source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-39697 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"2",
"2.4",
"1.2",
"2.1"
] | B | The distance of the street was 600 meters.
The made the roundtrip 6 times, which would be 2 trips for each roundtrip.
Multiply 12 times 600 to get the total distance. 600 * 12 = 7200 meters of 7.2 km.
The question asked for the speed in km/hour and 20 minutes is one third of an hour.
Multiply 7200 by 1/3 to get approxi... |
AQUA-RAT | AQUA-RAT-39698 | Re: How many 4 digit codes can be made, if each code can only contain [#permalink]
### Show Tags
05 Oct 2010, 12:37
utin wrote:
Hi Bunuel,
why can't i write TOO,OTO,OOT AS
(4^3)*3! , taking the T as one entity ans assuming that 3 things can be arranged in 3! ways???
Just one thing: TOO can be arranged in 3!/2! way... | [
"211",
"216",
"1075",
"1080"
] | C | An staff identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number i... |
AQUA-RAT | AQUA-RAT-39699 | # Physics kinematics SIN question
1. Dec 30, 2011
### ShearonR
1. The problem statement, all variables and given/known data
A car, travelling at a constant speed of 30m/s along a straight road, passes a police car parked at the side of the road. At the instant the speeding car passes the police car, the police car ... | [
"A)1km",
"B)300m",
"C)650m",
"D)750m"
] | B | Relative speed of the policeman = 20-15 = 5 km/hr
time taken by policeman to cover 100m = (100/1000)*(1/5) = 1/50 hr
In 1/50 hr the thief covers a distance of 15/50 km = 3/10 km = 300m
Answer is B |
AQUA-RAT | AQUA-RAT-39700 | ### Show Tags
26 May 2017, 05:36
1
Which of the following equals the ratio of 3 $$\frac{1}{3}$$to 1 $$\frac{1}{3}$$?
3$$\frac{1}{3}$$ = $$\frac{10}{3}$$
1 $$\frac{1}{3}$$ = $$\frac{4}{3}$$
Required ratio = (10/3) / (4/3) = $$\frac{10}{4}$$ = $$\frac{5}{2}$$
Director
Joined: 13 Mar 2017
Posts: 703
Location: India
Conc... | [
"24 years",
"32 years",
"34 years",
"38 years"
] | A | Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10) = 93.
‹=›9x = 63
x = 7.
∴ Jayant's present age = 2x + 10 = 24 years.
Answer A |
AQUA-RAT | AQUA-RAT-39701 | ### Show Tags
23 Dec 2016, 09:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios [#permalink]
### Show Tags
09 Nov ... | [
" 2:9",
" 2:7",
" 1:2",
" 1:4"
] | C | (8/100)A+(2/100)B = (4/100)(A+B)
4A =2B
=> A/B = 1/2
Answer is C. |
AQUA-RAT | AQUA-RAT-39702 | Question 9
Let $f(x) = \sqrt {x^2-2x-3}$.
a) Write $x^2-2x-3$ in the form $a(x-h)^2 + k$
b) Find the inverse of function $g$ defined by $g(x) = \sqrt {x^2-2x-3} \quad , \quad x \ge 3$
c) Find the range of the inverse of $g$ defined above.
Solution
a)
Complete the square of the given expression
$x^2-2x-3 = (x-1)^2 - 1 -... | [
"4",
"3",
"2",
"1"
] | C | we get 2 quadratic equations here ..
1) x^2-x-3=0 ....... roots 2 , -1
2) x^2+x-3=0 ........ roots -2, 1
Inserting each root in given equation , it can be seen that -1 and -2 do not satisfy the equations .
So value of x for given equation .... x=3 or x=1
I guess range is 3-1 =2
C |
AQUA-RAT | AQUA-RAT-39703 | 2. How many ways can one choose three distinct characters to be placed into the forms from above.
3. Watch out for any duplication or overcounting.
There are two options (using Joe's suggestion in the comments):
• $\{a,b,c,c,c\}$. We can choose $3$ of the $5$ positions for the $c$'s, then there are two options for t... | [
"390",
"2,340",
"4,320",
"7,020"
] | C | 10C1*9C1*8C1 = 720.
=>720 * 3 ! = 4320.
Option E is correct answer...but OA is C. |
AQUA-RAT | AQUA-RAT-39704 | 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... | [
"79.2 km/hr",
"82.4 km/hr",
"69.7 km/hr",
"49.8 km/hr"
] | A | The train can cover a distance equal to its length in 8 seconds. Therefore, additional
(20−8)=12 seconds was taken to cross the platform.
Hence, speed of the train=264/12=22 m/s
=22 × 18/5=79.2 km/hr
ANSWER:A |
AQUA-RAT | AQUA-RAT-39705 | ### Show Tags
23 Oct 2009, 23:42
14
KUDOS
Expert's post
12
This post was
BOOKMARKED
5. Mrs. Smith has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. S... | [
"112",
"118",
"121",
"124"
] | D | Explanation :
Let, there are x first class ticket and (18-x) second class tickets.
Then,
110 = 10x + 3(18−x).
=>110=10x+54−3x.
=>7x=56.
=>x=8.
If the number of the first class and second class tickets are interchanged, then the total cost would be 10×10 + 3 × 8=124.
Answer : D |
AQUA-RAT | AQUA-RAT-39706 | # Math Help - word problem.
1. ## word problem.
hi ! im having a difficult time answering this word problem.
"Alvin set out from a certain point and travelled at the rate of 6 kph. After Alvin had gone for two hours, Ben set on to overtake him and went 4km the first hour, 5 km the second hour, 6 km the third hour an... | [
"30",
"58",
"60",
"90"
] | B | I believe there is a better way to do it.
Basically one of the options should satisfy the given criteria.
60 did
1/5 *60 =12
2/3*60=40
so total distance
52 + remaining 6 =58
Answer B |
AQUA-RAT | AQUA-RAT-39707 | The price then decreased by 12% during 2013
A 12% DECREASE is the same a multiplying the price by 0.88
So, the new price = ($100)(1 + p/100)(0.88) The price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012 If the original price was$100, then the price at the end of 2013 was $110 So,... | [
"1.5 years",
"2 years",
"3 years",
"13 years"
] | B | I think the fastest way is
81 *(1/3)^n = 1
n =4
So 2 yrs
ANSWER:B |
AQUA-RAT | AQUA-RAT-39708 | python, beginner, algorithm, strings, regex
Test 8: 1e is an invalid number.
--------------------------------------------------
Test 9: e3 is an invalid number.
--------------------------------------------------
Test 10: 6e-1 is a valid number.
--------------------------------------------------
Test 11: 99e2.5 is a... | [
"23",
"26",
"40",
"42"
] | C | The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C |
AQUA-RAT | AQUA-RAT-39709 | # Finding the probability using a normal distrubtion.
I have a stats question that says, "An airline flies airplanes that hold 100 passengers. Typically, some 10% of the passengers with reservations do not show up for the flight. The airline generally overbooks fights in an attempt to fill them."
And the question is ... | [
"20%",
"30%",
"40%",
"70%"
] | A | To maximize the percentage of companies offering both, let's assume that all 20% of companies which offer wireless internet also offer snacks.
The answer is A. |
AQUA-RAT | AQUA-RAT-39710 | So, for 24 dollars 24/2=12 oranges can be purchased at the original price of $2. Answer: B. _________________ Intern Joined: 26 May 2012 Posts: 21 Re: When the price of oranges is lowered by 40%, 4 more oranges [#permalink] ### Show Tags 15 Jul 2012, 02:22 Bunuel wrote: farukqmul wrote: When the price of oranges is low... | [
"5",
"6",
"2",
"3"
] | D | 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer: D |
AQUA-RAT | AQUA-RAT-39711 | # 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... | [
"Rs. 21000",
"Rs. 17500",
"Rs. 19000",
"Rs. 24500"
] | A | Let the cost prices of the colour television sold at 30% profit and 40% profit be Rs. x and Rs. (35000 - x) respectively.
Total selling price of televisions = x + 30/100 x + (35000 - x) + 40/100 (35000 - x)
=> 130/100 x + 140/100 (35000 - x) = 35000 + 32/100 (35000)
x = 28000
35000 - x = 7000
Difference in the cost pri... |
AQUA-RAT | AQUA-RAT-39712 | units
(Note that $1\ \mathrm{Pa}=1\ \mathrm{kg\ m^{-1}\ s^{-2}}$ and that $1\ \mathrm J=1\ \mathrm{kg\ m^2\ s^{-2}}$.)
The following is multiple choice question (with options) to answer.
Mother,her daughter and her grand child weighs 140 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand m... | [
"44",
"47",
"48",
"49"
] | A | mother + daughter + child = 140kg
daughter + child = 60kg
mother = 140 - 60 = 80kg
child = 1/5th of mother = (1/5)*80 = 16kg
So now daughter = 140 -(mother + child) = 140 - (80+16) = 44kg
ANSWER:A |
AQUA-RAT | AQUA-RAT-39713 | If 2 fair dice are rolled, what is the probability that the sum is 6, given both dice show odd numbers?
When the sum is 6, there combinations are: (1,5),(2,4),(3,3),(4,2),(5,1). Probability = 5/36
Probability of 2 odd numbers is 1/2.
What I'm not sure about is when we work out Pr(sum is 6|both numbers odd). I initia... | [
"5/6",
"7/36",
"5/36",
"11/36"
] | D | The sum of numbers appeared is 6 or 7. Therefore, the required sums are 6 or 7, i.e., the required events are (1,5), (5,1), (2,4), (4,2), (3,3), (1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
i.e., for 6, n(E) = 5 and for 7, n(E) = 6
Therefore, the required probability = n(E)/n(S) = 11/36.
ANSWER:D |
AQUA-RAT | AQUA-RAT-39714 | EZ as pi
Featured 5 months ago
$\text{males : females } = 6 : 5$
#### Explanation:
When working with averages (means), remember that we can add sums and numbers, but we cannot add averages.
(An exception would be if there were the same number of males and females - in this case we may add the averages and divide by... | [
"66",
"77",
"51",
"98"
] | C | Explanation:
Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.
Answer: C) 51 years |
AQUA-RAT | AQUA-RAT-39715 | in the comments section. At what speed does the second train B travel if the first train travels at 120 km/h. You can approach this as if you were solving for an unknown in math class or you can use the speed triangle. Time, Speed and Distance: Key Learnings. ) Since the distances are the same, I set the distance expre... | [
"34 kmh",
"40 kmh",
"42 kmh",
"44 kmh"
] | A | Assume D/3 = 720 (this number is convenient because it is divisible by 80, 18 and 48)
So:
720 = 80*T1 = 9 hrs
720 = 18*T2 = 40 hrs
720 = 48*T3 = 15 hrs
T = T1 + T2 + T3 = 64 hrs
D = RT
(720*3) = R*64
R = 33.75
ANSWER: A |
AQUA-RAT | AQUA-RAT-39716 | # 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... | [
"$0.00",
"$1.00",
"$3.40",
"$5.00"
] | D | 0.85*{Original Price} = $68 --> {Original Price} = $80.
{Final Price} = $68*1.25 = $85.
The difference = $85 - $85 = $5.
Answer: D. |
AQUA-RAT | AQUA-RAT-39717 | 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... | [
"40 sec",
"11 sec",
"88 sec",
"33.33 sec"
] | D | Speed = 54 * 5/18 = 15 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/15 = 33.33 sec
Answer: D |
AQUA-RAT | AQUA-RAT-39718 | # Math Help - Calculus Help Please
Initially a population contains 1000 individuals. After t minutes the number N of individuals in the populataion is such that dN/dt = -0.25N.
a) write down the expression for N in terms of t
b) Find the rate at which the population is decreasing when it is half its orginal size.
Thi... | [
"7900",
"8200",
"8500",
"8800"
] | B | Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 5535
(27/40) * x = 5535
x = 5535 * 40 / 27 = 8200
The answer is B. |
AQUA-RAT | AQUA-RAT-39719 | A question on the same concept
The number of television sets sold by Store R last month was approximately what percent less than the number of television sets sold by Store T last month? ( The number of television sets sold by Store R was 20 and number of television sets sold by Store T was 45 as per the attached figu... | [
"12%",
"16%",
"20%",
"23%"
] | D | Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.3P = x*P
N*x = x/1.3 which is about 0.77x, thus a 23% reduction.
The answer is D. |
AQUA-RAT | AQUA-RAT-39720 | # 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... | [
"None of these",
"380",
"312",
"324"
] | B | Explanation :
He can go in any bus out of the 20 buses.
Hence He can go in 20 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 19 ways.
Total number of ways = 20 x 19 = 380. Answer : Option B |
AQUA-RAT | AQUA-RAT-39721 | 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... | [
"50 kmph",
"82 kmph",
"62 kmph",
"65 kmph"
] | B | Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 30) kmph = 82 kmph.
Answer : B. |
AQUA-RAT | AQUA-RAT-39722 | 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... | [
"15years",
"20years",
"22years",
"25years"
] | A | Total age of 3 boys = 30*3 = 90
ratio of their ages = 1:2:3
Age of the youngest = 90*1/6 = 15 years
Answer is A |
AQUA-RAT | AQUA-RAT-39723 | # 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... | [
"22",
"23",
"24",
"25"
] | C | 3-0=3
8-3=5
15-8=7
difference increasing by 2 every time
next difference 9
15+9=24
ANSWER:C |
AQUA-RAT | AQUA-RAT-39724 | MHF Helper
Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.
1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0... | [
"a. 0.156",
"b. 0.01506",
"c. 0.0156",
"d. 0.0001566"
] | C | Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 120 units are defective
So, Out of total 10,000 units 156 units are defective...
So the required probability = 156/10000 => 0.0156
Answer will be (C) |
AQUA-RAT | AQUA-RAT-39725 | homework-and-exercises, kinematics
Title: Average Velocity A car travels 100 miles in 2 hours, it then completes the return leg of the journey. How fast must it travel on the return leg to average 100mph over the total journey.
My thoughts on this are that it is impossible as if the total average was 100mph then the... | [
" d",
" 1/3*d",
" 1/2*d",
" 3/4*d"
] | A | Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = d
Distance travelled second hour = d
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information give... |
AQUA-RAT | AQUA-RAT-39726 | # When will train B catch up with train A?
Printable View
• January 27th 2010, 08:19 PM
bball20
When will train B catch up with train A?
Trains A & B are traveling in the same direction on a parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 5:15 PM. If tra... | [
"5:00",
"5:30",
"6:00",
"6:20"
] | D | Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph
120 mi/ 60 mph = 2 hrs
4:20pm + 2 hrs = 6:20pm
Answer:
D. 6:20 |
AQUA-RAT | AQUA-RAT-39727 | of 69” which states the doubling period as 0.35 + 69/Interest The time value of money is a concept integral to all parts of business. How to Calculate Present Value, and Why Investors Need to Know It, Understanding the Compound Annual Growth Rate – CAGR. We could put the equation more concisely and use the$10,000 as FV... | [
"10 %",
"15 %",
"20 %",
"40 %"
] | C | Sol.
Let sum = x. Then, S.I. = 3x
∴ Rate = [100 * S.I. / P*T] = [100 * 3x / x * 15]% = 20%.
Answer C |
AQUA-RAT | AQUA-RAT-39728 | Using the law of sines, one can get
$$s=\frac{1}{2}bc \sin(\alpha)=\frac{1}{2}bc \frac{a}{2R}=\frac{abc}{4R}$$
where $R$ is the radius of the circumscribed circle.
• note that : Dr. Sonnhard Graubner says this first of all – Khosrotash Jul 26 '15 at 13:28
• @Khosrotash comments should not be used to supply answers. ... | [
"16*(sqr2 -1)",
"8*(sqr3 -1)",
"25*(sqr2 - 1)",
"12* (sqr7 -1)"
] | C | I got 16/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is C |
AQUA-RAT | AQUA-RAT-39729 | 4,8),(3,5,8),(2,6,8),(1,7,8),(1,9,8),(9,0,9),(8,1,9),(7,2,9),(6,3,9),(5,4,9),(4,5,9),(3,6,9),(2,7,9),(1,8,9)]
The following is multiple choice question (with options) to answer.
78, 64, 48, 30, 10, (...) | [
"-12 number",
"-14",
"2",
"8"
] | A | Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A |
AQUA-RAT | AQUA-RAT-39730 | For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.
Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.
We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, ... | [
"1345",
"1197",
"1540",
"1600"
] | B | Let the smaller number be x. Then larger number = (x + 1365).
x + 1000 = 6x + 15
5x = 985
x = 197
Large number = 197 +1365 = 1197
B |
AQUA-RAT | AQUA-RAT-39731 | Related Rate Prob - Ships sailing in different directions
• November 5th 2010, 09:15 PM
dbakeg00
Related Rate Prob - Ships sailing in different directions
Ship A is 15 miles east of point O and moving west at 20mi/h. Ship B is 60 miles south of O and moving north at 15mi/h. a)Are they approaching or seperating after 1... | [
"8.8",
"12.",
"12.5.",
"14."
] | A | Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.3 *5= 6.5 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (6.5^2+ 6^2)^1/2= 8.8KM
A is the answer |
AQUA-RAT | AQUA-RAT-39732 | i.e. we need to check that $$-1-[-x]\leq x<-[-x].$$
The inequality on the right, $[-x]<-x$, is the first inequality of the definition of $[-x]$, i.e. $[-x]\leq-x<[-x]+1$, and therefore it is true. Notice the equality doesn't hold on the left, because it is not an integer.
The inequality on the left is $-x\leq [-x]+1$... | [
"|x|<3",
"|x+5|<4",
"|x-3|<2",
"|-5+x|<4"
] | C | 1<x<5 represents segment with
length: 5-1 = 4
center: (5+1)/2 = 3
For any |x-a|<b a is a center and b is a half of length. So, |x-3|<4/2 represents our inequality (answer C) |
AQUA-RAT | AQUA-RAT-39733 | # 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... | [
"2/15",
"7/5",
"9/5",
"It cannot be determined from the information given."
] | D | let the actual ratio be 5k/6k, increase numerator and denominator by 4=> 5k+3/6k+3
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 3 => 6/7
let the actual be 6/8. After increasing 3 => 9/11
Therefore without actual quantities we cannot determine the actu... |
AQUA-RAT | AQUA-RAT-39734 | What we're looking for: How many subsets have $6$ as an element but not $7$?
We must choose to include $6$, that gives $1$ choice. We may choose to to include $1$ or not, that gives $2$ choices. We may choose to include $2$ or not, that gives $2$ choices. We may choose to include $3$ or not, that gives $2$ choices. We... | [
"A.16",
"B.72",
"C.93",
"D.32"
] | C | Number of subset
Since we have 7 digits other than 0, we can take any numbers from the set of 7 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations.
7c1+7c2+7c3+7c4+7c5+7c6+7c7=92
And one set is the NULL set having no elements in it so
92+1=93.
ANSWER C. |
AQUA-RAT | AQUA-RAT-39735 | 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.
. .... | [
"4538",
"4529",
"4528",
"4530"
] | D | Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs. 4530
Answer: D |
AQUA-RAT | AQUA-RAT-39736 | # When will train B catch up with train A?
Printable View
• January 27th 2010, 08:19 PM
bball20
When will train B catch up with train A?
Trains A & B are traveling in the same direction on a parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 5:15 PM. If tra... | [
"09:20p.m",
"04:40p.m",
"10.30p.m",
"02.32p.m"
] | C | D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C |
AQUA-RAT | AQUA-RAT-39737 | Originally Posted by Archie
Because the question talks about all possible pairs of integers, not just 2 and 3.
I can see that every word in word problems is important.
8. ## Re: Positive Integers x & y
Originally Posted by Plato
To harpazo, I cannot understand how this can be so mysterious.
Learn this:
1. The sum of ... | [
"a) 3",
"b) 1",
"2",
"d) 21"
] | C | Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 4
or ((n+4)+n)/n(n+4) =4 or (n^2+4n)*4 =2n+4 or n=2 as n cannot be -negative
Solve for n => n=2. Hence,
C |
AQUA-RAT | AQUA-RAT-39738 | 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... | [
"7:4",
"7:5",
"6:4",
"5:5"
] | B | C:D= 49000 : 35000 = 7:5.
ANSWER:B |
AQUA-RAT | AQUA-RAT-39739 | 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... | [
"18 days",
"20 days",
"24 days",
"30 days"
] | C | Explanation:
2c = ¼ + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C |
AQUA-RAT | AQUA-RAT-39740 | Seven-game series: . $\_\:\_\:\_\:\_\:\_\:\_\:W$
The first six games must have three W's and three L's in some order.
There are: . ${6\choose3,3} = {\color{red}20}$ ways.
Therefore, there are: . $1 + 4 + 10 + 20 \:=\:{\color{blue}35}$ ways.
The following is multiple choice question (with options) to answer.
Look at t... | [
"66",
"67",
"68",
"69"
] | B | Explanation:
In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
Answer: Option B |
AQUA-RAT | AQUA-RAT-39741 | As others have said, one can ask that the girls' chairs, and the block of chairs for the boys, be chosen together (in this way, we treat the group of boys as "another girl", for a total of 5 "girls" choosing among 5 "seats"); thus, we can have the boys choose one of the 5 "seats" (in reality, it is their block of chair... | [
"80",
"100",
"25",
"206"
] | D | We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
= 209.
ANSWER D |
AQUA-RAT | AQUA-RAT-39742 | This is an A.P. The below workout with step by step calculation shows how to find what is the sum of natural numbers or positive integers from 1 to 250 by applying arithmetic progression. is 56. If n is an integer, then n, n+1, and n+2 would be consecutive integers. If A and G be A.M. and G.M., respectively between two... | [
"0",
"-2",
"-25",
"-49"
] | D | Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 d= -49.
D is the answer. |
AQUA-RAT | AQUA-RAT-39743 | Question
# Three natural numbers are taken at random from a set of numbers $$\left \{ 1, 2, .... 50 \right \}$$.The probability that their average value taken as $$30$$ is equals
A
30C289C2
B
89C250C47
C
89C8750C3
D
None of these
Solution
The following is multiple choice question (with options) to answer.
Of the fo... | [
"28",
"64",
"11",
"48"
] | B | Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 80 or x = (80 * 4) / 5 = 64
Answer: B |
AQUA-RAT | AQUA-RAT-39744 | 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.
. .... | [
"Rs.4532",
"Rs.4526",
"Rs.4598",
"Rs.4530"
] | D | Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5
= Rs.4530
Answer:D |
AQUA-RAT | AQUA-RAT-39745 | # another probability: number of ways for 4 girls and 4 boys to seat in a row
4 posts / 0 new
Ej-lp ACayabyab
another probability: number of ways for 4 girls and 4 boys to seat in a row
In how many ways can 4 girls and 4 boys be seated in a row containing 8 seats if boys and girls must sit in alternate seats?
The ans... | [
"700",
"720",
"780",
"800"
] | B | npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
B |
AQUA-RAT | AQUA-RAT-39746 | # How to calculate the area covered by any spherical rectangle?
Is there any analytic or generalized formula to calculate area covered by any rectangle having length $l$ & width $b$ each as a great circle arc on a sphere with a radius $R$?
Note: Spherical rectangle is a quadrilateral having equal opposite sides but n... | [
"440 sq.units",
"550 sq.units",
"455 sq.units",
"450 sq.units"
] | D | Given that the area of the square = 2500 sq.units
=> Side of square = √2500 = 50 units
The radius of the circle = side of the square = 50units.
Length of the rectangle = 3/5 * 50 = 30 units
Given that breadth = 15 units
Area of the rectangle = lb = 30 * 15= 450 sq.units
Answer:D |
AQUA-RAT | AQUA-RAT-39747 | # 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... | [
"16%",
"17%",
"18%",
"41%"
] | D | Total CP = Rs. 34000 + Rs. 12000
= Rs. 46000 and SP = Rs. 65000
Profit(%)
= (65000 - 46000)/46000 * 100
= 41%
Answer: D |
AQUA-RAT | AQUA-RAT-39748 | # 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... | [
"Rs. 21,000",
"Rs. 22,500",
"Rs. 25,300",
"Rs. 25,800"
] | C | Solution
85 : 18700 = 115 : x or x = (18700 x 115 / 85)
= 25300.
Hence, S.P. = Rs. 25300.
Answer C |
AQUA-RAT | AQUA-RAT-39749 | newtonian-mechanics, rotational-dynamics, estimation, stability
Title: Human Lean Equation For a medical experiment I am doing, I need an equation to find the angle at which someone will lean before falling. I am not mathematically inclined in terms of advanced stuff, I am more so of a trigonometry person.
I assume fa... | [
"10",
"20",
"30",
"17"
] | D | His height was = 5 feet 8 inch = 8 + 60 = 68 inch. Required % correction =68*(1.25-1) = 17
D |
AQUA-RAT | AQUA-RAT-39750 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"55%",
"56%",
"57%",
"60.8%"
] | D | Total number of votes polled = (1136 + 7636 + 13628) = 22400
So, Required percentage = 13628/22400 * 100 = 60.8%
ANSWER : D |
AQUA-RAT | AQUA-RAT-39751 | When morning comes and all $N$ pirates wake up, they see the greatly diminished pile and a happy fat monkey.
The question is: how many bananas could there have been in the original pile for this to occur?
• Is this for all sets of possible bananas? – awesomepi May 22 '14 at 15:58
• ...The number of possible bananas i... | [
"5 min",
"6 min",
"7 min",
"8 min"
] | D | there are equal no. of monkeys and equal no. of bananas and they take equal time and the time is 8 mint to eat a banana so each monkey take 8 mints to eat a banana's so 3 monkeys will take 8 mints to eat 3 banana's.
ANSWER:D |
AQUA-RAT | AQUA-RAT-39752 | ## 28.
The Correct Answer is (D) — Graphs for answer choices A and B imply that the area of this rectangle can be 800$\small&space;ft^{2}$ or greater. These values are not possible with only 40ft of fencing material. Similarly, the graph for answer choice C says that the area can be as large as 400$\small&space;ft^{2}... | [
"333",
"200",
"240",
"276"
] | C | Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6360
[4L - 40] = 6360 / 26.50 = 240
4L = 280
L = 280/4= 70 meters.
Answer: C |
AQUA-RAT | AQUA-RAT-39753 | EZ as pi
Featured 5 months ago
$\text{males : females } = 6 : 5$
#### Explanation:
When working with averages (means), remember that we can add sums and numbers, but we cannot add averages.
(An exception would be if there were the same number of males and females - in this case we may add the averages and divide by... | [
"50",
"56",
"58",
"62"
] | C | Given that, Total average T sold is 66, Male/Female = 1/2 and Female average is 70. Average of Male members isX.
(70*F+X*M)/(M+F) = 66 -> Solving this equation after substituting 2M=F, X = 58. ANS C. |
AQUA-RAT | AQUA-RAT-39754 | • Perfect thank you very much, just the guidance I needed – Darragh O'Flaherty Apr 20 '18 at 11:28
You have $v= \alpha u + w$. Now, dot product by $u$ gives $$v \cdot u = \alpha u \cdot u + w \cdot u$$ We know $w \cdot u=0$ so the equation gives $$3 =\alpha 9$$ so $$\alpha={ 1 \over 3}$$. Knowing $\alpha$ it is straig... | [
"5w + 14y",
"5x + 16y",
"5x + 5y",
"6x + 4y"
] | A | 3(5Y+2W) -W-Y= 14Y+5W
'A' is the answer |
AQUA-RAT | AQUA-RAT-39755 | 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... | [
"377",
"367",
"237",
"255"
] | D | Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (120 + x)/30 = 25/2
x = 255 m.
Answer: D |
AQUA-RAT | AQUA-RAT-39756 | => 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... | [
"\t26/27",
"\t13/17",
"\t13/19",
"\t12/19"
] | A | MAKE R = 10
P = 0.8R = 8
Q = 0.8P = 6.4
S= 0.6P = 4.8
FOR THAT WE GET S = 10.8
AND Q 10.4
SO 10.4/10.8= 2.6/2.7
Ans:A |
AQUA-RAT | AQUA-RAT-39757 | general-relativity, astrophysics, orbital-motion, perturbation-theory, differential-equations
$${\rm{perihelion}} \, {\rm{advance}}\,{\rm{relation:}}\,6\pi M{u_0} \to \frac{{6\pi GM}}{{{r_0}{c^2}}},$$
in which $r_0$ is the mean orbital radius (the mean distance from Sun). Considering Sun with the mass $1.989 \times 10... | [
"172,800",
"124,600",
"93,400",
"72,200"
] | A | The speed is 28.8 miles/s. Then 28.8/0.6 = 48 km/s
48*3600 = 172,800 kph
The answer is A. |
AQUA-RAT | AQUA-RAT-39758 | # 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... | [
"75%",
"25%",
"28%",
"85%"
] | B | 800 --- 200
100 --- ? => 25%
Answer: B |
AQUA-RAT | AQUA-RAT-39759 | 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... | [
"6.3",
"6.9",
"7.1",
"6.1"
] | C | 1 day work of the three persons = (1/15 + 1/10 + 1/25) = 21/150
So, all three together will complete the work in 150/21 = 7.1 days.
Answer:C |
AQUA-RAT | AQUA-RAT-39760 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"2660",
"1000",
"2300",
"4000"
] | A | Explanation :
A is a working member and for that, he receive 5% of the profit
= 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
= 65*6 : 84*5 : 100*3 = 13*6 : 84 : 20*3 = 13*2 : 28 : 20
= 13 : 14 : 10
Share of B in the profit = 7030 * (14/37) = 190... |
AQUA-RAT | AQUA-RAT-39761 | 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... | [
"Five hours and 0 minutes.",
"One hour and 10 minutes.",
"Two hours and 25 minutes.",
"Three hours and 15 minutes."
] | A | Answer is A. Five hours and 0 minutes.
Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)
So time before collision is total distance / total speed = 3010/602 = 5 hours |
AQUA-RAT | AQUA-RAT-39762 | 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... | [
"120 sec",
"176 sec",
"178 sec",
"187 sec"
] | A | Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A |
AQUA-RAT | AQUA-RAT-39763 | 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.
. .... | [
"41",
"36",
"38",
"19"
] | A | Explanation:
Total number of students = 50 x 25
When arranged in rows of 30, number of rows formed are,
= 41.
Answer: A |
AQUA-RAT | AQUA-RAT-39764 | materials, density
densitytotal = masstotal / volume =
volume = masstotal / densitytotal = 0.2 kg / 2300 kg/m3 = 0.00008696 m3
masssand = 2700 kg/m3 * 0.0000869 m3 = 0.2348 kg
massplastic = 1400 kg/m3 * 0.0000869 m3 = 0.1217 kg
But I don't think this step was the right choice since the mass of the sand came out to be ... | [
"24",
"26",
"28",
"30"
] | A | Let the total weight be x.
Sand content= (1/3)x
Water content= (1/4)x
Gravel=x-(1/3)x-(1/4)x=(5/12)x=10
x=24
Then answer will be A=24 |
AQUA-RAT | AQUA-RAT-39765 | Question
# The number of positive numbers less than $$1000$$ and divisible by $$5$$ ( no digits being replaced) is
A
150
B
154
C
166
D
None of these
Solution
## The correct option is B $$154$$Here, the available digits are $$0,1,2,3,4,5,6,7,8,9.$$The numbers can be of one, two or three digits and in each of them un... | [
"27",
"37",
"932",
"12"
] | A | ANSWER:A |
AQUA-RAT | AQUA-RAT-39766 | $\text{So we have shown:}$
$\setminus q \quad {\text{odd"_1 +"odd"_2 + "odd"_3 +"odd"_4 + "odd"_5 +"odd"_6 \ = "even}}_{5.}$
$\text{So we conclude:}$
$\setminus \quad \text{the sum of any 6 odd numbers (consecutive or not) is even.}$
The following is multiple choice question (with options) to answer.
If a sequence ... | [
"-8",
"-4",
"0",
"4"
] | C | Let x be the first term.
Then x + 12 = 5 and x = -7
The sum is: x + (x+2) +...+ (x+14) =
8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-7) +56 = 0
The answer is C. |
AQUA-RAT | AQUA-RAT-39767 | # 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... | [
"$500",
"$467.5",
"$935",
"$525.5"
] | B | Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 25% profit.
This means the clocks' selling price was C (1.25) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys... |
AQUA-RAT | AQUA-RAT-39768 | +0
# 3.00 x 10^8 / 6.50 x 10^-7 the result is 4.61 x 10^14 my question is how 10^8 / 10^-7 = 10^14? thank u
0
330
2
3.00 x 10^8 / 6.50 x 10^-7
4.61 x 10^14
my question is how 10^8 / 10^-7 = 10^14?
thank u
Guest Nov 21, 2014
#1
+91465
+5
3.00 x 10^8 / 6.50 x 10^-7
4.61 x 10^14
my question is how 10^8 / 10^-7 ... | [
"314",
"3140",
"3140000",
"None of these"
] | C | Solution
Given, 3.14 ×106 =3.140000×1000000
= 3140000.
Answer C |
AQUA-RAT | AQUA-RAT-39769 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"124%",
"120 %",
"96 %",
"80 %"
] | C | Tim=100
Mary's income is 60 percent more than tims income;
Mary's Income = T+0.6T = 1.6T = 1.6*100=160
Tims income is 40 percent less than juans income .
100 is 40% less than Juan's Income
100=J-0.4J
100=0.6J
J = 100/0.6=1000/6
What percentage of juans income is marts income
(160/(1000/6))*100 = (160*6*100)/1000 = 96%
... |
AQUA-RAT | AQUA-RAT-39770 | 4,8),(3,5,8),(2,6,8),(1,7,8),(1,9,8),(9,0,9),(8,1,9),(7,2,9),(6,3,9),(5,4,9),(4,5,9),(3,6,9),(2,7,9),(1,8,9)]
The following is multiple choice question (with options) to answer.
4, 9, 13, 22, 35, ? | [
"57",
"70",
"63",
"75"
] | A | Sum of two consecutive numbers of the series gives the next number.
Answer : A. |
AQUA-RAT | AQUA-RAT-39771 | 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... | [
"23 days",
"37 days",
"37 ½ days",
"40 days"
] | C | Explanation:
A can finish the whole work in 20 × 5/4 days = 25 days
A and B together finish the whole work in 5 × 3 days = 15 days
Therefore, B can finish the whole work in 25 B/ 25 + B = 15
25 B = 15 ( 25 + B)= 375 + 15B
10B = 375 and B = 375/10 = 37 ½ days.
Answer: Option C |
AQUA-RAT | AQUA-RAT-39772 | ### Show Tags
27 Oct 2016, 16:26
3
GMATPrepNow wrote:
Bill and Ted each competed in a 240-mile bike race. Bill’s average speed was 5 miles per hour slower than Ted’s average speed. If Ted completed the race 4 hours sooner than Bill did, what was Bill’s average speed in miles per hour?
A) 7.5
B) 10
C) 12
D) 12.5
E) 15... | [
"12",
"15",
"18",
"20"
] | D | Let v be team B's average speed.
Time = Distance/Rate and the time difference was 5 hours.
500/v - 500/(v+5)= 5
500v + 2500 - 500v = 5(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D. |
AQUA-RAT | AQUA-RAT-39773 | # Math Help - word problem.
1. ## word problem.
hi ! im having a difficult time answering this word problem.
"Alvin set out from a certain point and travelled at the rate of 6 kph. After Alvin had gone for two hours, Ben set on to overtake him and went 4km the first hour, 5 km the second hour, 6 km the third hour an... | [
"10 kmph",
"11 kmph",
"12 kmph",
"14 kmph"
] | C | Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C |
AQUA-RAT | AQUA-RAT-39774 | • #### 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... | [
"152600m2",
"153500m2",
"153600m2",
"153800m2"
] | C | Explanation:
Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
We are having speed and time so we can calculate the distance or perimeter in this question.
Then by applying the formula of perimeter of rectangle we can get value of length and bre... |
AQUA-RAT | AQUA-RAT-39775 | # another probability: number of ways for 4 girls and 4 boys to seat in a row
4 posts / 0 new
Ej-lp ACayabyab
another probability: number of ways for 4 girls and 4 boys to seat in a row
In how many ways can 4 girls and 4 boys be seated in a row containing 8 seats if boys and girls must sit in alternate seats?
The ans... | [
"40320",
"42345",
"23456",
"40567"
] | A | npn = n!
8p8 = 8 x 7 x 6 × 5 × 4 × 3 × 2 × 1 = 40320
A) |
AQUA-RAT | AQUA-RAT-39776 | 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... | [
"1/6",
"1/9",
"1/11",
"1/3"
] | A | A's 1 day work = 1/18
B's 1 day work = 1/9
(A+B)'s one day work = (1/18+1/9)=1/6
Answer: A |
AQUA-RAT | AQUA-RAT-39777 | $y = x$ if $x \geq -1$.
It also means
$y = -(x + 1) - 1$ if $x + 1 < 0$, i.e. $x < -1$
$y = -x - 2$ if $x < -1$.
So all the points which satisfy these two linear equations will be your solution.
The following is multiple choice question (with options) to answer.
If x ≠ 0 and (−y^2 + xy)/x=y+x, which of the followi... | [
"x^2",
"x^2 + y^2",
"y^2",
"(y + x)^2"
] | B | (−y^2 + xy)/x=y+x
=> −y^2 + xy = xy +x^2
=> x^2 + y^2 = 0
Answer B |
AQUA-RAT | AQUA-RAT-39778 | # 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... | [
"8%",
"12%",
"20%",
"16%"
] | C | Solution: He sells only 900 grams when he takes the money for 1 kg.
and
he sells at a 8% profit (20% markup, 10% discount).
Hence, his selling price is Rs. 108 for 900 grams.
% profit = (18/90)*100 = 20%.
Answer: Option C |
AQUA-RAT | AQUA-RAT-39779 | +0
# At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
0
2788
3
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Feb 25, 2015
#3
+99377
+5
At a party, everyone shook hands with everyb... | [
"5",
"6",
"7",
"8"
] | D | no. of handshakes (ie) n(n-1)/2= 28
therefore no. of people present
n(n-1)=56
n2-n-56=0
n=8
No. of people present = 8
ANSWER:D |
AQUA-RAT | AQUA-RAT-39780 | Shanonhaliwell April 8th, 2018 03:31 PM
Quote:
Originally Posted by romsek (Post 591335) outstanding, you seem to be getting the hang of things.
Thanks to you, I was able to do it.
All times are GMT -8. The time now is 12:30 AM.
The following is multiple choice question (with options) to answer.
If the time is cur... | [
"12:30am",
"1:30am",
"12:30pm",
"2:30pm"
] | C | Every 24 hours will bring us to the same 1:30pm. 240 is divisible by 24 (10*24=240), so if it were 240 hours we would have 1:30pm, but since it's 239 hours then it will be 1 hour less, so 12:30pm.
Answer: C. |
AQUA-RAT | AQUA-RAT-39781 | 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... | [
"Rs. 375",
"Rs. 400",
"Rs. 600",
"Rs. 800"
] | B | Explanation:
C's 1 day's work =1/3-(1/6+1/8)=1/3-7/24=1/24
A's wages : B's wages : C's wages =1/6:1/8:1/24=4:3:1
C's share (for 3 days) = Rs.(3X1/24X3200)=Rs. 400
ANSWER IS B |
AQUA-RAT | AQUA-RAT-39782 | ### Show Tags
18 Feb 2015, 07:51
1
Using smart numbers:
Jennifer Purchases watches for $5: B=5 Markup of 100%; now selling for$10: x=10
She sells 5 watches: N=5
Her total profit will be (N*x)-(B*N)
(5*10)-(5*5)= 25
T=25
Now using the variables we must look at the answer choices that will solve for the % markup of t... | [
"8692",
"8702",
"8712",
"8722"
] | C | Net price after two discounts=80% of 90% of Rs. 10000=Rs. 7200.
Net C.P.=(7200+10% of Rs. 7200)=7920.
Therefore, S.P. =110% of Rs. 7920=Rs. 8712.
ANSWER:C |
AQUA-RAT | AQUA-RAT-39783 | 3. How many numbers that are not divisible by 6 divide evenly into 264,600?
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
4.A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60,... | [
"32",
"36",
"42",
"48"
] | C | A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(90)/5 - 12 = 54-12 = 42
The answer is C. |
AQUA-RAT | AQUA-RAT-39784 | ### Show Tags
23 Dec 2016, 09:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios [#permalink]
### Show Tags
09 Nov ... | [
"40",
"77",
"48",
"52"
] | B | Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 14)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 14 = 4/9(T - 14)
10T = 1386 - 616 => T = 77.
ANSWER:B |
AQUA-RAT | AQUA-RAT-39785 | $\text{So we have shown:}$
$\setminus q \quad {\text{odd"_1 +"odd"_2 + "odd"_3 +"odd"_4 + "odd"_5 +"odd"_6 \ = "even}}_{5.}$
$\text{So we conclude:}$
$\setminus \quad \text{the sum of any 6 odd numbers (consecutive or not) is even.}$
The following is multiple choice question (with options) to answer.
The sum of thr... | [
"31",
"21",
"29",
"22"
] | C | Middle number =87/3
=29
Ans C |
AQUA-RAT | AQUA-RAT-39786 | # Number of ways in which they can be seated if the $2$ girls are together and the other two are also together but separate from the first two
$5$ boys and $4$ girls sit in a straight line. Find the number of ways in which they can be seated if $2$ girls are together and the other two are also together but separate fr... | [
"33",
"30",
"36",
"28"
] | A | Explanation :
-------------------------------------------------------------------
Solution 1
-------------------------------------------------------------------
Assume that the number of boys = b and number of girls is g
number of boys + number of girls = 41
=> b + g = 41 ------------ (Equation 1)
Given that each boy g... |
AQUA-RAT | AQUA-RAT-39787 | # 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... | [
"Rs. 258",
"Rs. 270",
"Rs. 273",
"Rs. 285"
] | C | Total CP per shirt = 215 + 1400/160 + 1.75 + 320/160 = Rs. 227.5
SP = CP[(100 + profit%)/100]
= 227.5 * [(100 + 20)/100] = Rs. 273.
ANSWER:C |
AQUA-RAT | AQUA-RAT-39788 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"57.25%",
"45.54%",
"75.20%",
"45.59%"
] | D | Explanation :
Total number of votes polled = (45990 + 20008 + 34884 )
= 61200.
Required percentage = (45990/ 100882) x 100%
= 45.59%.
Answer : D |
AQUA-RAT | AQUA-RAT-39789 | +0
# URGENT! I NEED HELP RIGHT AWAY!
0
261
1
+755
Larry has 4-cent stamps and 9-cent stamps, which he can combine to produce various amounts of postage. For example, he can make 40 cents by using four 9-cent stamps and a 4-cent stamp, or by using ten 4-cent stamps. However, there are some amounts of postage he can't... | [
"20",
"30",
"40",
"60"
] | A | P started with 5k stamps and Q started with 3k stamps.
(5k-10)/(3k+10) = 9/7
35k - 27k = 160
k = 20
P has 5(20) - 10 = 90 stamps and Q has 3(20)+10 = 70 stamps.
The answer is A. |
AQUA-RAT | AQUA-RAT-39790 | • $P_2$ will fly $\big[1-(d+r+y)\big]$ distance away from the airport in the counter-clockwise direction to meet up with $P_3$.
• At this point, $P_2$ will donate $z$ fuel to $P_3$.
• $P_2$ and $P_3$ will then both fly back $z$ distance, arriving at a distance of $1-d-r-y-z$ from the airport with no fuel.
• After refue... | [
"6",
"7",
"9",
"10"
] | B | We need on-time departure rate to be higher than 9/10, so it should be at least 10/11 which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10−3=7 subsequent flights need to depart on-time.
Answer: B |
AQUA-RAT | AQUA-RAT-39791 | $\therefore \sum_{n=1}^{20} (2^n) - 20 = 2097150 - 20 = 2097130$
Which is the same answer as yours, however the answer in the book says $2097170$. They must of added the 20 instead of subtracted it. OK thanks
4. Originally Posted by chancey
Right, but thats not the answer in the back of the book...
I did it this way... | [
"15",
"26",
"28",
"4"
] | D | Let the number be x. Then,
x + x2 = 20
(x + 5)(x - 4) = 0
x = 4
ANSWER:D |
AQUA-RAT | AQUA-RAT-39792 | $P(-5) = 100,000 * (1.0594631)^{-5} \approx 74,915$.
=====
Alternatively
$(1 + rate)^{12} = 2$. What is $(1 + rate)^5$?(1+rate)^{12} = 2 \implies rate = .0594631$so$(1+rate)^5 = 1.594631^5 = 1.3348398541700343648308318811845$So from$1995$to$2000$the population grew by a factor of$1.3348398541700343648308318811845$. ... | [
"320000",
"120029",
"187899",
"178968"
] | A | X * (105/100) * (105/100) * (105/100) = 370440
X = 370440/1.157625
X = 320000
Answer:A |
AQUA-RAT | AQUA-RAT-39793 | 3 , 10 , 12 , 5 , 18 , 6 = { x1 , x2 , x3 , x4 , x5 , x6 }
n = 6 , μ = 9
σ = $\dpi{80}&space;\fn_jvn&space;\sqrt{\frac{3^{2}+10^{2}+12^{2}+5^{2}+18^{2}+6^{2}}{6}\:&space;-\:&space;9^{2}}$ = $\dpi{80}&space;\fn_jvn&space;\sqrt{\frac{638}{6}\:&space;-\:&space;81}$ = $\dpi{80}&space;\fn_jvn&space;\... | [
" I only",
" III",
" IIII",
" IIIII"
] | D | (1) Multiplying all the numbers change Standard Deviation
(2) Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number ... |
AQUA-RAT | AQUA-RAT-39794 | Now
$$y+5 = 2k+5$$
Now we just need to show that $$2k+5$$ is 2 times an integer plus 1
$$2k+5 = 2(k+2)+1$$
So $$2k+5$$ is odd because it can be written in the form 2*integer +1 where the integer here is $$k+2$$. So $$y+5$$ is odd since $$y+5 = 2k+5$$
So if any number is even. Then that number plus 5 is odd. It doe... | [
"none of the following",
"x + y",
"x + 2y",
"3x-1"
] | A | x = 50y + 2, since y is integer, 50y will always be even hence 50y + 2 will be even hence x = even
you don't know whether Y is even or odd, so you need to try.
E: even * even = even ; ->not true
B: even + even = even ; > not true
C: even + 2*even = even ;
A |
AQUA-RAT | AQUA-RAT-39795 | ## Example 2: Surgical implants
Surgeries involving implants sometimes result in the patient's body rejecting the implant. A certain surgery has a rejection rate of 11, percent. The rest of the patients successfully accept the implant.
Assume that the results for each patient are independent.
Example 2
In a random sam... | [
"N/12",
"4N/15",
"14N/12",
"11N/12"
] | D | 1/3 of tested had infection A, thus N/2 had infection A;
Of those with infection A, 1/6 also had infection B, thus 1/2*N/6 = N/12 had both infections A and B.
Therefore, N - N/12 = 11N/12 did not have both infection A and B.
Answer: D. |
AQUA-RAT | AQUA-RAT-39796 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"32:45",
"32:37",
"32:41",
"32:47"
] | A | A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer: A |
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