source
string
id
string
question
string
options
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answer
string
reasoning
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AQUA-RAT
AQUA-RAT-39797
## Solution 4 Slightly expanding, we have that $\frac{(a-b)(a^2+ab+b^2)}{(a-b)(a-b)(a-b)}=\frac{73}{3}$. Canceling the $(a-b)$, cross multiplying, and simplifying, we obtain that $0=70a^2-149ab+70b^2$. Dividing everything by $b^2$, we get that $0=70(\frac{a}{b})^2-149(\frac{a}{b})+70$. Applying the quadratic formu...
[ "35", "42", "45", "49" ]
A
First step will be to break down all the numbers into their prime factors. 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so, (105)^3 = 3 * 7 * 7 * 5 * 3 *3 *5 *b Therefore (3 * 5 * 7) ^ 3 = 3^3 * 5^2 * 7^2 *b Therefore, b = 3^3 * 5^3 * 7 ^3/3 ^3 * 5 ^2 * 7^2 b = 5*7 = 35 Correct answer A.
AQUA-RAT
AQUA-RAT-39798
## anonymous one year ago Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out a...
[ "90 min", "100 min", "110 min", "120 min" ]
C
Solution Work done by the third pipe in 1 min. = 1/50 - (1/60+1/75) = (1/50 - 3/100) = -1/100. Therefore, the third pipe alone can empty the cistern in 100 min. Answer C
AQUA-RAT
AQUA-RAT-39799
(495, 1), (496, 1), (496, 3), (494, 3), (494, 1), (495, 1), (495, 2), (493, 2), (493, 1), (494, 1), (494, 3), (493, 3), (493, 2)$$ Here is an illustration of this cycle: The following is multiple choice question (with options) to answer. A shop has 3000 cycles. It sells 10% of the cycles daily. How many cycles remain ...
[ "2500", "2600", "2450", "2430" ]
D
Formula : ( After =100 denominator Ago = 100 numerator) 3000 × 90/100 × 90/100 = 2430 D
AQUA-RAT
AQUA-RAT-39800
# Clarification on language of a question on profit and loss. The question is: By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage. 1. 33 1/3% 2. 33 1/2% 3. 33% 4. 34 1/4% The answer provided by the book says it's the first one. But if he gains the cost of 11 meters sh...
[ "7%", "50%", "20%", "22%" ]
B
Suppose S.P of 33 meters of cloth = Rs 33 Therefore, Gain = Rs 11 => C.P = Rs 22 Gain % = 11/22 x 100 = 50% Gain = 50% ANSWER:B
AQUA-RAT
AQUA-RAT-39801
(1) The first $$n$$ people donated $$\dfrac1{16}$$ of the total amount donated. (2) The total amount donated was $$\120,000.$$ Source: GMAT Prep Target question: What was the value of n? When I scan the two statements, it seems that statement 2 is easier, so I'll start with that one first... Statement 2: The total a...
[ "8/5", "5/2", "3", "22/10" ]
D
Let monthly salary for each of the 11 months except December was x, then 11x*1/10 + Nx*1/4 = 1/8(11x + Nx); 11/10 + N/4 = 1/8(11 + N) => 44+10N/40= 11+N/8 352+80N = 440+40N => 40N = 88 N =88/40 =22/10 Answer: D.
AQUA-RAT
AQUA-RAT-39802
# Clock losing time puzzle The question goes as: A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. The table clock loses 5 minutes in the 1st hour, 10 minutes in the second hour and ...
[ "11", "66", "88", "55" ]
A
Time from 5 am. on a day to 10 pm. on 4th day = 89 hours. Now 23 hrs 44 min. of this clock = 24 hours of correct clock. 356/15 hrs of this clock = 24 hours of correct clock 89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock. = 90 hrs of correct clock. So, the correct time is 11 p.m. Answer: A) 11pm
AQUA-RAT
AQUA-RAT-39803
The probabilities I got for parking between 4 and 22 cars are: As it can be seen, there is a 'high' probability that the number of cars is going to move in the range $$(6,15)$$ (more or less). But as the question is for the most likely number, this number is $$10$$. • Edited - replaced text $>=$ with TeX $\ge$ (\ge)....
[ " $140", " $160", " $220", " $420" ]
D
10$ per week! An year has 52 weeks. Annual charges per year = 52* 15 = 780$ 30$ per month! An year has 12 months. Annual charges per year = 12 * 30 = 360$ 780 - 360 = 420 Ans D
AQUA-RAT
AQUA-RAT-39804
from (*) we have n= {(nth term-first term)/common difference}+1..... For our problem, n= {(11-1)}/2}+1 =6 here common difference is 2 as an odd number occurs by adding 2 to the previous odd number etc., If you use the formula $(b-a)/2 + 1$, then for some case it would give wrong answer. Say, $a = 2$ and $b = 4$, so...
[ "31, 20", "30, 19", "29, 18", "28, 17" ]
D
x − y = 11, x + y = 5 × 9 x − y = 11, x + y = 45, y = 17, x = 28 Answer: D
AQUA-RAT
AQUA-RAT-39805
# Difference between revisions of "2019 AMC 10A Problems/Problem 23" ## Problem Travis has to babysit the terrible Thompson triplets. Knowing that they love big numbers, Travis devises a counting game for them. First Tadd will say the number $1$, then Todd must say the next two numbers ($2$ and $3$), then Tucker must...
[ "Y/5", "3Y/10", "100Y/(15X)", "XY/250" ]
B
Rachel eats 4 scones/10 minutes = 2/5 scones per minute The time for Rachel to eat 1 scone is 5/2 minutes. The time for Rachel to eat Y scones is 5Y/2 minutes. The time for Henry to eat X scones is 5YX/200 minutes. The time for Henry to eat 1 scone is 5Y/200 minutes. The time for Henry to eat 12 scones is 60Y/200 = 3Y/...
AQUA-RAT
AQUA-RAT-39806
• #### 1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field. 1. \begin{aligned} 120m^2 \end{aligned} 2. \begin{aligned} 130m^2 \end{aligned} 3. \begin{aligned} 140m^2 \end{aligned} 4. \begin{aligned} 150m^2 \end{aligned} Explanation: \begin{aligned} \text...
[ "50", "60", "11", "80" ]
D
Let L be the length and W be the width. L = (7/5)W Perimeter: 2L + 2W = 384, 2(7/5)W + 2W = 384 Solve the above equation to find: W = 80 m and L = 112 m. correct answer D)80
AQUA-RAT
AQUA-RAT-39807
in n yrs and A 2 in (n+1) yrs, then Rate of compound interest =(A 2 - A 1)/A 1 *100% Sum = A 1 (A 1 /A 2) n. 596 APPENDIXC:COMPOUNDINTERESTTABLES 1/2% CompoundInterestFactors 1/2% SinglePayment UniformPaymentSeries ArithmeticGradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund ...
[ "3052.82", "3052.89", "3052.85", "3052.8" ]
D
R = 100 I / PT => R = (100 * 7200)/ (12000 * 5) = 12% CI = P{ [1 + R /100]n - 1} = 12000 { [ 1 + 12 / 100]2 - 1} = Rs.3052.80 Answer:D Answer:D
AQUA-RAT
AQUA-RAT-39808
=> 18x/4=154 x=308/9 TOTAL WAGES PAID WILL BE (12/11 + 18/7)*309/9 PLEASE TELL ME WHERE I AM WRONG Lets try - SW4 wrote: Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the differe...
[ "1 : 8", "1 : 1", "1 : 6", "1 : 5" ]
D
Ratio of investments of P and Q is 2 : 5 Total salary claimed by P = 12 * 5000 = Rs. 60000 Total profit = Rs. 2 lakhs. Profit is to be shared = Rs. 140000 Share of P = (2/7) * 140000 = Rs. 400000 Share of Q = Rs. 100000 Total earnings of P = (60000 + 40000) = Rs. 100000 Ratio of their earnings = 1 : 1.Answer: D
AQUA-RAT
AQUA-RAT-39809
n3 – n is divisible by 6. What Are the Probability Outcomes for Rolling Three Dice? Look Up Math Definitions With This Handy Glossary. So the least possible sum of their birth years is 2002 + 2001 + 2005 = 6008. Solution for Determine whether the statement is true or false. These are consecutive odd integers. Prove tha...
[ "13", "14", "16", "17" ]
A
12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48. 13 Numbers. 10/3 = 3 and 50/3 = 16 ==> 16 - 3 = 13. Therefore 13 digits. A)
AQUA-RAT
AQUA-RAT-39810
Since the number of ways in which $$5$$ books can be arranged is $$5!=120,$$ we have $$120$$ ways. • thanks for explanation. Can you point out what is wrong in my analysis Sep 17, 2020 at 11:24 • As mentioned in the comments, you calculated the $C$ books to be next to each other, but they do not need to be next to eac...
[ "12 books", "10 books", "0 books", "3 books" ]
D
The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 102 . In order to divide the sum in 9 parts, the amount must be divisible by 9 Divisibility rule of 9: The sum of the digits must be divisible by 9 Sum of digits of 102 =3 and 0 is divisible by 9. He...
AQUA-RAT
AQUA-RAT-39811
bruce the jet will fly 9.68 hours to cover either distance bruce Riley is planning to plant a lawn in his yard. He will need 9 pounds of grass seed. He wants to mix Bermuda seed that costs $4.80 per pound with Fescue seed that costs$3.50 per pound. How much of each seed should he buy so that the overall cost will be $4...
[ "3000", "900", "1800", "360" ]
C
Area of cube = 6× (side)2 = 6 × 10 × 10 = 600 square feet. Cost to paint outside of the cube = 600⁄20 × 60 = 1800 Answer C
AQUA-RAT
AQUA-RAT-39812
# Given relatively prime positive integers $a,b>1$, how many positive integers are there which are not non-negative integer combination sum of $a,b$? Let $a,b>1$ be relatively prime positive integers. I know that $ab-a-b$ is the largest positive integer which can not be written as a sum of non-negative integer combina...
[ "100", "120", "150", "160" ]
D
Since 400=2^4*5^2 then a number can not have 2 and/or 5 as a factor. The odd numbers do not have 2 as a factor and there are 200 odd numbers from 1 to 400. We then need to eliminate the 40 numbers that end with 5, that is 5, 15, 25,...,395. There are a total of 200 - 40 = 160 such numbers between 1 and 400. The answer ...
AQUA-RAT
AQUA-RAT-39813
A boy and his sister. When you subtract two from the boy’s real age and add two to his sister’s age, his sister becomes twice his NEW (subtracted) age. If you subtract three from his real age instead and add three to his sister then she becomes thrice his NEW (subtracted) age. What are their real ages? A little more de...
[ "15", "14", "10", "8" ]
C
Explanation: Clearly, x+15 = 5(x-5) <=> 4x = 40 => x = 10 Answer: Option C
AQUA-RAT
AQUA-RAT-39814
# Clarification on language of a question on profit and loss. The question is: By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage. 1. 33 1/3% 2. 33 1/2% 3. 33% 4. 34 1/4% The answer provided by the book says it's the first one. But if he gains the cost of 11 meters sh...
[ "32%", "11%", "20%", "17%" ]
D
Quicker Method: % profit which Somesh gets = –10 +30 – 10×30/100 = +17% Answer D
AQUA-RAT
AQUA-RAT-39815
Assuming the girls have sat down, they leave 3 gaps between them. 1 for each boy. Thus the first boy can pick between 3 chairs, the second boy 2 chairs, and the third doesn't get to pick. So there are $3\cdot 2=3!=6$ ways the boys can sit. Now the girls are a little bit more tricky. Notice that it isn't specified how t...
[ "96", "92", "82", "84" ]
D
Total ways of arranging 6 person in a circle = 5! = 120 ways If we consider three women as one, then we have 3+1=4 persons. Arranging these four persons in circle will take = 3! = 6 ways And two women can arrange themselves in 3! ways Total ways in which three women sit together in circle = 3!*3! = 36 ways Total ways i...
AQUA-RAT
AQUA-RAT-39816
# Find the probability that each person exits an elevator on a different floor. I have a question and I am working on to study for a test. I have a hard time deciding when to use certain techniques. Suppose you have $5$ people on an elevator that stops at $5$ floors. Each person has an equal probability of going to a...
[ "7!/7^7", "7^7/7!", "7/7!", "7/7^7" ]
A
Each person out of 7 has 7 options, hence total # of outcomes is 7^7; Favorable outcomes will be 7!, which is # of ways to assign 7 different buttons to 7 people So basically # of arrangements of 7 distinct objects: 7!. P=favorable/total=7!/7^7 Answer: A.
AQUA-RAT
AQUA-RAT-39817
Hello Matty R! No, that doesn't mean anything, does it? Hint: what will Bea's age be when Claire is as old as Dawn is now? 3. Feb 27, 2010 ### HallsofIvy Staff Emeritus "When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is. Claire is older than Bea." Claire will be as old as Dawn is no...
[ "8 years", "10 yrs", "12 years", "14 years" ]
B
Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years. (2x + 2) + 2x + x = 27 5x = 25 x = 5. Hence, Bruce's age = 2x = 10 years. B
AQUA-RAT
AQUA-RAT-39818
$\Rightarrow AC+CB=4(AB)$ $\Rightarrow (AB+BC)+CB=4(AB)$ $\Rightarrow BC+CB = 3(AB)$ $\Rightarrow BC=\dfrac{3}{2}(AB)$  -------- $(1)$ Similarly by the time Dinesh reaches point $D$ from $C$ walking, Mukesh and Suresh reach $D$ riding bike. Here also distance travelled by bike $(=BD)$ is 4 times the distance trave...
[ "1 km", "5 km", "7 km", "12 km" ]
B
Explanation: The walked will be of in triangular shape and from starting point is 5km ANSWER IS B
AQUA-RAT
AQUA-RAT-39819
27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14...
[ "1427", "1607", "1707", "2047" ]
C
2 2 × 4 - 1 = 7 7 × 4 - 1 = 27 27 × 4 - 1 = 107 107 × 4 - 1 = 427 427 × 4 - 1 = 1707 C
AQUA-RAT
AQUA-RAT-39820
Suppose the slower car stands still for one hour. How often will the faster car pass it? Then stop the faster car and start the slower car for another hour. How often will the slow car pass the stopped car? Add. Consider alternative case when cars complete exactly $4$ and $8$ rounds. It's easily seen that the number o...
[ "65", "38", "20", "28" ]
D
Answer: D) 28 km
AQUA-RAT
AQUA-RAT-39821
$\text{So we have shown:}$ $\setminus q \quad {\text{odd"_1 +"odd"_2 + "odd"_3 +"odd"_4 + "odd"_5 +"odd"_6 \ = "even}}_{5.}$ $\text{So we conclude:}$ $\setminus \quad \text{the sum of any 6 odd numbers (consecutive or not) is even.}$ The following is multiple choice question (with options) to answer. If b is the su...
[ "z - w = 3(y - x)", "b is divisible by 8", "The average of w, x, y, and z is odd", "b is divisible by 4" ]
B
Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6. b = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12 Focus on the easiest options first. You see that b is not divisible by 8. Answer (B)
AQUA-RAT
AQUA-RAT-39822
The Philosophical Question Then the original poster asked for someone “to post [actual] work done in calculus” and “to see some related rates.” So I posted some “calculus” and got to thinking – the philosophical question – isn’t my first answer calculus? I think it is. It makes use of an important calculus concept, n...
[ "Decrease by 14.3%", "Decrease by 19%", "Increase by 14.3%", "Increase by 12.5%" ]
B
416 is the LCM On Tuesday 416/32 =13 On Monday 416/26 = 16 Therefore, 13-16/16 = -1/5=-19% decrease Answer is B
AQUA-RAT
AQUA-RAT-39823
materials Title: Why are vehicle interiors susceptible to damage from the sun when some plastics seem to be fine? My vehicle built in '08 suffered extreme damage to the dashboard, it permanently melted and is now sticky to the touch even when cool. Presumably this is why so many vehicle owners use covers to block th...
[ "25%", "33 1/3%", "100%", "66 2/3%" ]
C
General formula for percent increase or decrease, (percent change): percent=Change/Original∗100 So, the time between maintenance checks increased by (60−30)/30∗100=100 Answer: C
AQUA-RAT
AQUA-RAT-39824
The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after 6. ### calculus The population of a certain community is increasing at a rate directly pr...
[ "9%", "2%", "5%", "7%" ]
C
Explanation: Increase in population in 10 years= 262500-175000= 87500 Now, % increase will be increase in (population /original population) * 100 => 87500/175000*100= 50% increase in population over 10 years Therefore, Average % increase each year= 50/10= 5% ANSWER: C
AQUA-RAT
AQUA-RAT-39825
The error lies in case $C1:$ . . the people are divided into two pairs. Call the people $A,B,C,D.$ How many pairings are possible? The answer is three: . $\{AB|CD\},\;\{AC|BD\},\;\{AD|BC\}$ . . Note that $\{CD|AB\}$ is not a different pairing. Make this correction and you will get 256. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~...
[ "240", "300", "200", "400" ]
C
{Total} = {Retirees} + {Bridge players} - {Both} + {Neither} x = 5/20*x + x/2 - 3/20*x + 120 20x = 5x + 10x - 3x + 120*20 (multiply by 20) 12x = 120*20 x = 200. Answer: C
AQUA-RAT
AQUA-RAT-39826
First we choose two values, there are 13 values (2 to A), so $$13\choose2$$. Then we want to choose two cards of the first value out of four cards, $$4\choose 2$$ Again, we want to choose two cards of the second value out of four cards, $$4\choose 2$$ And finally, choose one card not of the previously selected types...
[ "360", "12", "16", "24" ]
B
Solution We have to find number of permutations of 2 objects out of 4 objects. This number is 4P2=4(4-1)=4*3=12 Answer B
AQUA-RAT
AQUA-RAT-39827
# Roll a die probability question An unbiased six-sided die is to be rolled five times. Suppose all these trials are independent. Let $E_1$ be the number of times the die shows a 1, 2 or 3. Let $E_2$ be the number of times the die shows a 4 or a 5. Find $P(E_1 = 2, E_2 = 1)$. I have tried to solve this question this ...
[ "3/4", "2/8", "1/7", "1/3" ]
D
Here S={1,2,3,4,5,6} Let E be the event of getting the multiple of 3 then ,E={3,6} P(E)=n(E)/n(S)=2/6=1/3 Option D
AQUA-RAT
AQUA-RAT-39828
newtonian-gravity, mass, units, weight First off, the others posting answers to this question are ultimately correct - there really is no direct conversion between kilograms and Newtons. Kilograms is a unit of mass (how much matter is in an object) while Newtons is a measure of the force that the Earth's gravity exer...
[ "0.1 %", "1%", "1.5%", "2%" ]
A
1 kg = 1000 gm 1/1000 × 100 = 100/1000 =1/10 = 0.1 % A)
AQUA-RAT
AQUA-RAT-39829
+0 # the amount of the price 0 284 4 if the price of a pencil is 36% lower than the price of a pen,then the price of a pen is ? 1.)36%higher than a pencil 2.)43.75 higher than a pencil 3.)56.25 % higher than a pencil 4.)64% higher than a pencil Guest Feb 17, 2015 #1 +84384 +10 If the price of a pencil is 36% ...
[ "80%", "90%", "20%", "40%" ]
C
Explanation: Let C.P. of each pen be Re. 1. Then, C.P. of 10 pens = Rs. 10; S.P. of 10 pens = Rs. 12. Gain % = 2/10 * 100 = 20% Answer:C
AQUA-RAT
AQUA-RAT-39830
Sol: Folks, look at the relative calculation here. If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35. So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum. We got...
[ "22", "0", "19", "18" ]
A
It is clear that 22 x 46 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 22 Answer:A
AQUA-RAT
AQUA-RAT-39831
Kudos [?]: 13 [0], given: 21 GMAT 1: 570 Q46 V24 Re: There are 8 teams in a certain league and each team plays [#permalink] ### Show Tags 26 Dec 2013, 23:04 Lets assume the question asks There are 8 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams...
[ "4", "5", "6", "8" ]
C
6C2= 15 single games, & 30 in total. won by others= 24 30-24= 6 ANSWER:C
AQUA-RAT
AQUA-RAT-39832
So his specific question is this: • Why wouldn’t “three times as large” and “three times larger” mean the same thing? • How can “5 1/2 times greater” and “6 1/2 times what it was” mean the same thing? The two pages quoted are by me (1999) and Doctor Terrel (1997). The first is particularly worth reading in its entirety...
[ " 5", " 50", " 10^5", " 5^10" ]
C
To solve this problem we need to examine the information in the first sentence. We are told that “a reading of j + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of j.” Let’s practice this idea with some real numbers. Let’s say j is 2. This means that j + 1 = 3. With the informa...
AQUA-RAT
AQUA-RAT-39833
the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 ,  time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90...
[ "11", "30", "99", "48" ]
D
Speed of train relative to man = 63 - 3 = 60 km/hr. = 60 * 5/18 = 50/3 m/sec. Time taken to pass the man = 800 * 3/50 = 48 sec. Answer: D
AQUA-RAT
AQUA-RAT-39834
# Clock losing time puzzle The question goes as: A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. The table clock loses 5 minutes in the 1st hour, 10 minutes in the second hour and ...
[ "1: 36: 48", "1: 40: 48", "1: 41: 24", "10: 19: 12" ]
B
Solution: The clock loses 1% time during the first week. In a day there are 24 hours and in a week there are 7 days. Therefore, there are 7 * 24 = 168 hours in a week. If the clock loses 1% time during the first week, then it will show a time which is 1% of 168 hours less than 12 Noon at the end of the first week = 1.6...
AQUA-RAT
AQUA-RAT-39835
4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro...
[ "65mtr.", "84mtr", "70mtr.", "78mtr." ]
B
20 men is 6 days can build 112 metres 30 men in 3 days can build = 112*(30/20)x(3/6) = 84 meters Answer: B.
AQUA-RAT
AQUA-RAT-39836
1) Row 1: A-B, Row 2: C-D 2) Row 1: A-C, Row 2: B-D 3) Row 1: A-D, Row 2: B-C 4) Row 1: B-C, Row 2: A-D 5) Row 1: B-D, Row 2: A-C 6) Row 1: C-D, Row 2: A-B Thus, for each group of 4 dogs chosen, there could be 6 teams. Therefore, the total number of teams that can be formed is 70 x 6 = 420. _________________ # Jeffr...
[ "80", "70", "60", "50" ]
A
Lets work with the data given to us. We know that there ratio of cats to dogs is 5:10 or cats 5 dogs 10 we can write number of cats as 5x and number of dogs as 10x and we know that 10x-5x= 40(therefore 5x = 40 => x=8) Then # of dogs = 10x8= 80 Answer is A
AQUA-RAT
AQUA-RAT-39837
the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 ,  time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90...
[ "56 sec", "40 sec", "36 sec", "29 sec." ]
B
Time taken to cross a moving person = length of train/ relative speed Time taken = 400/((45-9) (5/18) = 400/ 36*(5/18) = 400/10 = 40 sec ANSWER:B
AQUA-RAT
AQUA-RAT-39838
hybridization Title: Determine percentage of crow hybrids We had in class following question which I had no idea how to get to the correct answer: The carrion crow and the hooded crow are fertile together, but their reproductive success is reduced by 50%. In a certain region exist two populations of both speci...
[ "40%", "50%", "60%", "80%" ]
B
This is less about percents and more about probability, particularly the probability OR-rule. Let R = the event that a young fox catches at least one rabbit, and let S = the event that a young fox catches at least one songbird. Using algebraic probability notation, we know P(R) = 0.8 and P(S) = 0.6. We know P((not R) a...
AQUA-RAT
AQUA-RAT-39839
I made a mistake. After I get 10 planes, I should count the lines, because 3 plane could share the same line. Let the 5 points be 12345. The 10 plane contain the points are 123 (the plane contain 123) 124 125 134 135 145 234 235 245 345 When two points appear on more than 2 row , it means more than two planes will shar...
[ "6", "7", "8", "9" ]
A
firstly factors of 200 = 1,2,4,5,8,10,20,25,40,50,100,200 the question says each row will have airplanes not less than 5 and not more than 40, therefore, we should be interested in the factors starting from 5 til 40 (inclusive) 5(in each row) * 40(number of columns) =200, similarly 8 * 25 10 * 20 20 * 10 25 * 8 40 * 5 ...
AQUA-RAT
AQUA-RAT-39840
4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro...
[ "32days", "34days", "36days", "38days" ]
A
one man can consume the same food in 40*40 = 1600 days. 10 more men join, the total number of men = 50 The number of days the food will last = 1600/50 = 32 days. Answer: A
AQUA-RAT
AQUA-RAT-39841
# How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$? How would I go about solving this math problem? if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$? I got $a/c = 2/5$ but that is not a corr...
[ "1:64", "1:62", "1:34", "8:27" ]
D
2^3: 3^3 = 8:27 ANSWER:D
AQUA-RAT
AQUA-RAT-39842
Alternate 10% of journey's = 40 km Then, total journey = 400 kms \eqalign{ & {\text{And,}}\,{\text{Average speed}} \cr & = \frac{{{\text{Total distance }}}}{{{\text{Total time}}}} \cr & 30\% {\text{ of journey}} \cr & = 400 \times \frac{{30}}{{100}} \cr & = 120{\text{ km}} \cr & \cr & 60\% {\text{ of journey}} \cr & =...
[ "15km/hr", "20km/hr", "32km/hr", "24km/hr" ]
D
Average speed = (2*30*20)/(30+20) = 24km/hr Answer is D
AQUA-RAT
AQUA-RAT-39843
# Is this a simple answer to the classic problem "A certain city has 10 bus routes..." A certain city has 10 bus routes. Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from anyone stop to any other (possibly changing along the way), but if any two rou...
[ "12", "24", "32", "64" ]
A
Number of ways in which one can travel from P to R =3×4=12=3×4=12 ANSWER A 12
AQUA-RAT
AQUA-RAT-39844
### Show Tags 16 Jun 2018, 09:16 agdimple333 wrote: During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale? 1) The average of the prices of all of the shirts and sweaters that the store sold during the sale wa...
[ "j/59", "7j/500", "140j", "j/100+40" ]
A
lets take j=1000, as decided by you.. now 70% increase makes it 1700.. this is the price for 100 jackets, so selling price for each jacket=1700/100=$17.. so ans is correct as A..
AQUA-RAT
AQUA-RAT-39845
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. First equation: It takes 6 days for 3 women and 2 men working together to complete a work: As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day...
[ "3.75 days", "3.33 days", "7.75 days", "3.95 days" ]
A
1/6 + 1/10 = 8/30 = 4/15 15/4 = 3.75 days Answer:A
AQUA-RAT
AQUA-RAT-39846
And, sure enough: . $8 + 2\sqrt{15} \;=\;(\sqrt{3} + \sqrt{5})^2$ The following is multiple choice question (with options) to answer. If 18 is 15 percent of 5 percent of a certain number, what is the number?
[ "9", "2400", "40", "81" ]
B
Let the certain number be x. => (15/100)*(5/100)*x = 18; => x=2400; Ans is (B).
AQUA-RAT
AQUA-RAT-39847
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. First equation: It takes 6 days for 3 women and 2 men working together to complete a work: As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day...
[ "10 days", "30 days", "20 days", "80 days" ]
C
C 20 days Given that 12m = 20w => 3m = 5w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 27 days. So, 27 women can do it in (20 * 27) /27 = 20 days.
AQUA-RAT
AQUA-RAT-39848
A boy and his sister. When you subtract two from the boy’s real age and add two to his sister’s age, his sister becomes twice his NEW (subtracted) age. If you subtract three from his real age instead and add three to his sister then she becomes thrice his NEW (subtracted) age. What are their real ages? A little more de...
[ "40", "45", "70", "12" ]
C
Answer: Option C a + b = 60, a = 2b 2b + b = 60 => b = 20 then a = 40. 5 years, their ages will be 45 and 25. Sum of their ages = 45 + 25 = 70.
AQUA-RAT
AQUA-RAT-39849
# Is “divisible by 15” the same as “divisible by 5 and divisible by 3”? Is stating that a number $x$ is divisible by 15 the same as stating that $x$ is divisible by 5 and $x$ is divisible by 3? - The two assertions are equivalent. –  André Nicolas Feb 1 '12 at 23:38 may be worth noting for somebody who might be new t...
[ " None", " I only", " II only", " I and II" ]
C
Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included. So w!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.
AQUA-RAT
AQUA-RAT-39850
Since he did not score 45, he lost an average of 4.5 upon the total number of innings, which includes the latest innings as well. So 45 runs upon x innings will give an average of 4.5 Hence 45/x = 4.5 i.e. x = 10. (Remember, x includes the latest inning as well) Problem 6: The average of 8 scores is 87. Of these, t...
[ "19", "29", "35", "49" ]
C
let the average after 17th inning =x Then average after 16th inning=(x-3) Therefore 16(x-3)+83=17x Therefore x=35 ANSWER:C
AQUA-RAT
AQUA-RAT-39851
the two rectangles = … Level 5 - Real life composite area questions from photographs. Math Practice Online > free > lessons > Texas > 8th grade > Perimeter and Area of Composite Figures. Match. Solving Practice Area of Composite Figures. The 2 green points in the diagram are the … Edit. Question 4 : Find the area of th...
[ "377", "800", "278", "277" ]
B
Area of the square = s * s = 5(125 * 64) => s = 25 * 8 = 200 cm Perimeter of the square = 4 * 200 = 800 cm. Answer: B
AQUA-RAT
AQUA-RAT-39852
Difficulty: 65% (hard) Question Stats: 53% (03:18) correct 47% (03:14) wrong based on 97 sessions ### HideShow timer Statistics Question of the Week #7 Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours....
[ "2 hours", "9 hours", "3 hours", "7 hours" ]
C
Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3 All the three pipes together will fill the tank in 3 hours. Answer:C
AQUA-RAT
AQUA-RAT-39853
Select Page #### Project Euler 15 Problem Statement Starting in the top left corner of a 2×2 grid, there are 6 routes (without backtracking) to the bottom right corner. How many routes are there through a 20×20 grid? #### Solution To add some context to this problem a similar question would be: “Starting at the to...
[ "6", "8", "10", "14" ]
C
In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT. So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10. Answer: C.
AQUA-RAT
AQUA-RAT-39854
+0 # the amount of the price 0 284 4 if the price of a pencil is 36% lower than the price of a pen,then the price of a pen is ? 1.)36%higher than a pencil 2.)43.75 higher than a pencil 3.)56.25 % higher than a pencil 4.)64% higher than a pencil Guest Feb 17, 2015 #1 +84384 +10 If the price of a pencil is 36% ...
[ "10%", "20%", "40%", "50%" ]
C
Explanation: Change in the price = Rs 420 – Rs 300 = Rs 120 Percentage of increase = Change in the price Initial Price * 100. Percentage increase in price =( 120 300 ) *100 = 40% C
AQUA-RAT
AQUA-RAT-39855
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. First equation: It takes 6 days for 3 women and 2 men working together to complete a work: As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day...
[ "1/3", "2/3", "4/3", "5/3" ]
B
Ans is:B A's 1 day's work =1/20 B's 1 day's work =1/30 (A + B)'s 1 day's work =(1/20+1/30)=1/12 (A + B)'s 4 day's work =(1/12*4)=1/3 Therefore, Remaining work =(1-1/3)=2/3
AQUA-RAT
AQUA-RAT-39856
~ Nafer ## Solution 3 (using PIE) Note that the requested probability is computed by dividing the number of configurations with no adjacent Birch trees by the total number of configurations. We can compute the number of configurations with no adjacent Birch trees using complementary counting and then the Principle of...
[ "18", "19", "10", "21" ]
D
Explanation: 14 trees have 13 gaps between them, Required distance (273/13) = 21 Option D
AQUA-RAT
AQUA-RAT-39857
the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 ,  time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90...
[ "70 km/hr", "72 km/hr", "79.2 km/hr", "80 km/hr" ]
C
Solution Speed = (132 / 6) m/sec = (22 x 18 /5)km/hr = 79.2 km/hr Answer C
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AQUA-RAT-39858
Difficult Probability Solved QuestionAptitude Discussion Q. If the integers $m$ and $n$ are chosen at random from integers 1 to 100 with replacement, then the probability that a number of the form  $7^{m}+7^{n}$ is divisible by 5 equals: ✔ A. $\dfrac{1}{4}$ ✖ B. $\dfrac{1}{7}$ ✖ C. $\dfrac{1}{8}$ ✖ D. $\dfrac{1}{49}...
[ "1/7", "3/14", "1/2", "2/7" ]
D
For n(n+1) to be a multiple of 7, either n or n+1 has to be a multiple of 7. Thus n must be of the form 7k or 7k-1. The probability is 2/7. The answer is D.
AQUA-RAT
AQUA-RAT-39859
# Sum and Product of n-positive integers If I have $n$-positive integers, and I compute their sum and product, is there any different group of $n$-positive integers that will have the same sum and product? For example, if $a,...,z$ denote 26 positive integers, and we define: \begin{align} a+b+c+d+....+z &= \text{Sum...
[ "I only", "II only", "III only", "II and III only" ]
D
for four int to have their product and sum as even.. 2 and 4 are ok.. but 0 even number will result in an odd integer as product.. ANSWER:D
AQUA-RAT
AQUA-RAT-39860
# Clarification on language of a question on profit and loss. The question is: By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage. 1. 33 1/3% 2. 33 1/2% 3. 33% 4. 34 1/4% The answer provided by the book says it's the first one. But if he gains the cost of 11 meters sh...
[ "40", "30/11", "20/9", "27/11" ]
C
CP=135*15=2025 and SP=115*18=2070 Gain %= 100*(2070-2025)/2025= 20/9 ANSWER:C
AQUA-RAT
AQUA-RAT-39861
a company has borrowed$85,000 at a 6.5% interest rate. Find the accrued interest for an investment amount of 500 $holding for 15 days at an interest rate of 3 %. Calculating accrued interest payable First, take your interest rate and convert it into a decimal. The interest rate is 5%. Accrued Interest is the Interest a...
[ "8 1/3", "8 1/6", "8 1/9", "8 1/1" ]
A
(4000*3*R)/100 = (5000*5*4)/100 R = 8 1/3 Answer: A
AQUA-RAT
AQUA-RAT-39862
## Dinner Party Seating A host invites $$n$$ guests to a party (guest #1, guest #2, … , guest #n). Each guest brings with them their best friend. At the party there is a large circular table with \2n\) seats. All of the $$n$$ invited guests and their best friends sit in a random seat. 1. What is the probability that ...
[ "15%", "16%", "18%", "23%" ]
B
20% of 180= 36 10% of 120=12 Total =48 percent for 2 days combined =48/300 ≈ 50/300=1/6 =0.1666. so it should be less than 0.1666 so it is 16% Another approach 48/300= 48/(3*100)= 16/100=0.16 Answer:B
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AQUA-RAT-39863
main: # @main pushq %rbp movq %rsp, %rbp pushq %r15 pushq %r14 pushq %r13 pushq %r12 pushq %rbx pushq %rax movl $1, %r15d leaq -42(%rbp), %r14 .LBB0_1: # %._crit_edge cmpl$100, %r15d movl $0, %edi movl$60, %eax cmovgl %eax, %edi movslq %r15d, %r15 cmpl $101, %r15d setl %al movzbl %al, ...
[ "86", "72", "64", "32" ]
C
coding follows (no. of letters)^3 emblem = 216 = 6^3 crude = 125 = 5^3 bump = 4^3 =64 ANSWER:C
AQUA-RAT
AQUA-RAT-39864
1111121, 1111202, 1111211, 1112002, 1120002, 1120012, 1120102, 1121002, 1121102, 1122002, 1200002, 1200012, 1200102, 1200112, 1200202, 1201002, 1201012, 1202002, 1210002, 1210102, 1210202, 1211002, 1212002, 1220002, 1220102, 2000002, 2000012, 2000022, 2000102, 2000112, 2000122, 2000202, 2000212, 2001002, 2001012, 20010...
[ "296", "210", "186", "124" ]
D
Evaluating the left side of the equation, we get 9210 -9124 = 86. Therefore the right side of the equation, 210 - , must also equal 86. Since 210 -124 = 86, then the value represented by the is 124. correct answer D
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AQUA-RAT-39865
(1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ...
[ "2", "4", "6", "8" ]
D
We're told that by selling cakes at W dollars/cake, a baker will make $320. Reducing the price by 20% and selling 2 MORE cakes will also make her $320. We're asked for the original number of cakes that the baker intends to sell. $320 is a rather interesting number. Based on the answer choices, we're almost certainly de...
AQUA-RAT
AQUA-RAT-39866
the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 ,  time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90...
[ "388", "267", "245", "288" ]
C
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
AQUA-RAT
AQUA-RAT-39867
• I see that I answered the question after it was edited to be correct. It was probably that edit which brought this question to the top of the front page just as I was looking. – robjohn Mar 15 at 22:09 Generalization of the problem: • What is the sum of number of digits of the numbers $$2^N$$ and $$5^N$$? $$10^m<\...
[ "337", "437", "457", "537" ]
B
There are 51 digits in 10^50 When we subtract 50 from it, there will be 50 digits left. 10^50 can be written as 9999999....(50 times) + 1 So, 10^50 - 50 = 9999999....(50 times) + 1 - 50 = 9999999....(50 times) - 49 Consider the last 2 digits, 99-49 = 50 The last 2 digits will be 50. And our number would be 99999......9...
AQUA-RAT
AQUA-RAT-39868
## eliassaab Group Title Let m and n be two positive integers. Show that (36 m+ n)(m+36 n) cannot be a power of 2. 2 years ago 2 years ago 1. sauravshakya LET (36m+n)=2^x AND (m+36n)=2^y THEN, (36m+n)(m+36n)=2^(x+y) AlSO, x and y must me both integers 2. sauravshakya Now, n=2^x - 36m THEN, m+36n=2^y m+36(2^x-36m)=2...
[ "54.5", "56.5", "59.2", "61" ]
B
Explanation : Solution: Assume Karthik's weight be x Kg. According to Karthik, 55 < x < 62 According to Karthik;s brother, 50 < x < 60. According to karthik's mother, x <58. The values satisfying all the above conditions are 56 and 57. .'. Required average = (56+57)/2 = 56.5. Answer : B
AQUA-RAT
AQUA-RAT-39869
Substitute 0.085 for interest rate, $3000 for the amount deposited and$6000 for the amount after t years in the formula, “A=Pert” as, $6000=$3000e0.085t Divide both sides by $3000 as,$6000$3000=$3000e0.085t$3000e0.085t=2 Take natural logarithm on both sides as, ln(e0.085t)=ln2 Now, apply the inverse property of lnex ...
[ "2 months", "4 months", "5 months", "6 months" ]
A
Solution S.I on Rs.1800 = T.D on Rs.1872. P.W on Rs.1872 is Rs.1800. Rs.72 is S.I on Rs. 1800 at 24%. Time =(100x72 / 24x1800) = 1/6 year = 2 months. Answer A
AQUA-RAT
AQUA-RAT-39870
only effective. Share, and after five years it earned you$ 15 in income 2 years or decreases ) in! A certain period of time that an investment over time as a percentage of investment. Zijn bidirectioneel, wat wil zeggen dat je woorden gelijktijdig in beide talen kan.! Are returned to you not reinvest would have $40 per...
[ "3", "4", "5", "6" ]
A
1 year: 100/3 = 33.33 approx $34: Total: 134 2nd year: 134/3 = 45: Total: 134+45 = 179 3rd year: 179/3 = 60: Total: 179+60 = 239 > 2 (100) ;3 years; ANSWER:A
AQUA-RAT
AQUA-RAT-39871
So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed. • it means that if they are covering 135km each our then they would be meet together in 135x...
[ "10", "15", "20", "25" ]
C
In 5 minutes, the cyclist travels a distance of (5/60)*25 = 25/12 km. The time it takes the hiker to complete this distance is (25/12) / 5 = 5/12 hours = 25 minutes The cyclist needs to wait 25 - 5 = 20 minutes The answer is C.
AQUA-RAT
AQUA-RAT-39872
in with angle 1 degrees, Area of a Parallelogram diagonal-e 83 m diagonal-f 73 ft with angle 0.5 radians, Area of a Parallelogram diagonal-e 75 in diagonal-f 22 yd with angle 130 degrees, Area of a Parallelogram diagonal-e 63 ft diagonal-f 47 m with angle 12 degrees, Area of a Parallelogram diagonal-e 23 cm diagonal-f ...
[ "600", "900", "800", "500" ]
C
Arear = 1/2 × ( diagonal )(power)2 = ( 1/2 × 40 × 40 )m(power)2 = 1600/2 = 800 m(power)2 Answer is C.
AQUA-RAT
AQUA-RAT-39873
5. Hello, James! Another approach . . . 12 Students are in a class. Five can go to room A, Four to room B, and Three to room C. How many ways can this happen? Assign 5 students to room A. . . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways. From the remaining 7 students, assign 4 students to room B. . ....
[ "23", "25", "30", "36" ]
C
Let the boys are X, then girls are 7X, total = X+7X = 8X So it should be multiple of 8, 30 is not a multiple of 8. C
AQUA-RAT
AQUA-RAT-39874
# 99 Consecutive Positive Integers whose sum is a perfect cube? What is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube? • What have you tried? What do you know about the sum of $99$ consecutive integers? If the first is $n$, what is the sum? – Ross Millikan Au...
[ "240", "273", "328", "428" ]
A
A 240 Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2) Their sum = 10x = 440 x = 44 => 2(x - 2) = 84 Second least number of the other set = 2(84) - 121 = 47 This set has its least number as 46. Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50 = 48 - 2 + 48 - 1 + 48 + 48 + 1 ...
AQUA-RAT
AQUA-RAT-39875
# Math Help - Annual Compounding Interest 1. ## Annual Compounding Interest Jane has $6 and Sarah has$8. Over the next few years, Jane invests her money at 11%. Sarah invests her money at 8%. When they have the same amount of money, how much will they have? Assume annual compounding interest, and round to the nearest...
[ "12,430.", "13,640.", "14,000.", "14,080." ]
D
dana borrows 5500 and returns 3% per month. so returns 165 per month. and 1980 per year. so dana owes 5500-1980=3520 per year. after 4 years she will owe 14080. Answer: (D)
AQUA-RAT
AQUA-RAT-39876
+0 # the amount of the price 0 284 4 if the price of a pencil is 36% lower than the price of a pen,then the price of a pen is ? 1.)36%higher than a pencil 2.)43.75 higher than a pencil 3.)56.25 % higher than a pencil 4.)64% higher than a pencil Guest Feb 17, 2015 #1 +84384 +10 If the price of a pencil is 36% ...
[ "Rs.200", "Rs.250", "Rs.300", "Rs.150" ]
C
Explanation: Let the cost of one pen is ‘5x’ and pencil is ‘x’ 3 X 5x + 5x = Rs.100 15x + 5x = Rs.100 X = 100/20 = 5 :. Cost of 1 pen = 5x = 5 x 5 = 25 :. Cost of 12 pens, i.e. (one dozen) = 25 x 12 = Rs.300 Answer: Option C
AQUA-RAT
AQUA-RAT-39877
c, json, formatting, c99 four times. That really asks for a function: /** * \brief Puts the given \c str \c count times on \c stream. * \param str null-terminated character string to be written * \param count number of times \c str shall be written * \param stream output stream * \returns a non-negative value on ...
[ "998", "1000", "1092 times", "1100" ]
C
1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 400 = 301 * 3 = 903 ----------- 1092 C
AQUA-RAT
AQUA-RAT-39878
Could you please verify that my 1st and 3rd prize probabilities are well calculated and help me calculate the 2nd prize probability? Your logic for case number (3) does not seem correct. First, you have to draw 6 balls with exactly 5 balls matching 5 numbers from your set of 6 picked numbers. In total There are C(42,...
[ "920", "120", "820", "720" ]
B
Out of 6 participants, the first three prizes can be won in, 6P3 = 6! / (6 - 3)! = 6 x 5 x 4 = 120 ways ANSWER:B
AQUA-RAT
AQUA-RAT-39879
We can argue that the are 21/7= 3 times as many men now so they will require three times as much water, 3(13)= 39 quarts just for the same two weeks. And they need the water for 4/2= 2 times as many weeks so need 2(39)= 78 quarts of water. The following is multiple choice question (with options) to answer. Average exp...
[ "350", "370", "390", "360" ]
D
Explanation: Assumed mean = Rs. 320 Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280 Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40 Therefore, Average expenditure for 7 days = Rs. 320 + Rs. 40 = Rs. 360 Correct Option: D
AQUA-RAT
AQUA-RAT-39880
the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 ,  time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90...
[ "288", "266", "245", "277" ]
C
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
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AQUA-RAT-39881
How do you solve this? There is this kind of question in our test and I don't know how will I do it. You're working in a company. Your starting income is 5000. Every year, the income will increase by 5%. What is your total income on your 25th year in the company? Related Precalculus Mathematics Homework Help News on ...
[ "13", "14", "15", "16" ]
A
1000+200x=3600 x=13 cars. The answer is A.
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• I am also stuck at this point. If the first rose is $Red$ then the Bride enters the Church and in that case the probability is $\frac{10}{20}$. But now come the cases when the first rose is $White$: $WRR$, $WWRRR$, $WRWRR$ and so on. No matter what, if the first rose is $White$, the last two roses must be $Red$. And ...
[ "1/12", "1/6", "1/5", "1/3" ]
B
We are asked to find the probability of one particular pattern: WRRW. Total # of ways a gardener can plant these four bushes is the # of permutations of 4 letters WWRR, out of which 2 W's and 2 R's are identical, so 4!/2!2!=6; So p=1/6 Answer: B.
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• #### 1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field. 1. \begin{aligned} 120m^2 \end{aligned} 2. \begin{aligned} 130m^2 \end{aligned} 3. \begin{aligned} 140m^2 \end{aligned} 4. \begin{aligned} 150m^2 \end{aligned} Explanation: \begin{aligned} \text...
[ "36", "32", "19", "10" ]
B
A/8 = 8 * 8 => A = 8 * 8 * 8 x * 2x = 8 * 8 * 8 x = 16 => 2x = 32 Answer: B
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AQUA-RAT-39884
Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 37109 Followers: 7252 Kudos [?]: 96499 [0], given: 10752 ### Show Tags 05 Jun 2013, 23:44 PKPKay wrote: Sarang wrote: For 1 hour- Machine A rate- 2000 envelopes Machine B+C rate- 2400 envelopes Since A + C = 3000 envelopes A's rate is 2000 envelopes as ab...
[ "30", "36", "70", "80" ]
B
Method I: the rates solution “Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12 That’s the combined rate. We need to m...
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AQUA-RAT-39885
# In how many ways can 3 distinct teams of 11 players be formed with 33 men? Problem: In how many ways can 3 distinct teams of 11 players be formed with 33 men? Note: there are 33 distinct men. The problem is similar to this one: How many distinct football teams of 11 players can be formed with 33 men? Fist, I thou...
[ "60%", "80%", "50%", "90%" ]
B
Explanation: Let total number of men = 100 Then 80 men are less than or equal to 50 years old (Since 80% of the men are less than or equal to 50 years old) => 20 men are above 50 years old (Since we assumed total number of men as 100)20% of the men above the age of 50 play football⇒Number of men above the age of 50 who...
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AQUA-RAT-39886
(1) The median of set {x,−1,1,3,−x} is 0 (2) The median of set {x,−1,1,3,−x} is x2 Merging similar topics. Please refer to the solutions above. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15958 Re: What is the value of x? [#permalink] ### Show Tags 09 Jun 2017, 15:49 Hello from the GMAT Club BumpB...
[ "-2", "-1", "0", "1" ]
B
So we have even no. of elements in the Set So median is the average of Middle two numbers (e+8)/2= (y+9)/2 y - e= -1 Answer B
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AQUA-RAT-39887
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. First equation: It takes 6 days for 3 women and 2 men working together to complete a work: As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day...
[ "days", "days", "days", "days" ]
A
Explanation: (woman + girl )’s 1 day’s work = 1/24 Their 20 day’s work = 1/24 × 20 = 5/6 The remaining 1/6 work is done by the woman in 6days Therefore, the woman alone will finish the work in 6 × 6 days = 36 days woMan’s 1 day’s work = 1/36 Therefore, girl 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72 Therefore, the g...
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AQUA-RAT-39888
# Reset the equation counter \documentclass{article} \usepackage{amsmath, amsfonts, chngcntr} \newcounter{problem} \newcounter{solution} \newcommand\Problem{% \stepcounter{problem}% \textbf{\theproblem.}~% \setcounter{solution}{0}% } \newcommand\TheSolution{% \textbf{Solution:}\\% } \newcommand\ASolution{% \stepcou...
[ "55", "56", "57", "58" ]
C
20x + 48 = 21(x – 5) X=57 ANSWER:C
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(1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ...
[ "400", "420", "445", "465" ]
B
Let the original average expenditure be `x. Then, 42(x – 1) – 35x = 42 ⇔ 7x = 84 ⇒ x = 12. ∴ Original expenditure = (35 × 12)= 420. Answer B
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Sol: Folks, look at the relative calculation here. If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35. So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum. We got...
[ "643", "677", "760", "767" ]
C
If Mike had scored 16 marks more, he could have scored 30% Therefore, Mike required 212 + 16 = 228 marks Let the maximum marks be m. Then 30 % of m = 228 (30/100) × m = 228 m = (228 × 100)/30 m = 22800/30 m = 760 Answer:C
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AQUA-RAT-39891
Let one woman complete the job in $$w$$ days and one man in $$m$$ days. First equation: It takes 6 days for 3 women and 2 men working together to complete a work: As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day...
[ "36", "42", "28", "32" ]
D
A’s one day’s work= 1/X B’s one day’s work= 1/3x A + B’s one day’s work= 1/x + 1/3x = 1/24 = 3+1/3x = 4/3x = 1/24 x = 24*4/3 = 32 ANSWER:D
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AQUA-RAT-39892
# Faulty Combinatorial Reasoning? I have 10 books, 4 of which are biographies while the remaining 6 are novels. Suppose I have to choose 4 total books with AT LEAST 2 of the 4 books being biographies. How many different combinations of choosing 4 books in such a way are there? The following line of reasoning is fault...
[ "4/25", "12/47", "2/5", "8/15" ]
B
let there be 100 books in all Historic fiction books = 30% of total = 30 Other books = 70 New historic fiction = 40% of 30 = 12 Other new books = 50% of 70 = 35 total new books = 35+12 = 47 fraction = 12/47 Ans: B
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1) Row 1: A-B, Row 2: C-D 2) Row 1: A-C, Row 2: B-D 3) Row 1: A-D, Row 2: B-C 4) Row 1: B-C, Row 2: A-D 5) Row 1: B-D, Row 2: A-C 6) Row 1: C-D, Row 2: A-B Thus, for each group of 4 dogs chosen, there could be 6 teams. Therefore, the total number of teams that can be formed is 70 x 6 = 420. _________________ # Jeffr...
[ "30", "60", "40", "45" ]
B
Make a Venn diagram, and enter your data. Let the number of houses be x 30+10+20=x x = 60 so number of houses were = 60 Answer B
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A. 1 B. 2 C. 4 D. 5 E. 6 After 17 trips, the worker has carried 17 x 4 = 68 jugs. From those 68 jugs, 68/7 = 9 cartons have been filled, with 5 extra jugs remaining. So, the worker needs one more trip to carry 2 more jugs to fill the partially filled carton with those 2 jugs. _________________ # Scott Woodbury-Stew...
[ "38", "12", "98", "27" ]
B
Explanation: 12 as all boxes are sealed. Answer: B
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# What is the next number in this sequence: $1, 2, 6, 24, 120$? [closed] I was playing through No Man's Sky when I ran into a series of numbers and was asked what the next number would be. $$1, 2, 6, 24, 120$$ This is for a terminal assess code in the game no mans sky. The 3 choices they give are; 720, 620, 180 • W...
[ "14", "15", "58", "19" ]
C
In this series, each number is repeated, then 10 is subtracted to arrive at the next number. The next number is 58 Answer : C
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python, algorithm, graph Using a graph gives the ability to check only the actual routes. And so it wouldn't check if it is possible to fly from say; FRA -> CPH, and then FRA -> MAD, as the original code does. This benefit is good, however there is a larger benefit when there are say two, or more, flights in each edge...
[ "13.12.11.10.4.4.", "13.12.11.10.4", "13.12.4.4.", "13.12.4" ]
C
flights paths can Anni choose fromThere are 13 ways to chose the first destination, then, 12 ways to chose next destination, with option of 4 airports (13x4) then, to return he has 4 options to chose the airports Thus, 13*12*4*4 ways. Using permutations: If the solution had written 13P1 instead of 13C1 it won't matter....