, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?	Select the correct option
A) 1/21n	B) (n-1)/14n	C) 1/7n	D) (n+2)/72n	E) (3n-2)/2n

Solution: 1/7 * 1/2 * (1-1/n)   = 1/14 * (n-1)/n   = (n-1)/14n   Answer - (n-1)/14n
Answer: B
A and B complete a work in 8 days. A alone can do it in 12 days. If both together can do the work in how many days?
Choose one:
A) 4.8 days B) 3.8 days C) 3.65 days D) 3.77 days E) 5.75 days

Solution: 1/8 + 1/12 = 5/24   24/5= 
24/5 = 24/5 = around 4.8
4.8 days   4.8 daysnswer:4.8 days
Answer: A
Aishwarya’s mom was 36 years of age at the time of her birth, while her mom was 30 years old when her 4 years younger sister was born. The variance between the parents ages is :	Pick one:
A) 6 years B) 11 years C) 10 years D) 9 years E) 4 years

Solution: C   10 years   Mom’s age when Aishwarya’s sister was born = 30 years.   Dad’s age when Aishwarya’s sister was born = (36 + 4)= 
(36 + 4) = 40
40 years.   Needed Variance= (40 – 30) years = 10 years.   Answer is 10 years
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train? Choose the correct answer:  A) 120 m  B) 100 m  C) 324 m  D) Cannot be determined  E) None of these

Solution: Speed = 60* 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 6= 
50/3 * 6 = 100
100 m   ANSWER:100 m
Answer: B
A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction T of the sum of the 21 numbers in the list?	Answers:
A) 1/20
B) 1/6
C) 1/5
D) 4/21
E) 5/21

Solution: This is how I used to calculate which I think works pretty well:   if you let the average of the 20 other numbers equal a, can you write this equation for sum of the list (S)   n + 20a = S   the question tells us that   n = 4a   plug this back into the first equation and you get that the sum is 24a   4a + 20a = 24a   therefore fraction T of n to the total would be   4a/24a or 1/6   answer 1/6 4  + 20= 
 4  + 20 = 24
24a   therefore fraction T of n to the total would be   4a/24a or 1/6   answer 1/6
Answer: B
The difference between the compound interest and simple interest on a certain sum at 10% per annum for 2years is $631. Find the sum?  Choose the correct option
A) $52000  B) $61000  C) $71540  D) $63100  E) $56210

Solution: Let the sum be $x   C.I. = x(1+10/100)^2 - x = 21x/100   S.I. = (X*10*2)/100 = X/5   C.I.- S.I. = (21x/100)-(x/5) = x/100   x/100 = 631   x = 63100   Answer is $63100
Answer: D
Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is: Choose the correct choice from the following choices:  A) 4  B) 5  C) 6  D) 7  E) 10

Solution: Let the number be x. Then,   3x2 - 4x = x + 50   3x2 - 5x - 50 = 0   (3x + 10)(x - 5) = 0   x = 5   ANSWER:5
Answer: B
The length of a brigade which a train 130 m long and traveling at 45kmph can cross in 30 seconds, is Choose the correct answer:
A) 196 mts
B) 220 mts
C) 230 mts
D) 245 mts
E) None of these

Solution: Explanation:   Let the length of the brigade is x mts   Then Distance = 130 + x mts   given speed = 45 kmph = 45 x5/18 m/s   Time = 30 sec   T = D/S   => 30 = 130+x/(45x5/18)   => x = 245 mts.   ANSWER IS 245 mts
Answer: D
A shopkeeper’s price is 50% above the cost price. If he allows his customer a discount of 30% what profit does he make? Choose the correct option:
A) 5%
B) 10%
C) 15%
D) 20%
E) None of these

Solution: Let C.P. = 100, then M. P. = 150   S.P. = 70% of 150 = 105   ∴ % profit = 105−100/100×100=5%   5%nswer 5%
Answer: A
Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
Choose the correct choice
A) 6	B) 5	C) 6	D) 3	E) 2

Solution: 9261 = 8000(21/20)N   (21/20)3 = (21/20)N => N = 3   Answer:3
Answer: D
What is the least possible value of x^2-15 where x is a positive number.	Select:
A) -15  B) -14  C) -13  D) -12  E) -11

Solution: If x is a positive integer, the lowest value would be x = 1, because 0 is not included in the natural numbers. That's a technicality the GMAT would not expect students to know.   If x = 1, then the expression equals -14.   Answer = (-14).
Answer: B
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?	Answers
A) 123 km/hr  B) 187 km/hr  C) 179 km/hr  D) 120 km/hr  E) 169 km/hr

Solution: Let speed of the car be x km/hr.   Then, speed of the train = 150/100 x = 3/2 x km/hr.   75/x - 75/(3/2 x) = 125/(10 * 60)   75/x - 50/x = 5/24 = 120 km/hr.   Answer:120 km/hr
Answer: D
If a and y are positive integer and a/y is an even integer, which of the following can be an odd integer?	Answers:
A) x B) xy C) x−y D) x+2y E) a/3

Solution: C a-Y   Let says a =12 Y=3 iT BECOMES a-Y =9 This is odd True   a = 12 Y = 6 THEN a-Y = 2, Which is even hence this is False.   so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: E
If cost of 15 eggs be 75 rupees, then find out the cost of 4 dozen eggs.  Choose the correct choice from the following choices:
A) 300 B) 240 C) 500 D) 600 E) 700

Solution: Cost of 15 eggs = 75 rupees   Cost of 1 egg = 75/15= 
75/15 = 5
5 rupees,   Cost of 4 dozens, i.e. 5 x 12= 60 x 4 = 240   Answer : 240
Answer: B
Convert the 10/36 m/s into kilometers per hour?
Select the correct option.
A) 2.9 kmph
B) 9.9 kmph
C) 1.3 kmph
D) 1 kmph
E) 5.7 kmph

Solution: 10/36 m/s = 10/36 * 18/5= 
10/36 * 18/5 = 1
1/1= 
1/1 = 1
1kmph.   Answer: 1 kmph
Answer: D
Find the total no of 10 digits whose sum is 4.  Select the correct option:
A) 210	B) 220	C) 230	D) 240	E) 250

Solution: 4=4+0(one 4 & 9 zeroes)=> 1   4=3+1(one 3,one 1 & 8 zeroes)=> 2*9!/8!=18   4=2+2(two 2's & 8 zeroes)=> 9   4=1+1+2(two 1's & one 2)=> 9!/7! + 9!/(7!*2!)=72+36= 
72+36 = 108
108   4=1+1+1+1(four 1's)=> 9!/(6!*3!)=84   total no. of 10 digits no. whose sum is 4 =1+18+9+108+84= 
1+18+9+108+84 = 220
220   ans 220   ANSWER:220
Answer: B
If 1.5 x= 0.04 y, then the value of (y-x) (y+x) is: Select the correct option
A) 1405.25
B) 1305.25
C) 1205.25
D) 1505.25
E) 1605.25

Solution: let us assume x=1 and y=37.5   then 1.5(x)=0.04(y)   that is 1.5(1)=0.04(37.5)   = 1.5 =1.5   therfore from given equation (37.5-1)(37.5+1)   =(36.5)(38.5)   =1405.25   1405.25NSWER:1405.25
Answer: A
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 68 km downstream?
Choose the correct answer
A) 2 hours B) 3 hours C) 4 hours D) 5 hours E) None

Solution: Solution   Speed Downstream	= (13 + 4) km/hr   = 17 km/hr.   Time taken to travel 68 km downstream	=(68 / 17)= 
(68 / 17) = 4
4 hrs.   Answer 4 hours
Answer: C
9 men working 7 hours a day can complete a piece of work in 15 days. How many days can 6 men working for 9 hours a day, complete the same piece of work?	Choose the most appropriate option:	A) 15 ¾ days	B) 16 days	C) 16 ¾ days	D) 17 ½ days	E) 18 days

Solution: Explanation:   1 work done = 9 × 7 × 15   9 × 7 × 15 = 6 × 9 × ? days   ? days = 9 × 7 × 15/6 × 9   = 35/2 = 17 ½ days.   Answer: Option 17 ½ days
Answer: D
A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.	Choose the most appropriate option
A) 248
B) 140
C) 287
D) 167
E) 111

Solution: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 23060⋅x23060⋅x km and 22060⋅(x+2)22060⋅(x+2) km. From the equation: 23060⋅x=22060⋅(x+2)23060⋅x=22060⋅(x+2) we get x=28x=28 km/hr.   The intial speed of the biker is 28 km/h.   Half the distance between the two towns is   2h30min×28=2.5×28=702h30min×28=2.5×28=70.   So the distance is 2×70=1402×70=140 km.   Answer:140
Answer: B
A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?  Choose the correct option:
A) 1.9
B) 1.5
C) 1.1
D) 1.3
E) 1.2

Solution: 72 --- 9 DS = 8   ? ---- 1   45 ---- 9 US = 5   ? ---- 1 S = ?   S = (8 - 5)/2= 
(8 - 5)/2 = 3/2 = around 1.5
1.5   Answer: 1.5
Answer: B
The total surface area of a solid hemisphere of diameter 14 cm, is :  Choose the correct choice from the following choices.
A) 462 cm²	B) 530 cm²	C) 1345 cm²	D) 1788 cm²	E) None

Solution: Sol.   Total surface area = 3∏R² = [3 * 22/7 * 7 * 7= 
3 * 22/7 * 7 * 7 = 462
462 cm²   462 cm²nswer 462 cm²
Answer: A
Can you replace the question mark with the correct number, given the pair of numbers exhibits similar relationship?
? : 3839 :: 11 : 1209 Choose the correct answer: A) 6 B) 16 C) 26 D) 36 E) 46

Solution: Formular used :   pow(x,3) - pow(x,2) - 1   11*11*11 - 11*11 - 1   1331 - 121 - 1   1209   Similarly, we can solve   pow($x,3) - pow($x,2) - 1 = 3839   This condition holds true for number-16.   correct answer is 16)16
Answer: B
If the S.P of Rs. 24 results in a 20% discount on the list price, What S.P would result in a 30% discount on the list price?
Options.
A) Rs. 27 B) Rs. 21 C) Rs.20 D) Rs. 9 E) Rs. 10

Solution: Let the list price be Rs. X,   80/100*x = 24, x = 24*100/80= 
24*100/80 = 30
30   Required S.P= 70% of Rs. 30   = 70*30/100= 
70*30/100 = 21
21   ANSWER:Rs. 21
Answer: B
What is 10-8+6-4+...+(-18)?  Choose the most appropriate option:  A) -8  B) 10  C) 12  D) -4  E) 16

Solution: The expression considers all even numbers between 10 and -18 with alternate addition and subtraction of the numbers.   The numbers to be used are: 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, and -18.   Now, the first term is positive and the next term is subtracted. So, the required expression becomes,   10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10) - (-12) + (-14) - (-16) + (-18)   = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 - 18   = 58 - 62   = -4   Hence the correct answer choice is -4.
Answer: D
In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.76 per kg?
Select:  A) 5:8  B) 4:7  C) 3:7  D) 9:5  E) 5:2

Solution: (96-76)/(76-68)=20/8=5/2   ANSW5:2R:5:2
Answer: E
The sum of the non-prime numbers between 10 and 20, non-inclusive, is Choose the correct choice from the following answers.
A) 60 B) 75 C) 90 D) 105 E) 120

Solution: sum of consecutive integers from 11 to 19, inclusive ====> (A1 + An)/2 * # of terms = (11 + 19)/2 * 9 = 15 *9= 
15 *9 = 135
135   sum of non-prime numbers b/w 10 and 20, non inclusive===> 135 - 60 (i.e., 11 + 13 + 17 + 19, being the prime #s in the range) = 75   Answer: 75
Answer: B
Two persons start running simultaneously around a circular track of length 100 m from the same point at speeds of 5 km/hr and 13 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?	Choose the correct choice:
A) 20 sec  B) 37 sec  C) 17 sec  D) 23 sec  E) 27 sec

Solution: Time taken to meet for the first time anywhere on the track   = length of the track / relative speed   = 100 / (5 + 13)5/18 = 100* 18 / 18 * 5 = 20 seconds.   20 secnswer : 20 sec
Answer: A
At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?  Choose the correct answer: A) 5 min. past 7 B) 5(2/11) min. past 7 C) 5(3/11) min. past 7 D) 5(5/11) min. past 7 E) 5(5/11) min. past 8

Solution: When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.   At 7 o'clock, they are 25 min. spaces apart.   Minute hand will have to gain only 5 min. spaces.   55 min. spaces are gained in 60 min.   5 min. spaces are gained in 5(5/11) min.   ANSWER:5(5/11) min. past 7
Answer: D
A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest were 3% higher, then revenue earned would be 20% higher. What is the rate of interest? Choose the most appropriate option.
A) 24% p.a.  B) 4% p.a.  C) 12% p.a.  D) 15% p.a.  E) 18% p.a.

Solution: Let the rate of interest be x%.   Now it will be (x + 3)%   % increase = (((x + 3) - x)/x) * 100 = 20   => x = 15   ANSWER:15% p.a.
Answer: D
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?	Choose one:
A) 5/21	B) 5/22	C) 5/12	D) 5/29	E) 5/21

Solution: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)   As remaining person can be any one among three couples left.   Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅   = (10 * 6)/252 = 5/21   5/21nswer: 5/21
Answer: A
A company’s four cars running 8 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?  Choices:  A) 1200 lt  B) 1555 lt  C) 1664 lt  D) 1728 lt  E) 2160 lt

Solution: Given that   4 cars running 8 hrs a day consume 1200 lts. of fuel in 10 days.   1 car consumption per hour per day = 1200 /4 *8 *10 = 3.75 litre   Now question say new car consume 20% less fuel than the company’s four cars = 80/100 of 3.75 = 3 ( 20 percent less than 3.75)   Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 3*12 *6*5= 
3*12 *6*5 = 1_080
1080   similarly= old 4 car consumption for next 6 days for 12 hrs = 3.75*6*12*4= 
3.75*6*12*4 = 1_080
1080   hence total is= 1080+1080= 
1080+1080 = 2_160
2160 lt   Ans is 2160 lt .
Answer: E
Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of three rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?	Choose the correct choice from the following answers: A) 15 B) 30 C) 45 D) 60 E) 75

Solution: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.   The relative speed of Sandy and Molly is   3 - 1= 
  3 - 1 = 2
2 rounds per hour.   The time required to complete one round at this speed is 1/2 hours= 30 minutes.   The answer is 30.
Answer: B
If it takes 10 days to dig a trench 100 m long, 50 m broad and 10 m deep, what length of trench, 25 m broad and 15 m deep can be dug in 30 days ?
Choose the correct choice from the following
A) 400 m B) 200 m C) 100 m D) 88(8 / 9) m E) 89(8 / 9) m

Solution: We can dig a trench of 100*50*10 in 10 days. The volume of this trench is 50 000m^3. This means that 50 000 m^3 of dirt is moved every 10 days. Thus, it is found that 3(50 000) of dirt, or 150 000 m^3 of dirt is moved in 30 days. Since we know that the dimensions of this hole are 25, 15, and x and the volume is 150 000, we can create the equation 15*25*x=150 000. Solving for x, we find that the missing dimension is 400m   400 mNSWER:400 m
Answer: A
A rectangular field is 63 yards long and 21 yards wide. A fence is needed for the perimeter of the
field. Fencing is also needed to divide the field into three square sections. How many feet of fencing
are needed? (It is a good idea to make a drawing for this one.) Choose the correct choice from the following choices:
A) 630 ft
B) 530 ft
C) 430 ft
D) 330 ft
E) 230 ft

Solution: 63 + 21 + 63 + 21= 
63 + 21 + 63 + 21 = 168
168 yds. for   outside of field.   21 + 21= 
21 + 21 = 42
42 yds. for dividing sections    168 + 42= 
 168 + 42 = 210
210 yds. of fencing   210 x 3= 630 ft. of fencing   correct answer 630 ft
Answer: A
The equation (M + )/21 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale? Options:	A) P	B) P-7	C) P-8	D) P-6	E) P-5

Solution: M/21 =(P-7)/21   M = (P-7)*21/21   =(P-7)*1 = P-7   P-7
Answer: B
Series E(n) is such that i*E(i) = j*E(j) for any pair of positive integers (i, j). If E(1) is a positive integer, which of the following is possible?
I. 2*E(100) = E(99) + E(98)
II. E(1) is the only integer in the series
III. The series does not contain negative numbers  Choose the correct choice:
A) I only
B) II only
C) IIII only
D) IIIII only
E) I, IIIII

Solution: First thing I want to understand is this relation: i*E(i) = j*E(j) for any pair of positive integers. I will take examples to understand it.   When i = 1 and j = 2, E(1) = 2*E(2)   So E(2) = E(1)/2   When i = 1 and j = 3, E(1) = 3*E(3)   So E(3) = E(1)/3   I see it now. The series is: E(1), E(1)/2, E(1)/3, E(1)/4 and so on...   II and III are easily possible. We can see that without any calculations.   II. E(1) is the only integer in the series   If E(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except E(1)   III. The series does not contain negative numbers   Again, same series as above applies. In fact, since E(1) is a positive integer, this must be true.   I. 2*E(100) = E(99) + E(98)   2*E(1)/100 = E(1)/99 + E(1)/98 (cancel E(1) from both sides)   2/100 = 1/99 + 1/98   Not true hence this is not possible   Answer (IIIII only)
Answer: D
If a man walks to his office at 3/4 of his usual rate, he reaches office 1/3 of an hour later than usual. What is his usual time to reach office.  Choose the correct choice from the following choices:
A) 1⁄2 hr	B) 1 hr	C) 3⁄4 hr	D) 2 hrs	E) None of these

Solution: If new speed is a⁄b of original speed, then usual time × (b⁄a - 1) = change in time   ∴ usual time × (4⁄3 - 1) = 1⁄3   ⇒ usual time = 1⁄3 × 3 = 1 hr   Answer 1 hr
Answer: B
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?  Choices:
A) 250 m B) 260 m C) 240 m D) 270 m E) 280 m

Solution: D   270 m   Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 27 sec= 27 * 10= 
27 * 10 = 270
270 m.   The length of the faster train= 270 m.
Answer: D
An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 11 o'clock in the morning?	Select the correct option:
A) 30	B) 60	C) 90	D) 120	E) 150

Solution: The hour hand will move 3/12 of a circle.   (3/12)*360= 
(3/12)*360 = 90
90 degrees.   The answer is 90.
Answer: C
There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?	Choices
A) 120	B) 380	C) 400	D) 800	E) 250

Solution: Explanation:   The total number of stations = 20   From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.   20P2 = 20 * 19= 
20 * 19 = 380
380.   Answer: 380
Answer: B
Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 20 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?  Choose the correct choice from the following options.
A) 0.1  B) 0.6  C) 1  D) 1.5  E) 2

Solution: Option 0.6   20+20t=50t   t=0.6
Answer: B