mathewhe/aqua_rat huggingface dataset:
Question: The first term in a sequence is 1 and the second term is 15. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 35th term in the sequence?
(A) 8
(B) 15
(C) 35
(D) 70
(E) 135
Rationale: The third term is 8 since this is the average of 1 and 15.
Then the next terms will all be 8 since the average stays at 8.
The answer is A.
Answer: (A) 8
Question: Anne traveled from City A to City B in 4 hours, and her speed was between or equal to 25 miles per hour and 30 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between or equal to 25 miles per hour and 55 miles per hour. Which of the following could be the distance, in miles, from City A to City B?
(A) 95
(B) 108
(C) 125
(D) 160
(E) 180
Rationale: In four hours Anne must travel 4 times her speed
so Anne's possible distances =
4(25 -30) or 100-120 miles
in two hours John travels 2 times his speed or
2(25-55) or 50-110 miles
the statement is only true if both distances are possible,
so you can tell its between or equal to
100-110
B is the answer.
Answer: (B) 108
Question: 1, 4, 27, 16, ?, 36, 343
(A) 125
(B) 50
(C) 78
(D) 68
(E) 58
Rationale: The series consists of cubes of odd numbers and square of even numbers.
Answer : A.
Answer: (A) 125
Question: In the game of Dubblefud, red balls,blue balls and green balls are each worth 2, 4 and 5 points respectively. In a certain selection of balls,the product of the point values of the balls is 16,000. If the number of blue balls in this selection equals the number of green balls, how many red balls are in the selection?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: this is equivalent to :-
2x * 4y * 5z = 16000
y = z (given)
2x * 4y * 5y = 16000
2x * y^2 = 16000/20
2x * y^2 = 800
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 4 as
2* 4 * y^2 =800
y^2 = 100
y =10
Number of red balls = 4 hence D
Answer: (D) 4
Question: Three dice are thrown together, Find the probability of getting a total of 6?
(A) 1/12
(B) 3/31
(C) 2/9
(D) 1/9
(E) 5/108
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of 6 = 10
i.e. (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2).
Therefore, probability of getting a total of 6
P(E) = Number of favorable outcomes/Total number of possible outcome
= 10/216
= 5/108
Answer: (E) 5/108
Question: A polling company reports that there is a 30% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
(A) 10
(B) 6
(C) 8
(D) 4
(E) 5
Rationale: 30% - Candidate Elected
100%-60% = 40% - Candidate doesnotsigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
30% x 40% x 50%
0.3 x 0.4 x 0.5 = 0.06 = 6%
Answer (B)
Answer: (B) 6
Question: Bill has a small deck of 10 playing cards made up of only 2 suits of 5 cards each. Each of the 5 cards within a suit has a different value from 1 to 5; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 3 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: P(no pairs) = 8/9*6/8 = 2/3
P(at least one pair) = 1 - 2/3 = 1/3
The answer is B.
Answer: (B) 1/3
Question: A shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee. Find his net profit or loss percent?
(A) 33 1/8 %
(B) 33 7/3 %
(C) 50 %
(D) 33 5/8 %
(E) 34 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 24.
If he buys 6 a rupee, his CP = 4
He selling at 4 a rupee, his SP = 6
Profit = SP - CP = 6 - 4 = 2
Profit Percent = 2/4 * 100 = 50 %
Answer: C
Answer: (C) 50 %
Question: The average runs of a cricket player of 13 innings was 22. How many runs must he make in his next innings so as to increase his average of runs by 5?
(A) 92
(B) 42
(C) 64
(D) 76
(E) 84
Rationale: Explanation:
Average after 14 innings = 27
Required number of runs = (27 * 14) – (22 * 13)
= 378 – 286 = 92
ANSWER A
Answer: (A) 92
Question: If a light flashes every 30 seconds, how many times will it flash in 1/2 of an hour?
(A) 30
(B) 42
(C) 61
(D) 59
(E) 45
Rationale: There are 60 minutes in an hour.
In 1/2 of an hour there are (60 * 1/2) minutes = 30minutes.
In 1/2 of an hour there are (60 * 30) seconds = 1800 seconds.
Light flashed for every 30 seconds.
In 1800 seconds 1800/30 = 60 times.
The count start after the first flash, the light will flashes 61 times in 1/2 of an hour.
Answer:C
Answer: (C) 61
Question: A man can row a boat at 40 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/83 hours
(B) 80/13 hours
(C) 30/13 hours
(D) 30/23 hours
(E) 32/13 hours
Rationale: Speed downstream = 40 + 6 = 46 kmph.
Time required to cover 60 km downstream
= d/s = 60/46
= 30/23 hours.
Answer:D
Answer: (D) 30/23 hours
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be.
(A) 60 km/h
(B) 55 km/h
(C) 40 km/h
(D) 70 km/h
(E) 65 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=40/60hr=2/3hr
New speed = 40* 3/2 kmph= 60kmph
Answer : A
Answer: (A) 60 km/h
Question: 357 : 73 ::?
(A) 429 : 94
(B) 201 : 21
(C) 138 : 38
(D) 93 : 39
(E) 95 : 39
Rationale: 357 : 73
to get 2nd number,middle digit is removed, 1st & last interchanged their position of 1st no.
only option a) match this.
ANSWER:A
Answer: (A) 429 : 94
Question: The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
(A) 10.5
(B) 11.5
(C) 12.5
(D) 13.5
(E) None of these
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5 Answer: B
Answer: (B) 11.5
Question: How many total number of ways in which n distinct objects can be put into two different boxes is
(A) n2
(B) 2n
(C) 2n
(D) 3n
(E) None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the n objects. So, the total number of ways is
2 × 2 ×.....× 2 (n times ) = 2n
Answer B
Answer: (B) 2n
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.15000. A's share is?
(A) s.7500
(B) s.7200
(C) s.6000
(D) s.5000
(E) s.6750
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 15000 = 5000
ANSWER:D
Answer: (D) s.5000
Question: Tom opened a shop investing Rs.3000. Jose joined him 2 months later, investing Rs.4500. They earned a profit of Rs.5400 after completion of one year. What will be Jose's share of profit?
(A) 3000
(B) 2200
(C) 2309
(D) 2400
(E) 3200
Rationale: SoL = ~s- So Anju’s share = [5/9] x 5400 = 3000
A
Answer: (A) 3000
Question: A train running at 25 km/hr takes 40 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform.
(A) a) 200/3m175/3m
(B) b) 45m160m
(C) c) 50m45m
(D) d) 100/3 m200/3
(E) e) none of these
Rationale: Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/40*12=15/2m so the train covered a distance in 12 sec= 25*5/40*12=75/2
so the length of the train(Lt) is 15/2+75/2=45m
Now crossing the platform means length of train+length of platform(Lt+p)= 40*25*5/40=125m Now the length of platform (Lp) is= 125-45=80m
So answer is 45m and 80m Must beBeven though its mentioned 45m and 160m thinking so typo mistake...........
Answer: (B) b) 45m160m
Question: At a garage sale, all of the items were sold at different prices. If the price of a radio sold at the garage sale was both the 17th highest price and the 24th lowest price among the prices of the items sold, how many items were sold at the garage sale?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: There were 16 items sold at a higher price than the radio and 23 items sold at a lower price than the radio. Including the radio, there were 16 + 23 + 1 = 40 items sold.
The answer is C.
Answer: (C) 40
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y?
(A) 5
(B) 6
(C) 15
(D) 16
(E) 18
Rationale: Basically the length of an integer is the sum of the powers of its prime factors. For example the length of 24 is 4 because 24=2^3*3^1 --> 3+1=4.
Given: x+3y<1,000. Now, to maximize the length of x or y (to maximize the sum of the powers of their primes) we should minimize their prime bases. Minimum prime base is 2: so if x=2^9=512 then its length is 9 --> 512+3y<1,000 --> y<162.7 --> maximum length of y can be 7 as 2^7=128 --> 9+7=16.
Answer: D.
Answer: (D) 16
Question: Ravi alone can do a work in 25 dyas while Syam alone can do it in 20 days. Ram started the work and joined by Syam after 10 days. How long did the work last?
(A) 9 2/3 days.
(B) 10 2/3 days.
(C) 11 2/3 days.
(D) 16 2/3 days.
(E) 13 2/3 days.
Rationale: Ram's 1 day work =1/25 Ram's 10 days work =10/25 =2/5 Remaing work =1-2/5 =3/5 Syam's 1 day work =1/20, Part of work finished by both =1/25+1/20 =9/100 Total work done by both = 100/9 days. Therefore the remaining 3/5 of work done by both =100/9*3/5 =6 2/3 days. Therefore the work lasted for ( 10+6 2/3 ) days =16 2/3 days. Answer : D
Answer: (D) 16 2/3 days.
Question: A room is 6 meters 72 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.
(A) 107
(B) 126
(C) 117
(D) 136
(E) 147
Rationale: Let us calculate both the length and width of the room in centimeters.
Length = 6 meters and 72 centimeters = 672 cm
width = 4 meters and 32 centimeters = 432 cm
As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.
Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 672 and 432 = 48
Thus, the number of square tiles required = (672 x 432 ) / (48 x 48) = 14 x 9 = 126
Answer: B
Answer: (B) 126
Question: The average age of a class of 25 students is 26 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
(A) 40
(B) 41
(C) 52
(D) 62
(E) 73
Rationale: Total age of all students =25Ã—26
Total age of all students + Age of the teacher =26Ã—27
Age of the teacher
=27Ã—26âˆ’25Ã—26=26(27âˆ’25)=26Ã—2=52
Answer is C.
Answer: (C) 52
Question: A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
(A) 77 cm
(B) 10 cm
(C) 55 cm
(D) 33 cm
(E) 11 cm
Rationale: 30 * 20 * x
= (8 * 5.5 * 1.5)/2
Answer: B
Answer: (B) 10 cm
Question: The simple interest on a sum of money will be Rs. 600 after 10 years.If the principal is trebled after 5 years,what will be the total interest at the end of the tenth year ?
(A) Rs. 600
(B) Rs. 900
(C) 1200 rupees
(D) Rs. 1500
(E) None
Rationale: Solution
22.22
Let the sum be Rs. x. Now, S.I. = Rs. 600,T = 10 years.
Rate = % = (100x600/X x 10)% =(6000/X)%
S.I. for first 5 years = Rs.(X x 5 x 6000/X x 100) = Rs. 300.
S.I. for first 5 years = Rs. (3X x 5 x 6000/X x 100)= Rs. 900.
∴ Total interest = Rs. 1200.
Answer C
Answer: (C) 1200 rupees
Question: If 75 percent of a class answered the first question on a certain test correctly, 30 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 25%
(B) (8) 20%
(C) 30%
(D) 50%
(E) 65%
Rationale: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(75 - x) + x + (30 - x)] = 20 .......... values are in percent
x = 20 - 100 + 105
x = 25
Ans: A
Answer: (A) 25%
Question: 1, 4, 27, 16, ?, 36, 343
(A) 112
(B) 125
(C) 183
(D) 153
(E) 162
Rationale: B
125
The series consists of cubes of odd numbers and square of even numbers.
Answer: (B) 125
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 6 p.c?
(A) 28000
(B) 29000
(C) 37600
(D) 38000
(E) 40000
Rationale: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(94/100) = 37600
Option C
Answer: (C) 37600
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 12 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
(A) y/30
(B) 5/6*y
(C) 6/5*y
(D) 5y
(E) 12y/7
Rationale: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 12r and p = r+y
Substitute for p: 5(r+y) = 12r
Distribute: 5r + 5y = 12r
Subtract 5r from both sides: 5y = 7r
Plug back into the first equation: 5p = 12(5y/7)
Distribute: 5p = 60y/7
Divide both sides by 5: p = 12y/7
The answer is E.
Answer: (E) 12y/7
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 28
(B) 89
(C) 77
(D) 66
(E) 21
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer: B
Answer: (B) 89
Question: 0.363*0.522+0.363*0.478 = ?
(A) 0.522
(B) 0.845
(C) 0.363
(D) 0.985
(E) 0.885
Rationale: Given Expression= 0.363*(0.522+0.478)
= 0.363*1
= 0.363
ANSWER:C
Answer: (C) 0.363
Question: In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 340 points, how many points is the third question worth?
(A) 39
(B) 24
(C) 28
(D) 26
(E) 30
Rationale: x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
x+32
x+36
10x+180=340
10x=160
x=16
3rd question = x+8 = 16+8 = 24
Answer B
Answer: (B) 24
Question: For which of the following does p(a)−p(b)=p(a−b) for all values of a and b?
(A) p(x)=x^2
(B) p(x)=x/2
(C) p(x)=x+5
(D) p(x)=2x−1
(E) p(x)=|x|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. p(a) = a^2 and p(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. p(a) = a/2 and p(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B
Answer: (B) p(x)=x/2
Question: Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 2/3 of its own speed and got to its destination in 20 hours?
(A) 5.67 hrs
(B) 9.67 hrs
(C) 8.95 hrs
(D) 8.67 hrs
(E) 6.67 hrs
Rationale: New speed = 2/3 of usual speed
New time = 2/3 of usual time
2/3 of usual time = 20 hrs
Usual time = 20*2/3 = 13.33 hrs
Time saved = 22-13.33 = 8.67 hrs
Answer is D
Answer: (D) 8.67 hrs
Question: If x=kc and y=kt,then 2y+x =?
(A) k(t-c)
(B) k(c-t)
(C) c(k-t)
(D) k(2t+c)
(E) k(1-t)
Rationale: Just put in the given values of y and x
2y +x =2 kt +kc
Now take k common
2y + x = k(2t +c)
You get (D) as your answer.
Answer: (D) k(2t+c)
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is
(A) 16cm
(B) 25cm
(C) 15cm
(D) 35cm
(E) None of these
Rationale: Explanation:
So by now, you must be knowing this is a question of HCF, right.
H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.
Option D
Answer: (D) 35cm
Question: A train passes a station platform in 36 sec and a man standing on the platform in 21 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 225 m
(B) 240 m
(C) 187 m
(D) 176 m
(E) 186 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 21 = 315 m.
Let the length of the platform be x m . Then,
(x + 315)/36 = 15 => x = 225 m.
Answer:A
Answer: (A) 225 m
Question: A mixture of three edible oils is composed of olive oil, sunflower oil, and ground nut oil. How many ml of ground nut oil is required to make 5 liters of oil mixture containing twice as much olive oil as sunflower oil, and three times as much olive oil as groundnut oil?(1L=100ml)
(A) 300ml
(B) 1000ml
(C) 500ml
(D) 800ml
(E) 60ml
Rationale: 1L=1000ml
5L=5000ml
sunflower oil=2 olive oil
olive oil=3 groundnut oil
sunflower oil+olive oil+groundnut oil=5000
2 olive oil+olive oil+1/3 olive oil=5000
10 olive oil=5000
olive oil=500 ml
Answer is C
Answer: (C) 500ml
Question: A missile flies 6,000 miles at a speed of r mph. If the missile flies at a speed of r + 500 miles per hour, it would fly the same distance in 2 hours less. What is the value of r?
(A) 1,500 mph
(B) 1,000 mph
(C) 800 mph
(D) 1,200 mph
(E) 1,050 mph
Rationale: Equation: 6,000/r = 6,000/(r + 500) + 2
Plug options into the equation:
B fits: 6,000/1,000 = 6,000/(1,000+500) + 2
Answer: B
Answer: (B) 1,000 mph
Question: It would take one machine 7 hours to complete a large production order and another machine 6 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
(A) A 13/42
(B) B 12/42
(C) C 11/42
(D) D 10/42
(E) E 42/13
Rationale: The rate of the first machine is 1/7 job per hour;
The rate of the second machine is 1/6 job per hour;
Thus, the combined rate of the machines is 1/7+1/6=13/42 job per hour, which means that it takes 1/(13/42)=42/13 hours both machines to do the job.
Answer: D.
Answer: (D) D 10/42
Question: If each term in the sum W=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: Min value of 'n' can be 10 i.e 4*22+6*12 =W=> 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Answer: (C) 40
Question: A furniture dealer purchased a desk for $120 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) 70
(B) 66.67
(C) 65
(D) 75
(E) 80
Rationale: Anyway, in this question, there is no discount but the mark up is given as 40% of the selling price. So it is not 40% of $150 but instead, 40% of Selling price which is obtained by adding mark up to $120.
So if selling price is S,
120 + 40% of S = S
S = 200
Profit = 80 which is calculated on cost price in % terms. So 80/120 * 100 = 66.67% is profit.
B
Answer: (B) 66.67
Question: In an examination, 34% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
(A) 975
(B) 1150
(C) 1175
(D) 1243
(E) 1525
Rationale: Failed in 1st subject = 34*2500/100 = 850
Failed in 2nd subject = 42*2500/100 = 1050
Failed in both = 15*2500/100 = 375
Failed in 1st subject only = 850-375 = 475
Failed in 2nd subject only = 1050-375 = 675
Passed in either subject but not in both = 675+475 = 1150
Answer is B
Answer: (B) 1150
Question: If sy > 0 and yz < 0, which of the following must be negative:
(A) syz
(B) sy(z^2)
(C) s(y^2)z
(D) x(y^2)(z^2)
(E) (x^2)(y^2)(z^2)
Rationale: sy > 0 means that sy is positive.
yz < 0 means that yz is negative.
s(y^2)z = (sy)(yz) = positive*negative = negative. Thus option C is always negative.
Answer: (C) s(y^2)z
Question: The water level in a reservoir has been dropping at the rate of 12 inches per day. Exactly 5 days ago, the water level was at w inches. What will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same?
(A) w − 108
(B) w − 56
(C) w − 14
(D) w + 14
(E) w + 126
Rationale: Drop=12 inches/day
5 Days ago=w, means now it's equal w-60 and in 4 days = w-60-48=w-108
Answer A
Answer: (A) w − 108
Question: A cyclist rides a bicycle 8 km at an average speed of 11 km/hr and again travels 11 km at an average speed of 8 km/hr. What is the average speed for the entire trip?
(A) 8.58
(B) 8.76
(C) 9.04
(D) 9.12
(E) 9.25
Rationale: distance = 19 km
time = 8/11 + 11/8 = (64 + 121) / 88 = 185 / 88 hours
average speed = (19 * 88) / 185 = 9.04 km/h
The answer is C.
Answer: (C) 9.04
Question: A boy was asked to find 7/9 of a x. But he divided the x by 7/9, Thus he got 32 more than theanswer. Find the x.
(A) 60
(B) 41
(C) 51
(D) 63
(E) 56
Rationale: x/7/9 = 9x/7 = 32 + y
Actualy he should do 7x/9 = y
y = (9x/7) - 32
y = (9x - 224)/7
(9x - 224)/7 = 7x/9
81x - 2016 = 49x
81x - 49x = 2016
32x = 2016
x = 63
D
Answer: (D) 63
Question: Of the 120 passengers on Flight 750, 45% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?
(A) 44
(B) 48
(C) 46
(D) 52
(E) 56
Rationale: Number of passengers on flight = 120
Number of female passengers= .45*120 = 54
Number of passengers in first class = (10/100)* 120 = 12
Number of passengers in coach class = (90/100)* 120 = 108
Number of male passengers in first class = 1/3 * 12 = 4
Number of female passengers in first class = 12-4 = 8
Number of female passengers in coach class = 54 - 8 = 46
Answer C
Answer: (C) 46
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is
(A) 1 hour
(B) 2 hour
(C) 3 hour
(D) 4 hour
(E) 5 hour
Rationale: Let the duration of the flight be x hours.
Then, 600/x - 600/0.5x = 200
--> 600/x - 1200/(2x+1) = 200
--> x(2x + 1) = 3
--> 2x^2 + x - 3 = 0
--> (2x + 3)(x - 1) = 0
--> x = 1 hr.
Answer : A.
Answer: (A) 1 hour
Question: What is 12 percent of 80?
(A) 11.21
(B) 9.6
(C) 8.66
(D) 12.23
(E) 13.1
Rationale: We assume that 80 is 100%
assume 'x' is value we looking for
here,
80 = 100% and
x = 12 %
therefore,
80/x = 100%/12%
80/x = 8.33
x = 9.6
B
Answer: (B) 9.6
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 12
(B) 77
(C) 48
(D) 54
(E) 11
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 1.25 = 2 km = 2250 m.
Required time = 2250 * 3/125 = 54 sec.
Answer: D
Answer: (D) 54