RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 5 of the slips are the drawn, without replacement, what is the probability that all 5 have a odd number written on it?
A.1/12
B.1/10
C.1/8
D.1/24
Answer: A.1/12
Explanation: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)
P(+ on 1st pick) = 5/10
P(+ on 2nd pick) = 4/9
P(+ on 3rd pick) = 3/8
P(+ on 4rd pick) = 2/7
P(+ on 5rd pick) = 1/6
5/10*4/9*3/8*2/7*1/6=1/252
A
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time G all five colored lights will all flash together at the exact same time?
A.0:03 AM
B.0:04 AM
C.0:06 AM
D.0:12 AM
Answer: D.0:12 AM
Explanation: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Question: Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 15% greater than any other employee, what is the lowest possible salary that any one employee earned?
A. $40,000
B. $41,667
C. $42,000
D. $43,750
Answer: D. $43,750
Explanation: Employee 1 earned $x(say)
Employee 2 will not earn more than $1.15x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees
(1.15x*20)+x=1,050,000
Solving for x=$43,750
Answer D
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
A.482
B.442
C.552
D.662
Answer: A.482
Explanation: 20000(11/10)4 - 20000(6/5)2 = 482
Answer: A
Question: The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in three colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
A.24
B.32
C.8
D.60
Answer: C.8
Explanation: I have no idea how you got 8C8, 7C6 and 4C1.
I could have understood 8C1*6C1*4C1 (I have explained why this doesn't work in the post above)
The best way to solve it is by first selecting 3 colors out of the given 4 in 4C3 ways. (say, you got black, red and green)
Now for each color, you have 2 choices - model A or B
So you select a model in 2 ways.
No of ways of selecting the 3 cars = 3C3 * 2 * 2 * 2 = 8
Well, my logic was
The number of ways of selecting r objects from n different objects is nCr.
We have 8 options and can select either of the 8 as the first - 8C8
One car is gone and one becomes a forbidden choice so we have 7 options and need to select either of the 6 as the first - 7C6
Two cars are gone and two becomes a forbidden choice so we have 6 options and need to select either of the 4 as the first - 6C4
C
Question: Of 70 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
A.54
B.55
C.59
D.71
Answer: C.59
Explanation: Total = 90
Thrower = 37
Rest = 90 - 37 = 33
Left Handed = 33/3 = 11
Right handed = 22
If all Thrower are right handed then total right handed is 37 + 22 = 59
so C. 59 is the right answer
Question: If p is the product of the integers from 1 to 36, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A.13
B.15
C.17
D.19
Answer: C.17
Explanation: 36! has 3, 6, 9,....30, 33, 36 as factors, which are 12 multiples of 3.
We need to add 5 more to these 12 because of 9, 18, 27, and 36.
The greatest integer of k is 17.
The answer is C.
Question: In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11. What is the number of cards in the stack?
A.10
B.11
C.12
D.15
Answer: C.12
Explanation: 9/(9+x)∗8/(8+x)=6/119/(9+x)∗8/(8+x)=6/11
0=17x+x2−600=17x+x2−60
0=(x+20)(x−3)0=(x+20)(x−3)
x=3
9+3 = 12
the answer is (C)
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days?
A.1/8
B.1/3
C.1/6
D.1/2
Answer: C.1/6
Explanation: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 3 days = 3 (1/18) = 1/6.
Answer:C
Question: Fourthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
A. 60
B. 70
C. 100
D. 120
Answer: B. 70
Explanation: 40% of the members have passed the test, thus 60% have not passed the test.
We also know that 30+12=42 members have not passed the test, thus 0.6*Total=42 --> Total=70.
Answer: B.
Question: When a producer allows 36% commission on retail price of his product, he earns a profit of 8.8%. what would be his profit % if the commission is reduced by 24%?
A.45.9
B.47.9
C.49.6
D.51.9
Answer: C.49.6
Explanation: Let the retail price =Rs 100.then, commission=Rs 36
S.P=Rs(100-36)=Rs 64
But, profit=8.8%
C.P=Rs(100/108.8*64)=Rs 1000/17
New commission =Rs12. New S.P=Rs(100-12)Rs 88
Gain=Rs(88-1000/17)=Rs 496/17
Gain%=(496/17*17/1000*100)%=49.6%
Answer is C.
Question: If four coins are tossed, the probability of getting two heads and two tails is?
A.3/8
B.2/7
C.2/5
D.1/4
Answer: A.3/8
Explanation: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 30% of that number?
A.A)148
B.B)210
C.C)63
D.D)248
Answer: C.C)63
Explanation: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 30/100 = 126/2 = 63
ANSWER:C
Question: If the two hands in a clock are 15 minutes divisions apart,then the angle between them is
A.3Â°
B.18Â°
C.24Â°
D.90Â°
Answer: D.90Â°
Explanation: In a clock, each minute makes 6Â°
âˆ´ 15 minutes will make 6 Ã— 15 = 90Â°
Answer D
Question: Alex bought 160 shirts at the rate of $225 per shirt. The transport expenditure was $1400. He paid an octroi at the rate of $1.75 per shirt and labour charges were $320. What should be the selling price of one shirt, if he wants a profit of 20%?
A.$244
B.$255
C.$285
D.$277
Answer: C.$285
Explanation: C
$285
Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = $237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = $285.
Question: 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?
A.833 8/3 grams
B.833 1/3 grams
C.837 1/3 grams
D.533 1/3 grams
Answer: B.833 1/3 grams
Explanation: 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:B
Question: A school bus travels from kormangala to Electronic City. There are four children in the bus. Each child has four backpacks with him. There are four dogs sitting in each backpack. Every dog has four puppies with her. All these dogs have four legs, with four toes at each leg.
A.5150
B.5160
C.5170
D.5180
Answer: C.5170
Explanation: 16 backpacks(Each child has 4 backpacks)
64 dogs (Each backpack has 4 dogs)
256 puppies (Each dog has 4 puppies)
Now 256 puppies had total= 256*4 legs =1024 * 4 toes = 4096 toes
64 dogs had total = 64 * 4 legs = 256 * 4 toes =1024 toes
4 chidren had total =4 * 10 toes = 40 toes
So the total toes on bus will be(except driver) = 4096+1024+40= 5160 toes
or
If considering driver answer will be = 5160 + 10 =5170
ANSWER:C
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?
A.10
B.37
C.27
D.18
Answer: A.10
Explanation: Let the total profit be Rs. z. Then,
B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.
A : B = z/3 : 2z/3 = 1:2
Let the total capital be Rs, X and suppose B's money was used for x months. Then.
(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .
Thus, B's money was used for 10 months.
Answer: A) 10 months
Question: Given that E and F are events such that P(E) = 36, P(F) = 24 and P(E n F) = 36,
find P (E|F) and P(F|E)
A.5
B.8
C.2
D.6
Answer: C.2
Explanation: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 36/36 = 1
P(F|E) = P(EnF)/P(E) = 36/24 = 2.
C)
Question: If 0.5% of A =85 paise, then the value of A is ?
A.Rs. 170
B.Rs. 17
C.Rs. 1.70
D.Rs. 4.25
Answer: A.Rs. 170
Explanation: Answer
∵ 0.5/100 of A = 85/100
∴ A = Rs. (85 / 0.5) = Rs. 170
Correct Option: A
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
A.1/4
B.1/8
C.1/5
D.1/9
Answer: C.1/5
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6!
= 1/5
Answer: Option C
ExplanaC
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
A.135/9
B.135/2
C.135/1
D.135/7
Answer: B.135/2
Explanation: Sol:
Apply the formula:
θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|
⇒ Angle = 30 × 5 –11/2 × 15 = 150 – 165/2 = 135/2
Answer:B
Question: Two trains 300m and 400m long run at the speed of 36kmph and 18 kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
A.5.6sec
B.46.67 sec
C.10.8sec
D.12.6sec
Answer: B.46.67 sec
Explanation: Relative speed = 36+18 = 54 kmph * 5/18 = 15 m/s
Distance covered in crossing each other = 300+400 = 700m
Required time = 700*1/15=46.67 sec
Answer is B
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 3.5 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
A.5,500,000
B.3,200,000
C.55,000
D.28,000
Answer: B.3,200,000
Explanation: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 3.5 gms
In 400,000 cm^3 , X = 3.5 * 400,000 = 1,400,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 1,400,000 + 1,800,000 = 3,200,000
ANSWER:B
Question: If six persons sit in a row, then the probability that three particular persons are always together is -.
A.1/5
B.1/7
C.1/9
D.1/2
Answer: A.1/5
Explanation: 3!4! Required probability = 3!4!/6! = 1/5
ANSWER A
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is ?
A.25/42
B.25/49
C.25/27
D.25/19
Answer: A.25/42
Explanation: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
=25/42.
Answer:A
Question: Sum of two numbers is 80. Greater number exceeds by 5 from four times of the smaller. Find the numbers?
A.65,15
B.40,15
C.30,20
D.35,20
Answer: A.65,15
Explanation: x + y = 80
x â€“ 4y = 5
x = 65 y = 15
ANSWER A
Question: If a+ |a| + b= 7 and a+ |b| - b=6 , then a+ b=
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: If a+ |a| + b= 7 and a+ |b| - b=6 , then a+ b=
can be done in 2.3 mins :
there are 4 cases to be tested :
1) a is -ve and b is -ve
substituting in the equation , we get a-a+b=7 and a-b-b=6 solve for a and b we get a=20 and b=7 , so a+b=27 REJECT
2)a is +ve and b is +ve
substitute in the equation, we ger a+a+b=7 and a+b-b=6 solve for a and b we get a=6 and b=-5 ,therefore a+b=1 not on list so REJECT
3) a is -ve and b is +ve
substitute , we get a-a=b=7 and a+b-b=6 solve fo a and b we get a=6 and b=7, a+b=13 not on list so REJECT
4) a is +ve and b is -ve
substitute , we get a+a=b=7 and a-b-b=6 solve for a and b , we get a=4 and b= -1 ,a+b=3 , ANSWER A
Question: x is a positive integer less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
A.21
B.22
C.23
D.24
Answer: D.24
Explanation: when x divided by 7 and leave reminder 1. x could be 1,8,15,....
when divided by 3 and leave reminder 2- x could be 2,5,8,....
so x must be of the form 21m+8 where m=0,1,2,.....
first no will be 8 and last no will be 491.
so total no. less than 500 will be 24.
Answer:D
Question: Tough and Tricky questions: Combinations.
Five contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
A.6
B.7
C.15
D.16
Answer: C.15
Explanation: Number of ways First-place medal can be awarded to four contestants = 5
Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3
Therefore number of possibilities = 5 *3 =15
Answer:C
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.287 Sec
B.190 Sec
C.277 Sec
D.177 Sec
Answer: B.190 Sec
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
A.42, 33
B.42, 36
C.44, 33
D.44, 36
Answer: A.42, 33
Explanation: Explanation:
Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x + 9) = 56/100(2x + 9)
=> (x + 9) = 14/25 (2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99 => x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
Answer: Option A
Question: On the x-y coordinate plane there is a parabola, y=x(4-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 4) II. (2, 3) III. (4, 1)
A.I only
B.II only
C.III only
D.I and II
Answer: B.II only
Explanation: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 3 lies on the parabola, so (1, 4) will not be enclosed by the parabola and x axis.
When x = 2, y = 4 lies on the parabola, so (2, 3) will lie below it and this point will be enclosed by the parabola and x axis.
When x = 4, y = 0 lies on the parabola, so (4, 1) will not be enclosed by the parabola and x axis.
The answer is B.
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.176
B.375
C.355
D.326
Answer: B.375
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375
Answer: B
Question: (y^n - b^n) is completely divisible by (y - b), when
A.n is odd natural number
B.n is even natural number
C.n is any natural number
D.n is prime
Answer: C.n is any natural number
Explanation: For every natural number n, (y^n - b^n) is completely divisible by (y - b).
C
Question: A rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
A.a) 4 inches
B.b) 6 inches
C.c) 5 inches
D.d) 8 inches
Answer: C.c) 5 inches
Explanation: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
35=5*7
45=3*3*5
GCF = 5
P.S you can make squares with side of 5
Answer : C
Question: A 8% product yields 10%. The market value of the product is:
A.Rs. 60
B.Rs. 40
C.Rs. 70
D.Rs. 80
Answer: D.Rs. 80
Explanation: Let the face value of the product is Rs.100
It yields Rs.8
Market value of the stock=(8/10)*100=Rs.80
ANSWER:D
Question: Which answer is closest to the √36?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Try some examples.....
4 x 4 = 16
5 x 5 = 25
Answer C
Question: If positive integer k is divided by 4, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a even number
III. k is divisible by 3
A.None
B.I
C.II
D.III
Answer: A.None
Explanation: k = 4m+2 = 2(2m+1)
I. k + m = 2(2m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Question: An choclate store received shipments of ingredients on Monday and Tuesday . Tuesday's shipment had 3 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?
A.0 and 1/10 pounds
B.9 and 6/7 pounds1
C.10 and 2/5 pounds
D.11 pounds
Answer: A.0 and 1/10 pounds
Explanation: Solution: Average weight = Total weight/number of packages. The total weight on Monday was 3 * (11 and 2/3 pounds), or 35 pounds. The total weight on Tuesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 35, or 101 pounds. The average is 101 pounds/10 packages, or 10 and 1/10 pounds per package.
Answer : A
Question: John deposited $10,000 to open a new savings account that earned 10 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John’s account 6 months after the account was opened?
A.$10,100.75
B.$10,101.75
C.$10,506.25
D.$10,201.35
Answer: C.$10,506.25
Explanation: 10 percent annual interest compounded quarterly --> 2.5% in 3 moths.
For the first 3 moths interest was 2.5% of $10,000, so $250;
For the next 3 moths interest was 2.5% of $10,000,plus6.25 earned on previous interest of $250, so $250+$6.25=$256.25;
Total interest for 6 months was $250+$256.25=$506.25, hence balance after 6 months was $10,000+ $506.25=$10,506.25.
Answer: C.
Question: A committee of four people is to be chosen from five married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
A.16
B.48
C.64
D.80
Answer: D.80
Explanation: Each couple can send only one representativeto the committee. Let's see in how many ways we can choose 4 couples (as there should be 4 members) out of 4 to send only one representatives to the committee: 5c4=5.
But each of these 5 couples can send two persons (husband or wife): 2*2*2*2=2^4=16.
Total # of ways: 5C4*2^4=80
Answer: E.
Question: Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 27 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
A.27/8
B.3
C.4
D.9
Answer: A.27/8
Explanation: In 15 mins, Timothy travels=9/4 miles.
Now, let his mother takes x hours to reach him, traveling at 27mph.
So, 27x=9x+9/4
x=1/8 hrs.
Thus, the distance traveled by his mother to reach= 27*1/8=27/8miles. Ans A
Question: Sandy invested a certain sum of money at 12% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 4 times the original investment. What is the value of n?
A.20
B.25
C.30
D.35
Answer: B.25
Explanation: n* 0.12 * principal + principal = 4 * principal
n * 0.12 = 3
n = 25 years
The answer is B.
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
A.2%
B.2.02%
C.4%
D.4.04%
Answer: D.4.04%
Explanation: Correct value is 100x100.
Measured value is 102x102.
Therefore ERROR Value is (102x102)-(100x100) = 404.
Error% = (error value/ true value)*100.
= (404/100x100)x100 = 4.04.
answer :D
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 200 revolutions. How many revolutions does the second wheel make in covering d feet?
A.200x/y
B.200y - x
C.200x - y
D.200y/x
Answer: A.200x/y
Explanation: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
200 = d/(x*pi)
d = 200 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (100 * x * pi) / (y*pi) = 200x/y
Answer (A)
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 300 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
A.There is no empty capacity
B.2100 gallons
C.2300 gallons
D.2100 gallons
Answer: D.2100 gallons
Explanation: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diamter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=300
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=300 in the second cylinder,volume= pie (r^2)*4*2=300*8=2400 gallons
Empty capacity=2100 gallons
Answer D
Question: Tommie spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommie won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?
A.330
B.500
C.520
D.540
Answer: C.520
Explanation: I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, tommie earned$520. Answer choice C.
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. Line L must passes through the first quadrant.
2. Line L does pass the origin.
3.The slope of L is negative
A.I only
B.II only
C.III only
D.I and II
Answer: C.III only
Explanation: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
Answer C