mathewhe/aqua_rat huggingface dataset:
Question: Anand starts from a point P towards point Q, where PQ = 50 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
(A) (45/7) kmph
(B) (100/21) kmph
(C) (40/7) kmph
(D) (30/7) kmph
(E) (65/7) kmph
Rationale: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (50-x) km
Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph
So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km
And between their first meeting point and second, they both together covered a distance of 2(90-x) km.
2x+3x=2(50-x)
5x=100-2x
7x=100
x=100/7 km
Anand's speed=x/3=100/(3*7)=100/21 kmph
Ans:B
Answer: (B) (100/21) kmph
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 2 second to produce a bolt but 1 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?
(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,000 seconds
(E) 3,000 seconds
Rationale: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.
Two machines to produce 1,000 bolts will need (1,000*2)/2 = 1,000 seconds.
Two machines to produce 1,000 nuts will need (1,000*1)/2 = 500 seconds.
Total = 1,000 + 500 = 1,500.
Answer: B.
Answer: (B) 1,500 seconds
Question: An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?
(A) 10.29
(B) 10.25
(C) 10.27
(D) 10.24
(E) 10.21
Rationale: Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5
S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = %.
Answer: B
Answer: (B) 10.25
Question: total num of pupiles in 3 grades of scholl is 333 . the no of pupiles in grades 1 and 2 are un 3:5 ratio and 2 and 3 grades are 7:11 ratio .what is the strength of class that has highest no of pupils
(A) 145
(B) 155
(C) 165
(D) 175
(E) 185
Rationale: Ratio G1:G2=3:5 and G2:G3=7:11
So G1:G2:G3=21 : 35 : 55
Let the strength of three classes are 21x, 35x and 55x respectively, then 21x+35x+55x= 333
=> 111x= 333 or x=3
So strength of the class with highest number of pupils=55x=55*3= 165
ANSWER:C
Answer: (C) 165
Question: On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 2 is how many times as great as the frequency corresponding to a reading of 8?
(A) 40
(B) 50
(C) 10^4
(D) 10^5
(E) 10^6
Rationale: If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 2 to 3 it will be 10
if Richter scale reading goes from 3 to 4 it will be 10
if Richter scale reading goes from 4 to 5 it will be 10
if Richter scale reading goes from 5 to 6 it will be 10
Similarly if Richter scale reading goes from 6 to 7 it will be 10
and if Richter scale reading goes from 7 to 8 it will be 10
so it will from 2 to 8 i.e 3,4,5,6,7,8 = 10*10*10*10*10*10 = 10^6
Answer is E
Answer: (E) 10^6
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 9 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) 23 years
Rationale: Explanation:
Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
54 - x = 5x - 30
6x = 84
x = 14.
Son's age after 9 years = (x+ 9) = 23 years..
Answer: E
Answer: (E) 23 years
Question: What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage?
(A) 96.9
(B) 96.3
(C) 96.2
(D) 96.7
(E) 96.21
Rationale: Explanation:
Use the formula,
CP= 100 – discount + brokerage%
CP= 100-4+1/5
96.2
Thus the CP is Rs 96.2.
ANSWER: C
Answer: (C) 96.2
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many F cents does a liter of kerosene cost? [One dollar has 100 cents.]
(A)  0.33
(B)  0.44
(C)  0.55
(D)  44
(E)  55
Rationale: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $
Just multiply by 100, Answer F= 44.D
Answer: (D)  44
Question: Dana borrows 4000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after four years of college?
(A) 11100
(B) 11260
(C) 12050
(D) 12156
(E) 12160
Rationale: dana borrows 4000 and returns 2% per month.
so returns 80 per month. and 960 per year.
so dana owes 4000-960=3040 per year.
after 4 years she will owe 12160.
Ans (E)
Answer: (E) 12160
Question: If 60% of 3/5 of a number is 18, then the number is?
(A) 80
(B) 100
(C) 75
(D) 50
(E) None of these
Rationale: Let the number be x. Then 60% of 3/5 of x=18
60/100*3/5*x=18
x=(18*25/9)=50
Required number=50.
Correct Option: D
Answer: (D) 50
Question: A diner is having lunch at a salad bar. There are two types of lettuce to choose from, as well as four types of tomatoes, and five types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 2*4*5 = 40
The answer is D.
Answer: (D) 40
Question: A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
(A) $150.000
(B) $160.000
(C) $132.000
(D) $148.000
(E) $176.000
Rationale: 6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x.
Answer: (D) $148.000
Question: With an average speed of 40 km/hr a car takes 7 hrs to reach a certain distance. With what speed will it be able to cover the same distance in 5 hours ?
(A) 46 km/hr
(B) 56 km/hr
(C) 58 km/hr
(D) 48 km/hr
(E) 54 km/hr
Rationale: 40:x= 5:7, x being the speed of the car. ie) 5x =40*7/5 =56 The speed of the car =56 km/hr Answer : B
Answer: (B) 56 km/hr
Question: Efficiency with which Adam and Mike work is in the ratio 2:1. How much time will they, working together, take to complete a job which Adam alone could have done in 10 days?
(A) 15 days
(B) 20 days
(C) 6 days
(D) 6 1â„3 days
(E) None of these
Rationale: Ratio of times taken by Adam and Mike = 100 : 200 = 1 : 2.
Suppose Mike takes x days to do the work.
Then, 1 : 2 : : 10 : x â‡’ x = (10Ã—2)/1 â‡’ x = 20
Adamâ€™s 1 dayâ€™s work = 1â„10; Mikeâ€™s 1 days work = 1â„20
(Adam + Mike)â€™s 1 dayâ€™s work = (1â„10 + 1â„20) = 3â„20
âˆ´ Adam and Mike together can complete the job in 20â„3 days or 6 2â„3 days.
Answer E
Answer: (E) None of these
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 22
(B) 66
(C) 30
(D) 77
(E) 12
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
== (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: (C) 30
Question: A box contains 2 red, 3 yellow. 2 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
(A) 2/3
(B) 3/5
(C) 2/5
(D) 1/3
(E) 2/7
Rationale: Total number of balls = 3+2 = 5
n(S) = 5C2 = 5*4 / 2 = 10
n(E) = 2C1 * 3C1 = 2*3 = 6
Probability = 6/10 = 3/5
Answer is B
Answer: (B) 3/5
Question: If 6 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in
(A) day
(B) days
(C) days
(D) days
(E) days
Rationale: The length of cloth painted by one boy in one day = 48 / 6 × 2 = 4 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 4 × 6 = 3/2 day.
A)
Answer: (A) day
Question: A certain amount earns simple interest of Rs. 1750 after 7 years.Had the interest been 2% more,how much more interest would it have earned ?
(A) Rs. 35
(B) Rs. 245
(C) Rs. 350
(D) Cannot be determined
(E) None
Rationale: Solution
We need to know the S.I. , Principal and time to find the rate.Since the principal is not given,so, data is inadequate.
Answer D
Answer: (D) Cannot be determined
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 2 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 30
(C) 43
(D) 45
(E) 10
Rationale: Ans.(E)
Sol. Number of choices to go by ship = 2 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 2 x 5 = 10 ways
Answer: (E) 10
Question: Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 57.2 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
(A) 1.3
(B) 1.0
(C) 1.1
(D) 10.5
(E) 41.8
Rationale: Change in production of motor vehicles = 57.2 - 3.9 = 53.3 million in 41 years (1987 - 1946)
average increase per year = 53.3/41 = 1.3 million (apporx.)
Answer (A)
Answer: (A) 1.3
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 28.9 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
(A) 16.2
(B) 16.4
(C) 16.6
(D) 16.8
(E) 17.0
Rationale: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 28.9
x^2=2.89
x=1.7
At 4:00 pm, the amount of bacteria was 10(1.7)=17 grams.
The answer is E.
Answer: (E) 17.0
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 11/4 days
(B) 16/4 days
(C) 18/4 days
(D) 15/4 days
(E) 13/4 days
Rationale: D
15/4 days
3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Answer: (D) 15/4 days
Question: The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit H on the height of vehicles that are allowed to use the tunnel?
(A) 5½ ft
(B) 7½ ft
(C) 8 ½ ft
(D) 9½ ft
(E) 10 ft
Rationale: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.
We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.
Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).
Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).
Finally: AB=8, so the correct answer H is 8 - .5 = 7.5... choose (B)!
From a strategic guessing point of view, as soon as we realize that the height of the tunnel is 10 in the middle, we should quickly eliminate (D) and (E) as too big; worse case you have a 1/3 shot at picking up the points.B
Answer: (B) 7½ ft
Question: Statements: In a one day cricket match, the total runs made by a team were 200. Out of these 160 runs were made by spinners.
Conclusions:
1) 80% of the team consists of spinners.
2) The opening batsmen were spinners.
(A) Only conclusion I follows
(B) Only conclusion II follows
(C) Either I or II follows
(D) Neither I nor II follows
(E) Both I and II follow
Rationale: According to the statement, 80% of the total runs were made by spinners. So, I does not follow. Nothing about the opening batsmen is mentioned in the statement. So, II also does not follow.
D
Answer: (D) Neither I nor II follows
Question: At 3.40, the hour hand and the minute hand of a clock form an angle of
(A) 378
(B) 277
(C) 297
(D) 267
(E) 130
Rationale: Sol:
Use formula θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|
Angle = 30×3 – 11/2 × 40 = 90 – 220 = 130°
Answer:E
Answer: (E) 130
Question: In 1982 and 1983, Company B’s operating expenses were $13.0 million and $15.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
(A) 3%
(B) 46 1/6%
(C) 25%
(D) 33 1/3%
(E) 60%
Rationale: Profit in 1982 = 15.6 - 13 = 2.6 million $
Profit in 1983 = 18.8 - 15 = 3.8 million $
Percentage increase in profit = (3.8-2.6)/2.6 * 100 %
= 46 1/6 %
Answer B
Answer: (B) 46 1/6%
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.815 per pound?
(A) 1:3
(B) 1:2
(C) 6:1
(D) 2:1
(E) 3:1
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.815
0.9 – 0.1x = 0.815
x = 0.85
Thus ratio of both flours is 6:1
C
Answer: (C) 6:1
Question: A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 37.5
(B) 32.25
(C) 24.45
(D) 26.46
(E) 27.35
Rationale: Explanation:
g% = 15 + 15 + (15*15)/100
= 32.25%
Answer: B
Answer: (B) 32.25
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 460 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
(A) 8/3
(B) 3/8
(C) 8/5
(D) 5/8
(E) 40/23
Rationale: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 600/3 = 200 km/hour
Distance traveled by Freddy = 460 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 460/4 = 115 km/hour
Ratio of average speed of Eddy to Freddy = 200/115 = 40/23
Answer E
Answer: (E) 40/23
Question: The odds against ram solving the problem are 4 to 5 and the odds in favour of krishna solving the same are 7 to 5. What is the chance that it will be solved when they both try?
(A) 1/4
(B) 5/21
(C) 16/21
(D) 23/28
(E) 22/27
Rationale: Odds against Ram are 4:5 so probability that he will solve the problem is 5/9.
Odds in favor of Krishna are 7:5 so probability that he will solve it is 7/12
It will be solved means that either Ram or Krishna or both will be able to solve it.
P(A or B) = P(A) + P(B) - P(A and B) = 5/9 + 7/12 - (5/9)*(7/12) = 22/27
E
Answer: (E) 22/27
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 450 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?
(A) $ 1.50
(B) $ 1.88
(C) $ 2.25
(D) $ 2.50
(E) $ 3.25
Rationale: 7 regular days --> sales = 7*32*x = 224x;
3 hot days --> sales = 3*32*(1.25x) = 120x;
Total sales = 224x+120x = 344x.
Total cost = 10*32*0.75 = 240.
Profit = 344x - 240 = 450 --> x=2.
1.25x=~2.50.
Answer: D.
Answer: (D) $ 2.50
Question: In a 2 digit no unit's place is halved and tens place is doubled. diff bet the nos is 37.digit in unit's place is 2 more than tens place.
(A) 36
(B) 46
(C) 56
(D) 66
(E) 76
Rationale: let tenth place digit be x & unit place be y
then no. is = 10x + y
if unit place is halved and tens place is doubled
then no. is = 10*2x + y/2
10*2x + y/2 -(10x+y)=37
=> 10x - y/2 = 37 .....(1)
and, y-x=2 ....(2)
solving, x=4,y=6
no. is 46
ANSWER:B
Answer: (B) 46
Question: The ratio between the perimeter and the width of a rectangle is 5:1. If the area of the rectangle is 294 square centimeters, what is the length of the rectangle in centimeters?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: Perimeter = 2(W+L) = 5W
3W = 2L
W = 2L/3
WL = 294
2L^2/3 = 294
L^2 = 441
L = 21 cm
The answer is C.
Answer: (C) 21
Question: Using all the letters of the word "LAKSHMI", how many words can be formed, which begin with L and end with I?
(A) 111
(B) 145
(C) 110
(D) 119
(E) 120
Rationale: There are five letters in the given word.
Consider 7 blanks ....
The first blank and last blank must be filled with L and I all the remaining three blanks can be filled with the remaining 5 letters in 5! ways.
The number of words = 5! = 120.
Answer:E
Answer: (E) 120
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but the last one contained 8 books and that last shelf contained 7 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
12x - 21 = 8(x-1) + 7
4x = 20
x= 5
The answer is A.
Answer: (A) 5
Question: If a 3-digit integer is selected at random from the integers 700 through 899, inclusive, what is the probability that the second digit is one greater then the first digit, and the third digit is one greater than the second digit?
(A)  2/225
(B)  2/200
(C)  8/700
(D)  1/50
(E)  1/200
Rationale: Hundreds digit can be 7 or 8
If the hundreds digit is 7, then the tens digit has to be 8 and the units digit has to be 9
If the hundreds digit is 8, then the tens digit has to be 9 and the units digit has to be 10
A digit has to fall between 0 and 9, so 10 cannot be a digit
The number is 789
Total numbers between 700 and 899 = (899-700)+1 = 200
Probability = 1/200
Answer E
Answer: (E)  1/200
Question: 2, 5, 10, 17, 26, 37, 50, 64
(A) 50
(B) 26
(C) 37
(D) 64
(E) 55
Rationale: Solution
The pattern is x2 +1,where x=1,2,3,4,5,6,7,8 etc.But,64 is out of pattern. Answer D
Answer: (D) 64
Question: In the first M games of a team's season, the ratio of the team's wins to its losses was 3:1. In the subsequent N games, the ratio of the team´s wins to losses was 1:4. If M:N = 4:5, what was the ratio of the team's wins to its losses for all M+N games?
(A) 1:2
(B) 2:3
(C) 3:4
(D) 4:5
(E) 5:6
Rationale: M = 4/9 of total games
N = 5/9 of total games
Wins = 3/4*4/9 + 1/5*5/9 = 3/9 + 1/9 = 4/9
Losses = 1 - 4/9 = 5/9
The ratio of wins to losses is 4:5.
The answer is D.
Answer: (D) 4:5
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
(A) 1500
(B) 2000
(C) 300
(D) 8000
(E) 500
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
Answer : D
Answer: (D) 8000
Question: The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
(A) 75 Kg
(B) 50 Kg
(C) 85 Kg
(D) 90 Kg
(E) 60 KG
Rationale: Explanation:
Total increase in weight = 10 Ã— 2.5 = 25
If x is the weight of the new person, total increase in weight = xâˆ’65
=> 25 = x - 65
=> x = 25 + 65 = 90
Answer: Option D
Answer: (D) 90 Kg
Question: Each of the following numbers has a remainder of 2 when divided by 13 except:
(A) 15
(B) 28
(C) 42
(D) 54
(E) 67
Rationale: It's C
42 = 13*3+3
Answer: (C) 42
Question: 8 bottles need to be arranged togather. 2 of the bottles contain milk and 2 other contain water must sit togather. In how many arrangements can the bottles be arranged?
(A) A.1296
(B) B.1850
(C) C.2880
(D) D.3546
(E) E.4200
Rationale: Glue milk and water bottlestogether: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each bottle within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: C.
Answer: (C) C.2880
Question: What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?
(A) Rs. 14705.24
(B) Rs. 14602.25
(C) Rs. 14822.26
(D) Rs. 14322.10
(E) Rs. 15350.23
Rationale: Explanation:
Amount after 3 years = P(1+R/100)T=40000(1+11/100)3
=40000(111/100)3=40000×111×111×111/100×100×100
=4×111×111×111/100=54705.24
Compound Interest = 54705.24 - 40000 = Rs. 14705.24
Answer : Option A
Answer: (A) Rs. 14705.24
Question: Find the odd man out. 1050, 510, 242, 103, 46, 16, 3
(A) 103
(B) 106
(C) 510
(D) 1050
(E) None of these
Rationale: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 103. Answer : Option A
Answer: (A) 103
Question: In a class test, out of N students, if only 1/3 of passed in science and, of those who passed in science subject, 1/5 also passed in maths subject, how many students did not pass in both subjects ?
(A) N/15
(B) 4N/15
(C) 14N/15
(D) N/5
(E) 4N/5
Rationale: 1/3 of tested passed in Science, thus N/3 had passed in science.
Of those who passed in science, 1/5 also had passed in maths, thus 1/5*N/3 = N/15 had passed in both subjects.
Therefore, N - N/15 = 14N/15 did not pass in both subjects.
Answer: C.
Answer: (C) 14N/15
Question: Distance between A and B is 54 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 3 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 2 mph, in the second hour it was 2.25 mph, in the third hour it was 2.5 mph, and so on. How fast was B walking when the two men finally meet?
(A)  3 mph
(B)  3.5 mph
(C)  4 mph
(D)  4.5 mph
(E)  5 mph
Rationale: Since the question is about speed, we know the answer will be in rate, which in this case is miles per hour.
In such questions, look for the symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 3 mph and distance is 54 miles. So this means that A would take a total of 54/3 = 18 hours to cover the distance from A to B. So, if B's speed were also 3, both A and B would travel for 9 hours to meet in the middle.
B has uniform speed per hour so its average will be the simple average of all speeds: 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5...
and since 3 is actually right in the middle of the 9 speeds, both A and B will end with same average speed, and will meet after 9 hours.
Once this is determined, see what the final speed of B (during the ninth hour) is. In this case, B's speed during the ninth hour was 4 mph, so the correct answer is (C): 4 mph.
Answer: (C)  4 mph