MU-NLPC/Calc-aqua_rat huggingface dataset:
A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction W of the selected films are in color?	Choose the correct choice from the following answers:
A) 1/130	B) 1/5	C) 3/13	D) 10/13	E) 30/31

Solution: It's y/xpercentnot y/x.   If x=20 and y=10. Then:   20x=400 black-and-white films;   6y=60 color films.   y/x%=10/20= 
10/20 = 1/2 = around 0.5
0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.   Color films thus compose W 60/62=30/31 of the selected films.   Answer: 30/31.
Answer: E
he average of 25 numbers is zero. Of them, at the most, how many may be greater than zero? Answers.
A) 0 B) 1 C) 24 D) 19 E) 8

Solution: Average of 25 numbers = 0.   Sum of 25 numbers (0 x 25) = 0.   It is quite possible that 24 of these numbers may be positive and if their sum is a the 25th number is (-a).   Answer: Option 24
Answer: C
John tossed a fair coin 3 times. What is the probability that the outcome was “tails” exactly twice?
Choose the correct answer
A) 1/8 B) 1/4 C) 3/8 D) 1/2 E) 9/10

Solution: Total number of outcomes = 2*2*2= 
2*2*2 = 8
8   Number of favorable outcomes= Number of ways two places (for tails) can be chosen out of 3 slots = 3C2 = 3   So probability = 3/8   Alternative   Probability of getting tail in single toss = 1/2   Probability of getting head in single toss = 1/2   Probability of getting First Tail = 1/2   Probability of getting Second tail (Such that first tail has occurred, this incidentally is also the probability when first was head and second is tail) = 1/2 * 1/2 = 1/4   Probability of getting Third Head ( such that first was tail and second was tail) = 1/2 * 1/2 * 12 = 1/8   As you can notice the probability will be 1/8 whatever the sequence of Heads and tails.   We can arrange 2 Tails and one head in 3 ways (33/82 ways OR (3P3)/2! OR enumeration, whichever method you prefer to get here)   Since the favorable even can happen in either of these 3 ways, so Probability = 3 * 1/8 = 3/8   Answer:3/8
Answer: C
A machine can filled a tank in 25 minutes and another machine can empty it in 50 minutes. If the tank is already half full and both the taps are opened together, then the tank is filled in how many minutes?
Choose the correct choice from the following:
A) 25min B) 20min C) 10min D) 15min E) 30min

Solution: T = 1/2 (25*50 / 50-25) = 25 minutes   Tank is filled in 25 minutes   25minnswer is 25min
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 15 seconds. What is the length of the train?
Choose the correct choice from the following answers:
A) 120 metres B) 180 metres C) 324 metres D) 250 metres E) 180 metres

Solution: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train =	50 x 15/3 m = 250 m.   ANSWER : OPTION 250 metres
Answer: D
A committee of 5 is to be selected from among 5 boys and 4 girls. I how many ways can this be done if the committee is to consist of at-least one Girl?
what is the answer choice and how?  Choose the most appropriate option:
A) 105 B) 225 C) 209 D) 350 E) 455

Solution: I'm sure there is some problem with the question.   R U sure its atleast one boy and not atleast 1 boy and 1 girl?   if its 1 boy and 1 girl   62091*42091 + 62092*42092 + 62093*42093 + 62094*42094   6*4 + 15*6 + 20*4 + 15*1   24 + 90 + 80 + 15   209   209
Answer: C
In a class of 39 students 26 play football and play 20 long tennis, if 17 play above, many play neither?	Answers:
A) 6
B) 8
C) 10
D) 12
E) 14

Solution: 26 + 20 - 17= 
26 + 20 - 17 = 29
29   39 - 29= 
39 - 29 = 10
10 play neither   Answer is 10
Answer: C
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
Answers.
A) 28%	B) 25%	C) 23%	D) 45%	E) 15%

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   Answer: 25%
Answer: B
A certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ? Choose the correct choice from the following answers: A) 30% B) 33 1/2% C) 40% D) 60% E) 200%

Solution: Original visual range = 50 km   New visual range = 150 km   Percent increase in the visual range by using the telescope   = (150-50)/50 * 100%   = 2 * 100= 
2 * 100 = 200
200 %   Answer 200%
Answer: E
Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 60,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?	Choose the correct choice from the following options
A) 70,000 B) 60,000 C) 128,000 D) 90,000 E) 10,000

Solution: The distance traveled by each tyre:   4/5 * 1, 60, 000km = 128,000 km. 128,000
Answer: C
A vendor sold two things at same cost of 16 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much  Choose one
A) 0.60 loss
B) 0.70 loss
C) 0.80 loss
D) 0.50 loss
E) 0.40 loss

Solution: 0.80 lossP when profit of 25% = 12.8   0.80 lossP when loss of 20% = 20   Total 0.80 lossP = 32.8   Total SP = 32.00   Total loss = 0.80   ANSWER:0.80 loss
Answer: C
If PINTU is coded as 79523 in a certain code language, how would you code MINTU in the same language? Choose the most appropriate option.
A) 13426 B) 14236 C) 49523 D) 14263 E) 15263

Solution: 1 2 3 4 5 6 7 8 9   a b c d e f g h i   j k l m n o p q r   s t u v w x y z   sooo...MINTU is 49523...   ANSWER:49523
Answer: C
14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish Choose one:	A) 1 day	B) 2 days	C) 3 days	D) 4 days	E) 5 days

Solution: 14 men make toy in 5 days   after 1 day 14 more worker join   m1/m2=d2/d1   14/28=d2/4   =2 day   ANSWER:2 days
Answer: B
A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 61 unique alphanumeric case sensitive characters.
Choose the correct choice from the following choices:
A) 63^4
B) 62^5
C) 62(61^4)
D) 63(62^4)
E) 63(62^6)

Solution: Total number of passwords = number of 4 character password +number of 5 character password   = 61^4 + 61^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )   =61^4(1+ 61)   =61^4 * 62   Answer 62(61^4)
Answer: C
John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?	Choose the correct answer.
A) 16% B) 16.66% C) 18.23% D) 19% E) 19.12%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: B
John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $50. What is the percent decrease?
Answers:  A) 20%  B) 30%  C) 50%  D) 70%  E) 80%

Solution: The is always the difference between our starting and ending points. In this case, it’s 100 – 50 = 50. The “original” is our starting point; in this case, it’s 100. (50/100)*100 = (0.5)*100= 
(0.5)*100 = 50
50%.   50%
Answer: C
Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.4500. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?  Answers:
A) Rs.750, Rs.2250 B) Rs.2000, Rs.750 C) Rs.750, Rs.2000 D) Rs.800, Rs.1250 E) Rs.900, Rs.1250

Solution: Minu’s one day’s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18   Rs.750, Rs.2250nu’s wages: Binu’s wages: Minu’s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2   Minu’s share = Rs.4500* 2/12 = Rs.750   Rs.750, Rs.2250nu’s share = Rs.4500* 6 /12= 
.4500* 6 /12 = 0.225
Rs.2250   Rs.750, Rs.2250NSWER:Rs.750, Rs.2250
Answer: A
A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start? Choose the correct choice:
A) A)1.33
B) B)5
C) C)7
D) D)5
E) E)8

Solution: Explanation:   |-----------20--------------------|   55 40   D = 20   RS = 55 – 40 = 15   T = 20/15 = 1.33 hours   1.33nswer: Option 1.33
Answer: A
Ed and Flora drive at constant speeds toward each other on a highway. Ed drives at a constant speed of 31 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Ed is 120 km away from Flora at 6 am, and also 120 km away from Flora at 11 am, then how fast is Flora driving (in kilometers per hour)?  Options.
A) 13
B) 15
C) 17
D) 19
E) 21

Solution: Ed and Flora complete 240 km / 5 hours = 48 km/hour   Flora's speed is 48-31= 
48-31 = 17
17 km/hour   The answer is 17.
Answer: C
Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?	Select
A) 4 hrs 29 min B) 4 hrs 24 min C) 8 hrs 24 min D) 4 hrs 44 min E) 5 hrs 24 min

Solution: 1/4 + 1/5 = 9/20   20/9 = 2 2/9   9/20 * 2 = 9/10 ---- 4 hours   WR = 1 - 9/10 = 1/10   1 h ---- 1/4   ? ----- 1/10   2/5 * 60= 
2/5 * 60 = 24
24= 4 hrs 24 min   Answer:4 hrs 24 min
Answer: B
The area of the largest circle that can be drawn inside a square of side 98 Cm in length is:
Select:
A) 8600  B) 3646  C) 7546  D) 7636  E) 1606

Solution: Radius of required circle = 49 7546m   its area = 22/7 × 49 × 49   154 × 49 = 7546 7546m(power)2   Answer is 7546.
Answer: C
SI on a sum of money for 2yrs at 5% per annum is Rs.50, what is the CI on the same at the same rate & for the same time?
Choose the correct choice:
A) Rs. 34.24
B) Rs. 41.25
C) Rs. 51.25
D) Rs. 59
E) Rs. 65

Solution: Sum = Rs. 50 x 100 = Rs. 500.   2 x 5   Amount   = Rs. 500 x 1 +	5 2   100   = Rs. 500 x	21	x	21   20	20   = Rs. 551.25   C.I. = Rs. (551.25 - 500) = Rs. 51.25   Rs. 51.25
Answer: C
A bowl contains many kinds of fruit. In the bowl there are twice as many pears then there are oranges, and twice times as many plums as oranges. If the total number of pieces of fruit is X, then how many oranges are in the bowl as a fraction of X
Pick one.
A) X/2  B) X/3  C) X/4  D) X/5  E) X/6

Solution: Since X equals the number of fruit, X = pears + oranges + plums.   Since there are twice as many pears as oranges, then pears = 2*oranges.   Since there are twice as many plums as oranges, then plums = 2*oranges   Hence X = 2*oranges + oranges + 2*oranges, which simplifies to X = 5*oranges   Thus Oranges = X/5   Answer: X/5
Answer: D
man walks at speed of 8 km/h 300 mtrs length train crosses man in 30 sec from back, find speed of train?	Choose one:	A) 40 km/hr	B) 44 km/hr	C) 42 km/hr	D) 43 km/hr	E) 45 km/hr

Solution: if speed of train is x kmph, then   relative speed =(x-8 ) km/hr = (x-8)*5/18 m/sec   (x-8)*(5/18)*30=300   x-8=36   x= 44 km/hr   ANSWER:44 km/hr
Answer: B
What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?
Choose the correct choice from the following
A) 13m	B) 14m	C) 15m	D) 16m	E) NONE OF THESE

Solution: Explanation:   the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is   => mts.   13mNSWER IS 13m
Answer: A
Beginning in Town A, Biker Bob rides his bike 20 miles west, 6 miles north, 10 miles east, and then 18 miles north, to Town B. How far apart are Town A and Town B? (Ignore the curvature of the earth.)
Choose the correct choice from the following answers:
A) 28 miles  B) 30 miles  C) 26 miles  D) 18 miles  E) 22 miles

Solution: Using Pythagoras we have one side i,e total distance traveled in north direction = 18+6= 
18+6 = 24
24m   other being the base ie distance traveled west- distance traveled eat=20-10= 
20-10 = 10
10 m   now this third side or the distance between town A and Town B=24^2+ 10^2=sq root 676=26m   Answer : 26 miles
Answer: C
A sum of money lent out at S.I. amounts to Rs. 710 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is? Choose the correct choice
A) s.440
B) s. 586
C) s. 540
D) s. 740
E) s. 840

Solution: S.I for 5 years = (1020 - 710) = Rs. 310.   S.I. for 2 years = 310/5 * 2 = Rs. 124.   Principal = (710 - 124) = Rs. 586.   ANSWER:s. 586
Answer: B
Which of the following fractions is greater than 2/3? Choose one.
A) 1. 12/50	B) 2. 3/11	C) 3. 2/9	D) 4. 4/17	E) 5. 6/24

Solution: 1. 12/50   12.5/50 = 1/4 thus 12/50 < 1/4   2. 3/11   3/12 = 1/4 thus 3/11 > 1/4   3. 2/9   2/8 = 1/4 thus 2/9 < 1/4   4. 4/17   4/16 = 1/4 thus 4/17 < 1/4   5. 6/24   6/24 = 1/4   3. 2/9
Answer: C
A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
A. 20 B. 54 Pick one
A) 20  B) 27  C) 28  D) 22  E) 27

Solution: There are three ladies and five gentlemen and a committee of 5 members to be formed.   Number of ways such that two ladies are always included in the committee   = ⁶C₃ = (6 * 5 * 4)/6= 
(6 * 5 * 4)/6 = 20
20.   20nswer:20
Answer: A
Two numbers are respectively 40% and 60% more than a third number. What percentage is the first of the second?	Choose the correct choice:
A) 72% B) 87.5% C) 63.7% D) 56.9% E) 90%

Solution: Required answer = (100+x)/(100+y)*100 = 140*100/160= 
140*100/160 = 175/2 = around 87.5
87.5%   Answer is 87.5%
Answer: B
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?	Choose the correct choice from the following answers:
A) 12  B) 24  C) C is elder than A  D) Data inadequate  E) None

Solution: Solution   [(A+B) - (B+C)]	= 12   ‹=›A - C   = 12.   12nswer 12
Answer: A
Find a sum for first 7 prime numbers? Options:
A) 22	B) 58	C) 29	D) 32	E) 34

Solution: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17)= 
(2 + 3 + 5 + 7 + 11 + 13 + 17) = 58
58   Note: 1 is not a prime number   Option 58
Answer: B
Set Q consists of the following five numbers: Q = {5, 8, 11, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}	Choose the correct answer
A) I only
B) III
C) IIII
D) IIIII
E) I, II,III

Solution: (1)	Multiplying all the numbers change Standard Deviation   (2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.   If you observe Set I and III are added versions of Set Q .   Set I: 5 has been added to the Set Q   Set III: Subtract each element from 80 and you would find a number there in the Set Q.   Set II: elements are multiplied by 2 and standard deviation changes.   Hence the answer is IIIII.
Answer: D
A number when divided by a divisor leaves a remainder of 25. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? Choose the correct choice from the following answers:
A) 12
B) 13
C) 35
D) 38
E) 59

Solution: Let the number is N, the divisor = D,   I will make the two equations-   N = xD+25   2N = yD+11   where x and y are integers   Solving them: D(y-2x) = 38   as D is also integer and 38 is a prime number, the D should be 38 to satisfy the above equation.   Hence answer is '38'
Answer: D
Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/5 full, while jug Y is 4/7 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?	Choose the correct choice from the following:
A) 0 B) 1/15 C) 2/15 D) 1/20 E) 2/10

Solution: Suppose the water in each jug is L liters   CX x (1/5) = L   CX = 5L liters   CX is capacity of X   CY x (4/7) = L   CY = 7L/4 liters   CY is capacity of Y   Now, Y is 7L/4 - L empty = 3L/4 empty   So, we can put only 3L/4 water in jug Y from Jug X   Jug X's remaining water = L - 3L/4 = L/4   Fraction of X which contains water = water / CX   = (L/4)/ 5L   = 1/20   Answer will be 1/20
Answer: D
There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total? Select:
A) 700
B) 721
C) 702
D) 703
E) None of the above

Solution: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.   Answer 721
Answer: B
The area of a triangle is with base 4m and height 5m?  Select the correct option:
A) 11 B) 10 C) 787 D) 122 E) 12

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer: 10
Answer: B
If a and b are positive integers such that a/b = 1.92, which of the following must be a divisor of a?
Choose the correct answer
A) 19 B) 13 C) 9 D) 8 E) 15

Solution: 1) A and B are positive INTEGERS   2) A/B = 1.92   A = 192   B = 100   192/100= 
192/100 = 48/25 = around 1.92
1.92   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 96   B = 50   96/50= 
96/50 = 48/25 = around 1.92
1.92   Dividing by 2 again:    48/25= 
 48/25 = 48/25 = around 1.92
1.92   There is no other way to reduce this fraction, so A must be a multiple of 48 and B must be an equivalent multiple of 25. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 48, we have to 'factor-down' 48. This gives us (6)(8). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.   Answer: 9
Answer: C
If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 28, 19, 33 and 35 ?
Choose one:
A) 33 B) 25 C) 27 D) 24 E) 23

Solution: It is given that a quartile is the middle number of all numbers less than median..   so lets arrange the number in ascending order- 42, 24, 30, 22, 28, 19, 33 and 35   19, 22, 24, 28, 30 , 33, 35, 42...   numbers less than median are 19, 22, 24, 28..   the median of these numbers = center of 22 and 24 = 23   23
Answer: E
A car travels at a speed of 65 miles per hour. How far will it travel in 9 hours?  Choose the correct choice from the following choices:
A) 125 miles  B) 225 miles  C) 585 miles  D) 425 miles  E) 525 miles

Solution: During each hour, the car travels 65 miles. For 9 hours it will travel   65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65= 9 × 65 = 585 miles   correct answer is 585 miles) 585 miles
Answer: C
100 liter solution of cool-drink is made from 10% jasmine water. If 5 liters of jasmine and 10 liters of water were added to the solution, what percent of the solution is jasmine?  Choose the correct choice from the following choices:
A) 1/13  B) 2/23  C) 3/31  D) 4/15  E) 2/3

Solution: Denominator   100+5+10   115   Numerator   100*0.1= 
100*0.1 = 10
10--->Jasmine water     10+5= 
  10+5 = 15
15--->New content of Jasmine water in new solution   Ratio   3/23   Answer is 2/23
Answer: B
Which of these expressions has the greatest value? Choose the correct answer:
A) 1532672/1532676 B) 1423765/1423769 C) 1215672/1205679 D) 1823561/1823566 E) 1237842/1788545

Solution: Using elimination method on options   1215672/1205679 = 1.00828827574...   ANSWER:1423765/1423769
Answer: B
The product of two successive numbers is 7832. Which is the smaller of the two numbers?
Choose the most appropriate option:
A) 78  B) 68  C) 88  D) 97  E) 37

Solution: 88   88   From the given alternatives,   88 × 89 = 7832   ∴ Smaller number = 88
Answer: C
A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram? Choose one
A) 233 1/6  B) 833 1/3  C) 833 1/9  D) 833 1/6  E) 833 1/2

Solution: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.   If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.   How many grams he has to give instead of one kilogram(1000 gm).   120 gm ------ 100 gm   1000 gm ------ ?   (1000 * 100)/120 = 2500/3 = 833 1/3 grams.   Answer: 833 1/3
Answer: B
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?	Choose one.
A) 27 km
B) 26 km
C) 60 km
D) 28 km
E) 20 km

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1)   = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40   = 9/2 => x = 20 km.   Answer:20 km
Answer: E
0, 2, 4, 8, 12, 18, 24, 32, ?What number should replace the question mark?  Pick.
A) 24	B) 20	C) 40	D) 26	E) 47

Solution: 40 40add 2, 2, 4, 4,6, 6,.....
Answer: C
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The sum of the first 55 positive even integers is 2550. What is the sum of the even integers from 108 to 200 inclusive?
Select:
A) 5,100	B) 8,085	C) 10,100	D) 15,500	E) 20,100

Solution: even numbers from 94 to 200=108/2+1= 
108/2+1 = 55
55   Sum= (200+94)x55/2=8085   So 8,085 is the ans
Answer: B
If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ......... 1/[n(n+1)], for some positive integer n, what is the smallest value of n such that T>0,97?	Choose the correct choice from the following answers.
A) 29  B) 30  C) 31  D) 32  E) 33

Solution: we can break the T as : (n + 1 -n)/n(n+1)----for n=1 to n   1/n - 1/ n + 1   plug value ,1,2..n we will get a pattern   1-1/2---for 1   1/2-1/3--for 2   1/3-1/4--for 4   now work with options..   for 31,T =1- 1/32=30/31=0.968   for 32,T=1-1/33=0,9696   for 33,T=1-1/34=33/34-0.97   so 33 is correct answer
Answer: E
Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car?
Pick one.
A) 277	B) 266	C) 960	D) 77	E) 211

Solution: 60(x + 1) = 64x   X = 15   60 * 16= 
60 * 16 = 960
960 km   Answer960
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct choice:
A) 10 kmph B) 76 kmph C) 12 kmph D) 97 kmph E) 15 kmph

Solution: Speed of the boat in still water   = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph.   10 kmphnswer:10 kmph
Answer: A
In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate?	Choose the most appropriate option: A) 358000 B) 368000 C) 357000 D) 358000 E) 367000

Solution: Total number of invalid votes = 15 % of 560000   = 15/100 × 560000   = 8400000/100= 
8400000/100 = 84_000
84000   Total number of valid votes 560000 – 84000= 476000   Percentage of votes polled in favour of candidate A = 75 %   Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000   = 75/100 × 476000   = 35700000/100= 
35700000/100 = 357_000
357000   Answer:357000
Answer: C
The product of two numbers a and b equals one-quarter their average. What is a in terms of b?
Select the correct option:  A) a= b/(8b-1)  B) a= b/(7b-1)  C) a= b/(8b)  D) a= b/(8b-4)  E) a= 2b/(8b-1)

Solution: a*b = ( a+b)/8   8ab =a+b   a= b/(8b-1)   a= b/(8b-1)NSWER:a= b/(8b-1)
Answer: A