mathewhe/aqua_rat huggingface dataset:
Question: The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: The question basically asks how many minutes it takes for a population to increase by factor 200 (200,000 / 1,000 = 200).
Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:
2^x >= 200, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^8 = 256, i.e. the population has to double 8 times.
Since it takes the population 2 minutes to double once it takes 8*2 minutes = 16 minutes to double 8 times.
Thus, solution D = 16 is correct.
Answer: (D) 16
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long?
(A) 65sec
(B) 70sec
(C) 74sec
(D) 80sec
(E) 85sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 500)/10 = 74 sec.
Answer:C
Answer: (C) 74sec
Question: The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?
(A) 40°
(B) 49°
(C) 43°
(D) 41°
(E) 42°
Rationale: Explanation:
The temperature for first 4 days = 4 * 36 = 144
The temperature for last 4 days = 4 * 38 = 152
The difference between the temperatures is (152 – 144) = 8
The ratio of temperature between first and fifth day is 4 : 5
The temperature on fifth day is 5*8 = 40
ANSWER: A
Answer: (A) 40°
Question: A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?
(A) 9
(B) 18
(C) 27
(D) 36
(E) 34
Rationale: all sparrows bt six i.e. those six can b 3 pigeons and 3 ducks,
similarly the other 2 conditions will apply..
ANSWER:A
Answer: (A) 9
Question: Find the number which multiplied by 15 is increased by 196.
(A) 14
(B) 20
(C) 26
(D) 28
(E) 27
Rationale: Let the number be x. Then,
15x - x = 196
x = 14
ANSWER:A
Answer: (A) 14
Question: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tom is what percent lesser than the quantifying chopped by Tammy?.
(A) 44%
(B) 100%
(C) 105%
(D) 225%
(E) 125%
Rationale: Tom chops 4 lbs in 6 minutes
Tammy chops 9 lbs in 6 minutes
So in the same amount of time, Tom chops 125% less than Tammy, since 9 is 125% greater than 4. So 125% is the answer.
Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.
Ans:E
Answer: (E) 125%
Question: If a randomly selected non-negative single digit integer is added to {2, 3, 4, 8}. What is the probability that the median of the set will increase but the range still remains the same?
(A) 0.2
(B) 0.3
(C) 0.4
(D) 0.5
(E) 0.6
Rationale: We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.
Hence, the total number of outcomes is 10.
We need to find the probability that the median of the set will increase but the range still remains the same.
The median of the set is (3 + 4)/2 = 3.5, thus the number selected must be 4 or greater.
For the range to remain the same, the number must be between 2 and 8 inclusive.
To satisfy both conditions, the number selected must be 4, 5, 6, 7, or 8.
The probability is 5/10 = 0.5
The answer is D.
Answer: (D) 0.5
Question: In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 5 people read all three newspapers. Find the minimum number of people who read both A and B but not C.
(A) A)1
(B) B)2
(C) C)3
(D) D)0
(E) E)5
Rationale: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.
A and B and C is 5 - that means A and B is at least 5. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C
A and B but not C = |A|-|B| - 5
So i would pick A=25 and B =50 to minimize the value to a 0. (ANS D)
Answer: (D) D)0
Question: 6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week
(A) 6500
(B) 6580
(C) 7200
(D) 7120
(E) 6800
Rationale: 6% of customers do not pay taxes.
6/100 * 1000 customers do not pay taxes.
6/100 * 1000 = 60
Therefore 1000 - 60 customers do pay taxes.
1000 - 60 = 940
940 * 7 days per week = 6580
B)
Answer: (B) 6580
Question: A taxi owner buys diesel at Rs.8.50, Rs. 9 and Rs. 9.50 per litre for three successive years. What approximately is the average cost per litre of diesel if he spends Rs. 5000 each year?
(A) 7.98
(B) 8.98
(C) 9.98
(D) 6.98
(E) 8.12
Rationale: Total Cost = 5000 × 3=15000
Total diesel used = 5000/8.50 + 5000/9 +5000/9.50
=588+555+527
=1670
Average cost per litre of diesel=15000/1670
=8.98
ANSWER:B
Answer: (B) 8.98
Question: With the wind, an airplane travels 1120 miles in seven hours. Against the wind, it takes eight hours. Find the rate of the plane in still air and the velocity of the wind.
(A) 10 kmph
(B) 11 kmph
(C) 12 kmph
(D) 13 kmph
(E) 14 kmph
Rationale: 1120 miles in seven hrs that means up speed is 1120/7=160.
for against the wind 1120 miles in 8 hrs so down speed 1120/8=140.
now plain speed in still air=1/2(160+140)=150 kmph
wind speed=1/2(160-140)=10 kmph
ANSWER:A
Answer: (A) 10 kmph
Question: x = 13.165
y = 7.496
z = 11.557
The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?
(A) 0.01
(B) 0.02
(C) 0.03
(D) 0.1
(E) 0.2
Rationale: Rounding off the values:
x = 13.17
y = 7.50
z = 11.56
A = 13.17 + 7.50 + 11.56= 32.23
x + y + z = 13.165 + 7.496 + 11.557 = 32.206
B = 32.21
A - B = 0.02
Option B
Answer: (B) 0.02
Question: If a 3-number code is formed of the integers from 1 to 14 inclusively, and each of the numbers in the code is different, how many possible codes are there?
(A) 1744
(B) 1854
(C) 1964
(D) 2074
(E) 2184
Rationale: 14*13*12=2184
The answer is E.
Answer: (E) 2184
Question: If a car travels a distance of 300 km in 8 hours, partly at a speed of 40 kmh-1 and partly at 30 kmh-1, what is the distance it travelled at the speed of 40 kmh-1?
(A) 200 km
(B) 210 km
(C) 220 km
(D) 240 km
(E) 250 km
Rationale: let the distance travelled at 40 kmph=x km
distance travelled at 30 kmph =300-x km
x/40 + (300-x)/30 = 8
x = 240
ANSWER:D
Answer: (D) 240 km
Question: If the length of the longest chord of a certain circle is 18, what is the radius of that certain circle?
(A) 2.5
(B) 9
(C) 10
(D) 15
(E) 20
Rationale: Longest chord of a circle is the diameter of the circle
diameter = 2 * radius
If diameter of the circle is given as 18 = 2 * 9
so radius of the circle = 9
correct answer - B
Answer: (B) 9
Question: Nick took a bus from home to market, that travels at 80 kmph. While walking back at 8 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph. Find the average speed.
(A) 49.5 kmph
(B) 49.0 kmph
(C) 48.5 kmph
(D) 48.0 kmph
(E) none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/80, by walking =x/8, by cycling = x/60 hours
:. Average speed = Total Distance/Total time
= 8x / x/40 + x/8 + x/60
= 8 *60 / 1.5+7.5+1
= 12.0
ANSWER:D
Answer: (D) 48.0 kmph
Question: At the faculty of Aerospace Engineering, 310 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
(A) 430
(B) 432
(C) 440
(D) 442
(E) 446
Rationale: 310 + 232 - 112 (since 112 is counted twice )= 430
A is the answer
Answer: (A) 430
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?
(A) 52%
(B) 64%
(C) 72%
(D) 76%
(E) 80%
Rationale: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: (A) 52%
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 176 m
(B) 189 m
(C) 245 m
(D) 189 m
(E) 197 m
Rationale: Speed = (45 * 5/18) m/sec
= (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X)
= 750 ==> X = 245 m.
Answer:C
Answer: (C) 245 m
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 40%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
Rationale: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 40%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer B.
Answer: (B) 50% decrease
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $8.00 per hour and a standard tip rate of 30% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 1120
(B) 300
(C) 320
(D) 350
(E) 400
Rationale: Jill earns 8 dollars/hour and the hourly tip is (3/10)*40.
Jill thus earns 8*14+14*12 per day(or 8(14)+12(14)=20(14)=280).
Jill has worked for 4 days -> 280*4=1120.
This matches answer choice A.
Answer: (A) 1120
Question: Which number is a factor of 20?
(A) 3
(B) 4
(C) 7
(D) 18
(E) 9
Rationale: A whole number that divides exactly into another whole number is called a factor
20/5 =4
answer B
Answer: (B) 4
Question: A and B play a series of 5 games in badminton. A's chance of winning s single game against B is 2/3. Find the chance that A wins exactly 3 games.
(A) 64/81
(B) 35/128
(C) 80/243
(D) None of these
(E) cannot be determined
Rationale: Explanation :
Here, each game is a trial and A's winning the game is a success. All games are independent , so, using the binomial distribution.
P(X) = nCx px(1 - p)n-x.
Where, x= wins exactly 3 games
=> x = 3.
p= 2/3, 1-p=1/3, n=5.
P(3) = 5C3 (2/3)3(1/3)2 .
=> 10 x (2(3)/3(5)).
=> 80/243.
Answer : C
Answer: (C) 80/243
Question: 852.68 âˆ’ 4.5 + 108.94 = ? âˆ’ 2132.54
(A) 6078.58
(B) 5225.9
(C) 6078.54
(D) 6088.58
(E) None
Rationale: Option 'C'
Answer: (C) 6078.54
Question: A bag contains 6 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
(A) 2/5
(B) 3/5
(C) 11/17
(D) 7/15
(E) 8/15
Rationale: Total number of balls = (6 + 5 + 6) = 17.
Therefore, n(S) = 17.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (6/17 + 5/17) = 11/17.
ANSWER:C
Answer: (C) 11/17
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) 99 sec
(B) 89 sec
(C) 54 sec
(D) 27 sec
(E) 22 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10
= 89 sec.
Answer: B
Answer: (B) 89 sec
Question: What will be the cost of building a fence around a square plot with area equal to 49 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 1624
(C) 2999
(D) 2667
(E) 2121
Rationale: Let the side of the square plot be a ft.
a2 = 49=> a = 7
Length of the fence = Perimeter of the plot = 4a = 28 ft.
Cost of building the fence = 28 * 58 = Rs. 1624.
Answer: B
Answer: (B) 1624
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 8 minutes?
(A) 36
(B) 54
(C) 108
(D) 216
(E) 432
Rationale: ONE Veggiematik machine can chop 36 carrots in 4 minutes
So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes
In other words, ONE Veggiematik machine can chop 54 carrots in8minutes
So,SIXVeggiematik machines can chop (8)(54) carrots in6minutes
In other words, SIX Veggiematik machines can chop 432 carrots in8minutes
Answer: (E) 432
Question: Two numbers are in the ratio of 5:8. If 30 be subtracted from each, they are in the ratio of 5:9. Find the numbers?
(A) 122,195
(B) 121,199
(C) 120,192
(D) 102,192
(E) 126,109
Rationale: (5x-30):(8x-30) = 5:9
x = 24=> 120,192
Answer: C
Answer: (C) 120,192
Question: A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours.
(A) 10 h
(B) 14 h
(C) 16 h
(D) 20 h
(E) 24 h
Rationale: DETAILED SOLUTION
The 475 litres is filled in 19 hours by the two pipes when they are opened simultaneously.
Therefore, rate of water flow by A and B,
A + B = 47519 = 25 litres/hour………….(1)
Let pipe B was opened for t hours
Then, pipe A was opened for t + 5 hours
A x (t+5) + B x t = 475
(A + B) x t + 5A = 475
25t + 5A = 475
=) 5t + A = 95
Now, using option analysis
a) t = 10 =) 5 x 10 + A = 95 =) A = 45 (not possible from (1))
b) t = 14 =) 5 x 14 + A = 95 =) A = 25 (not possible from (1) as B can’t be zero)
c) t = 16 =) 5 x 16 + A = 95 =) A = 15
CORRECT ANSWER C
Answer: (C) 16 h
Question: Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?
(A) 11 1/7%
(B) 11 7/7%
(C) 11 1/9%
(D) 71 1/9%
(E) 25%
Rationale: 800 --- 200
100 --- ? => 25%
Answer:E
Answer: (E) 25%
Question: How many three letter words are formed using the letters of the word TIME?
(A) 66
(B) 57
(C) 88
(D) 24
(E) 21
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 4P3
= 4 * 3 * 2 = 24.
Answer: D
Answer: (D) 24
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) 44%
(B) 48%
(C) 32%
(D) 45%
(E) 34%
Rationale: g% = 15 + 15 + (15*15)/100
= 32%
Answer: C
Answer: (C) 32%
Question: Rachel and Sarah started out to visit Grandma. They drove for 50 miles and stopped to rest
before driving for 30 more miles. They decided to go back 10 miles to a restaurant they had seen.
After leaving the restaurant, they drove 80 more miles to Grandma’s house. How many miles did the
girls drive on the way to Grandma’s house?
(A) 150 miles
(B) 160 miles
(C) 170 miles
(D) 180 miles
(E) 200 miles
Rationale: 50 + 30 = 80 to turn around
80 + 10 = 90 backtrack to restaurant
90 + 80 = 170 miles is total distance driven
correct answer C
Answer: (C) 170 miles
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours C will it take 12 beavers that work at the same pace, to build the same dam?
(A) 2.
(B) 4.
(C) C=5.
(D) C=6.
(E) 8.
Rationale: C. 5 hrs
If there were 10 beavers it qould have taken double C= 6hrs.. so closest to that option is 5.
Answer: (C) C=5.
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue R, in dollars, from the sale of cars priced at $ 15,000?
(A) 50,000
(B) 750,000
(C) 850,000
(D) 7,500,000
(E) R=750,000,000
Rationale: number of cars sold = x=800000-50y
y= 15000
x=800000-750000=50000
revenue from 50000 cars=15000*50000=750000000 E
Answer: (E) R=750,000,000
Question: In an examination, 300 students appeared. Out of these students; 26 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
(A) 33
(B) 37
(C) 54
(D) 60
(E) 01
Rationale: The number of students with first division = 26 % of 300 = 26/100 × 300 = 7800/100 = 78
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (78 + 162) = 60
Answer:D
Answer: (D) 60
Question: If |x| = 4x - 1, then x = ?
(A) 3
(B) 1/2
(C) 1 and 1/2
(D) -1/2
(E) -1
Rationale: Answer: A
Approach:
Substituted option A i.e x=1. Inequality satisfied.
Answer: (A) 3
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 8
(A) 1/2
(B) 7/12
(C) 3/7
(D) 5/12
(E) 6/17
Rationale: Total number of cases = 7*7 = 49
Favourable cases = [(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,4),(5,5),(5,6),(5,7),(6,3),(6,4),(6,5),(6,6),(6,7),(7,2),(7,3),(7,4),(7,5),(7,6),(7,7)] = 21
So Probability = 21/49 = 3/7
Answer is C
Answer: (C) 3/7
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 1034355
(B) 1035677
(C) 1045778
(D) 1067675
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
(A) 6 days
(B) 2 days
(C) 8 days
(D) 4 1/5 days
(E) 9 days
Rationale: Work done by A in 3 days = 3/10
Remaining work = 7/10
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 7/10 * 6/1 = 21/5 = 4 1/5 days.
Answer: D
Answer: (D) 4 1/5 days
Question: A block of wood has dimensions 10cm x 10cm x 80cm. The block is painted red and then cut evenly at the 40 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
(A) 5.6%
(B) 8.4%
(C) 11.2%
(D) 14.8%
(E) 17.5%
Rationale: The area of each half is 100+4(400)+100 = 1800
The area that is not painted is 100.
The fraction that is not painted is 100/1800 = 1/18 = 5.6%
The answer is A.
Answer: (A) 5.6%
Question: Which of the following equations represents a line that is perpendicular to y=1/4*x+2?
(A) y−2x=8
(B) 2x+4y=10
(C) 3y+6x=12
(D) 4y−8x=16
(E) 5x−10y=20
Rationale: For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
Answer: D
Answer: (D) 4y−8x=16
Question: If a man can cover 15 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 196km
(B) 190km
(C) 200km
(D) 202.5km
(E) 210km
Rationale: 15 m/s = 15 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 15 * 18/5 * 15/4 km = 202.5 km.
Answer:D
Answer: (D) 202.5km
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 6000 Km?
(A) 10.
(B) 25.
(C) 300.
(D) 38.
(E) 50.
Rationale: Total distance= Distance travelled by A +Distance travelled by car B
Distance= speed*time
Distance of A= 3x * 6
Distance of B= x*2
(3x * 6) + (x*2) = 6000
x= 300 KM/hr
C is the answer
Answer: (C) 300.
Question: If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :
(A) 22
(B) 37
(C) 38
(D) 398
(E) 72
Rationale: Explanation:
3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)
= (6 + 10 - 9 + 15) = 22.
Answer: A) 22
Answer: (A) 22
Question: A water tank is one-fourth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 8 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 4 min. to empty
(B) 6 min. to full
(C) 10 min. to empty
(D) 9 min. to full
(E) 8 min. to full
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 1/4
Part emptied by (A + B) in 1 minute = (1/8 - 1/10) = 1/40
1/40 : 1/4 :: 1 : x
x = (1/4 * 1 * 40) = 10 min.
So, the tank will be emptied in 10 min.
ANSWER:C
Answer: (C) 10 min. to empty
Question: The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#30?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: First, let's translate the expression 21#30, using the definition given:
21#30 = 21×24×27×30
We need the prime factorization of this product.
Let's factor out 3 from each multiple.
21#30 = 3^4(7×8×9×10)
Now let's replace each consecutive integer with its prime factorization:
21#30 = 3^4(7×2^3×3^2×(2×5))
Let's group the prime bases:
21#30 = 2^4×3^6×5×7
The sum of the exponents is 4 + 6 + 1 + 1 = 12
The answer is C.
Answer: (C) 12
Question: The average of five consecutive odd numbers is 51. What is the difference between the highest and lowest number?
(A) .8
(B) 9
(C) 6
(D) 5
(E) 2
Rationale: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)] / 5 = 51
5x + 20 = 255
x = 47
So, required difference = (47 + 8) – 47 = 8
ANSWER: A
Answer: (A) .8
Question: A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $810 was the net sum to be paid for the entire work, what was the average daily wage of B?
(A) $144
(B) $90
(C) $60
(D) $54
(E) $48
Rationale: The correct answer is D.
Answer: (D) $54