source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38397 | $\text{So we have shown:}$
$\setminus q \quad {\text{odd"_1 +"odd"_2 + "odd"_3 +"odd"_4 + "odd"_5 +"odd"_6 \ = "even}}_{5.}$
$\text{So we conclude:}$
$\setminus \quad \text{the sum of any 6 odd numbers (consecutive or not) is even.}$
The following is multiple choice question (with options) to answer.
The sum of fou... | [
"33",
"38",
"70",
"123"
] | B | Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 140 => x = 18
Smallest number is: 2(x +1) = 38.
Answer: B |
AQUA-RAT | AQUA-RAT-38398 | The heights 60 through 61.5 inches are in the interval 59.95–61.95. The heights that are 63.5 are in the interval 61.95–63.95. The heights that are 64 through 64.5 are in the interval 63.95–65.95. The heights 66 through 67.5 are in the interval 65.95–67.95. The heights 68 through 69.5 are in the interval 67.95–69.95. T... | [
"1/3.",
"3.",
"2.",
"1/2."
] | B | Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 18 and L be 6, 18 - 6 = (18 + 6)/2
B |
AQUA-RAT | AQUA-RAT-38399 | Suppose that 5 cards are dealt from a 52-card deck. What is the probability of drawing at least two kings given that there is at least one king?
The Attempt at a Solution
Let ##B## denote the event that at least 2 kings are drawn, and ##A## the event that at least 1 king is drawn. Because ##B## is a strict subset of ... | [
"1/26",
"1/07",
"1/22",
"1/29"
] | A | Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A |
AQUA-RAT | AQUA-RAT-38400 | # 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... | [
"50%",
"25%",
"35%",
"40%"
] | A | Cost price of article = 48$
% of overhead cost = 25
Net profit = 12 $
We need to calculate % markup
Net profit as % of cost price = (12/48)*100 = 25%
Total markup should be = 25 + 25 = 50%
Answer A |
AQUA-RAT | AQUA-RAT-38401 | 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... | [
"70 minutes",
"80 minutes",
"85 minutes",
"90 minutes"
] | D | Let us consider that speed of train , first man and second man are respectively t, f and s.
According to first given condition goods train crossed the first person moving in same direction in 20 sec.
so length of the will be 20(t-f)
similarly train crossed the second man in 18 sec.
so length of the train will be 18(t+s... |
AQUA-RAT | AQUA-RAT-38402 | Note: The author(s) of your text are calculating the probability that the top-ranked woman is in the $k$th position. For that to occur, we must select $k - 1$ of the five men to be ranked ahead of her and one of the five women to fill the $k$th position while choosing $k$ of the $10$ people. Hence, the answer in the te... | [
"11th",
"13th",
"12th",
"14th"
] | B | when considered from last, 12 (i.e 26-14) students are ranked before her. so she is 13th rank from last.
ANSWER:B |
AQUA-RAT | AQUA-RAT-38403 | # Probability of a certain ball drawn from one box given that other balls were drawn
Box 1 contains 2 green and 3 red balls, 2 has 4 green and 2 red, and 3 has 3 green and 3 red. Only one ball is drawn from each of the 3 boxes. What is the probability that a green ball was drawn from box 1 given that two green balls w... | [
"2/3",
"8/21",
"3/7",
"9/22"
] | B | Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: Option B |
AQUA-RAT | AQUA-RAT-38404 | # Probability Problem with $n$ keys
A woman has $n$ keys, one of which will open a door. a)If she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her $k^{\mathrm{th}}$ try?
Attempt: On her first try, she will have the correct key with probability $\f... | [
"1/18",
"1/9",
"5/36",
"1/4"
] | B | P(not winning) = 17/18*16/17 = 8/9
P(winning) = 1 - 8/9 = 1/9
The answer is B. |
AQUA-RAT | AQUA-RAT-38405 | 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... | [
"4 min",
"2 min",
"8 min",
"9 min"
] | C | S = 600/40 = 15 mps
S =7200/15 =480 sec =8 min.Answer:C |
AQUA-RAT | AQUA-RAT-38406 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"40",
"45",
"50",
"55"
] | B | From the question stem we know that we need a mixture of 100 pounds of peanuts and cashews. If we represent peanuts as x and cashews as y, we get x + y = 100. Since the wholesaler wants to sell the mixture of 100 pounds @ $2.50, we can write this as: $2.5 * (x + y) = $1.5x + $4y
From the equation x + y = 100, we can re... |
AQUA-RAT | AQUA-RAT-38407 | 5 miles per hour. g. It shows how three runners ran a 100-meter race. Distance, Time and Speed Challenge. Calculate the average speed (in meters/sec) if a golf cart runs 140 meters in 10 seconds What is the average speed (in miles per hour) of the car that traveled a …Distance, Time and Speed Challenge. Speed Distance ... | [
"252 kms",
"152 kms",
"732 kms",
"752 kms"
] | C | Explanation:
Total distance travelled in 12 hours =(50+52+54+.....upto 12 terms)
This is an A.P with first term, a=50, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 50+{12-1) x 2]
=6(122)
= 732 kms.
Answer: C |
AQUA-RAT | AQUA-RAT-38408 | => 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... | [
"300",
"230",
"500",
"560"
] | A | N * 50 = (315000 - 300000) = 15000
N = 15000 / 50
= 300
A |
AQUA-RAT | AQUA-RAT-38409 | 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... | [
"20",
"25",
"45",
"65"
] | C | The arithmetic mean of 4 equally weighted tests was 60. So what we can assume is that we have 4 test scores, each 60.
He dropped his lowest score and the avg went to 65. This means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too. When the lowest score wa... |
AQUA-RAT | AQUA-RAT-38410 | 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 ... | [
"$2456",
"$2436",
"$2446",
"$2466"
] | B | 6 percent compounded semiannually --> 3% in 6 moths.
For the first 6 moths interest was 3% of $40,000, so $1200
For the next 6 moths interest was 3% of $41,200, so $1236
Total interest for 1 year was $1200+$1236=$2436
Answer : B |
AQUA-RAT | AQUA-RAT-38411 | 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... | [
"40 days",
"30 days",
"60 days",
"70 days"
] | C | Explanation:
12 = (15 * x)/(15 + x)
180+12x=15x
3x=180
X=60
Answer: Option C |
AQUA-RAT | AQUA-RAT-38412 | 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 days",
"7 days",
"8 days",
"9 days"
] | B | Explanation:
1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work =
(5/70+10/140)=1/7
So 5 women and 10 children will finish the work in 7 days
Option B |
AQUA-RAT | AQUA-RAT-38413 | Your mistake is in 4th step. When you are taking $(-1+i)$ common from $R_2$. Then element at 2nd row and 3rd column is wrong I think.
• Sorry, I meant to multiple by $\frac{1}{-1+i}$. Already edited. – AndreGSalazar Apr 18 '17 at 16:58
• Then it becomes $\frac{i}{1-i}$. – Kanwaljit Singh Apr 18 '17 at 17:25
The follow... | [
"[A] two",
"[B] three",
"[C] five",
"[D] ten"
] | A | NON- multiples of 2 would always be ODD and sum of two odd would be EVEN.
so irrespective of value of non-multiples, sum of two them would always be even and thus multiple of 2..
A |
AQUA-RAT | AQUA-RAT-38414 | $\Rightarrow AC+CB=4(AB)$
$\Rightarrow (AB+BC)+CB=4(AB)$
$\Rightarrow BC+CB = 3(AB)$
$\Rightarrow BC=\dfrac{3}{2}(AB)$ -------- $(1)$
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... | [
"15 min",
"16 min",
"17 min",
"18 min"
] | D | Consider 1 mile = 1.6 km
so 10 miles = 16 km
both are walking in at an angle 90 from same point so pythagorous theorem can be apply hence
(15x)^2 + (25x)^2 = 16^2
by solving and x hours are converted into min we got
approximate 18 min
ANSWER:D |
AQUA-RAT | AQUA-RAT-38415 | $\displaystyle \frac{3}{4} \times 0.04 = 0.03$
4. Outch ! Sorry, I'll think again about it !
5. Ok, so $\displaystyle P(A/R)=\frac{P(A \cap R)}{P\color{red}(R)}$
Plus $\displaystyle P(R/A)=\frac{P(A \cap R)}{P(A)} \Longleftrightarrow P(A \cap R)=P(R/A)P(A)$
Hence : $\displaystyle {\color{blue} P(A/R)=\frac{P(R/A)P(A... | [
"0.18",
"0.21",
"0.22",
"0.34"
] | A | Formula = Fourth propotional = (b × c)/a
A = 0.2 , B = 0.12 and C = 0.3
(0.12 × 0.3)/0.2
0.036/0.2 = 0.18
A |
AQUA-RAT | AQUA-RAT-38416 | Manager
Joined: 07 Jul 2016
Posts: 79
GPA: 4
Re: Two bottles are partially filled with water. The larger bottle current [#permalink]
### Show Tags
04 Aug 2016, 22:33
AbdurRakib wrote:
Two bottles are partially filled with water. The larger bottle currently holds $$\frac{1}{3}$$ of its capacity. The smaller bottle, w... | [
" $0.04",
" $0.12",
" $0.05",
" $0.03"
] | A | Cost per capsule in R is 6.30/100=0.063
Cost per capsule in T is 2.99/130=0.023
The difference is 0.004
The answer is A |
AQUA-RAT | AQUA-RAT-38417 | regular-languages, finite-automata, nondeterminism
Title: Minimal number of states for an NFA of all different words Given $\Sigma =\{0,1,@\}$, I am looking at a language $L=\{u@v | u,v\in \{0,1\}^k\wedge u\neq v\}$. So $u,v$ have only $0,1$s, same length $k$, yet are different.
Also, for me $k$ is a known constant. S... | [
"8",
"2",
"9",
"3"
] | B | There are five letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 2! ways.
The number of words = 2! = 2.
Answer:B |
AQUA-RAT | AQUA-RAT-38418 | Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have
48(35) = 22(38) + 26x
1680 = 836 + 26x
26x = 844
x = 844/26
x = 32 12/26 ≈ 32.5
_________________
Scott Woodbury-Stewart
Founder and CEO
GMAT Quant Self-Study Course
50... | [
"15.5",
"15.4",
"15.25",
"20.4"
] | D | Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 141.
Total age of five men added later = 414 - 312 = 202.
Hence, the total average of five men = 102/5 = 20.4
ANSWER:D |
AQUA-RAT | AQUA-RAT-38419 | If we take $F_1=F_2=1$, then we certainly have that $5|F_5=5$. Let's look at the Fibonacci numbers, reduced modulo $5$:
$F_1\equiv 1\\ F_2\equiv 1\\ F_3\equiv 2\\ F_4\equiv 3\\ F_5\equiv 0\\ F_6\equiv 3\\ F_7\equiv 3\\ F_8\equiv 1\\ F_9\equiv 4\equiv -1\\ F_{10}\equiv 0\\ F_{11}\equiv -1\\ F_{12}\equiv -1\\ F_{13}\equ... | [
"107",
"101",
"147",
"None of these"
] | B | Solution:
The function f(a, b) = a3 + b2
f(1, 2) therefore is = 1^3 + 2^2 = 1 + 4 = 5 and
f(1, 5) = 1^3 + 5^2 = 1 + 25 = 26
Therefore, f(1, 10) = 1^3 + 10^2 = 1 + 100 = 101
Answer B |
AQUA-RAT | AQUA-RAT-38420 | visualization
equating "relationship wealth" with "proportion of people of the opposite gender attracted"
the more a person is attractive the more they go for the top attractive people of the opposite gender,
Then for each gender the average number of likes received by level of attractiveness is calculated, for examp... | [
"70%",
"55%",
"60%",
"65%"
] | A | T=100
A=30
B=50
Both=x
A only=30-x
B only=50-x
N=Neither
Given:
A only+B only=2*Both
30-x+50-x=2x
80=4x
x=20
T=A only+B only+Both+Neither
100=30-20+20-20+20+N
100=30+N
N=100-30=70
Ans:A |
AQUA-RAT | AQUA-RAT-38421 | ### 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... | [
"14299",
"27888",
"26687",
"14000"
] | D | 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000 .Answer: D |
AQUA-RAT | AQUA-RAT-38422 | What length of string will make 4 complete revolutions in a length of 12 inches around the cylinder of radius $\frac{2}{\pi}$?.
$t_{0}=8{\pi}$, because we have 4 rev.
a=radius of cylinder = $\frac{2}{\pi}$
$c=\frac{12}{8\pi}=\frac{3}{2\pi}$
$\boxed{8{\pi}\sqrt{\left(\frac{2}{\pi}\right)^{2}+ \left(\frac{3}{2\pi}\ri... | [
"338",
"140",
"287",
"277"
] | B | Explanation:
distance covered in 1 revolution = {\color{Blue} 2\Pi r} = 2 *(22/7) *20 = 880/7 cm
required no of revolutions = 17600 *(7/880) = 140
Answer: B) 140 |
AQUA-RAT | AQUA-RAT-38423 | 4. ## Re: find length of rectangle given diagonal and area
Originally Posted by Bonganitedd
Rectangle has area=168 m^2 and diagonal of 25. Find length
This is how tried to attempt the problem
Area= L X W
168 = L x W ..........(1)
L^2 + W^2 =25^2 ............(2)
From (1) L = 168/W...........(3)
Substitute (3) into (2)
... | [
"12cm",
"14cm",
"16cm",
"18cm"
] | C | Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 65 => 5x - 25 = 65 => x = 16.
Length of the rectangle = 16 cm.
Answer: Option C |
AQUA-RAT | AQUA-RAT-38424 | (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 ... | [
"$1.50",
"$6",
"$8",
"$7"
] | C | The jelly is extra information. 16.00 – 3 x 1 – 5.00 =
16.00 – 3 – 5.00 = 8
You have $8 left.
correct answer C |
AQUA-RAT | AQUA-RAT-38425 | # 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... | [
"7000",
"6700",
"6695",
"7645"
] | C | X * (70/100) * (75/100) = 3515
X = 6695
Answer: C |
AQUA-RAT | AQUA-RAT-38426 | # Kinematics Problem
1. Feb 24, 2008
### undefinable
1. The problem statement, all variables and given/known data
Alvin races Ophelia to Physics class. Alvin has a headstar of 13m and travels at a constant speed of 7m/s. Phelia is initially travelling at 1.2m/s but then begins to accelerate at 1.5m/s2 until she rea... | [
"1/14",
"1/17",
"3/14",
"3/17"
] | D | Let x be the fraction of the distance that B runs.
Let v be the speed at which B runs.
The time should be the same for both runners.
Time = D / (17v/14) = xD/v
(14/17)*D/v = x*D/v
x = 14/17
B should have a head start of 3/17 of the full distance.
The answer is D. |
AQUA-RAT | AQUA-RAT-38427 | Thus, the difference is 27-18 = 9 hours, which is answer choice A.
Originally posted by bbear on 17 Jun 2016, 14:31.
Last edited by bbear on 17 Jun 2016, 16:04, edited 1 time in total.
##### General Discussion
VP
Joined: 07 Dec 2014
Posts: 1157
Re: Six machines at a certain factory operate at the same constant rate. ... | [
"50 hours",
"40 hours",
"25 hours",
"12 hours"
] | C | Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by... |
AQUA-RAT | AQUA-RAT-38428 | 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... | [
"1/2 day",
"1/8 day",
"1/3 day",
"8/2 day"
] | A | Two men take four days to complete the work four men would take (2 * 4)/4 = 2 days to complete it.
Similarly four women would take two days to complete it and 20 children would take one day to complete it.
All the three groups working togerther will complete 1/2 + 1/2 + 1/1 work in a day
= 2 times the unit work in a da... |
AQUA-RAT | AQUA-RAT-38429 | # Random Gift Giving at a Party - Combinatorics Problem
Each of $$10$$ employees brings one (distinct) present to an office party. Each present is given to a randomly selected employee by Santa (an employee can get more than one present). What is the probability that at least two employees receive no presents?
Firstl... | [
"15",
"320",
"400",
"150"
] | C | The number of children is not specified. We are just given that there are no more than 100 children.
If we assume that number of children is 75 then answer will be D.
If we assume that number of children is 100 then answer will be C because only 400 is divisible by 100. |
AQUA-RAT | AQUA-RAT-38430 | 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 ... | [
"2 1/2 %",
"4%",
"5%",
"6 2/3 %"
] | C | S.I. on Rs. 800 for 1 year = (840 - 800) = Rs. 40 Rate = (100 * 40)/(800 * 1) = 5%
ANSWER:C |
AQUA-RAT | AQUA-RAT-38431 | # Question on arithmetic (Percentages)
A machine depreciates in value each year at the rate of 10% of its previous value. However every second year there is some maintenance work so that in that particular year, depreciation is only 5% of its previous value. If at the end of fourth year, the value of the machine stand... | [
"87,508",
"87,502",
"87,500",
"87,509"
] | C | Explanation:
No explanation is available for this question!
ANSWER: C |
AQUA-RAT | AQUA-RAT-38432 | c#, parsing
\n20150805 0900| 6| 91| | 0| | 0| | 0| 0| 0.0| | 13.0| 10.0| 0| 0| |15.00| |
\n20150805 1000| 8| 84| | 0| | 0| | 0| 0| 0.0| | 13.0| 11.0|230| 8| |15.00| |
\n20150805 1100| 10|113| -RW |100| | 0| | 0|100| 0.1| RA| 13.0| 11.0|277| 11| |10.00| |
\n--... | [
"15060000",
"0.001506",
"1.506e-06",
"0.1506"
] | C | Explanation:
Clearly after decimal 9 digits should be there.
Option C |
AQUA-RAT | AQUA-RAT-38433 | I see from your profile that you’re a programmer. Extreme cases like these are analogous to testing boundary conditions in your code (things like loops that execute 0 times).
Let x to be your gross salary and y = 1600 to be your net salary. Because tax is 20% of gross salary then we have
x = y + tax = 1600 + 0.2x
=> ... | [
"5500",
"2999",
"2878",
"2990"
] | A | Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 220 => 5500
Answer: A |
AQUA-RAT | AQUA-RAT-38434 | 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... | [
"(5!)^2",
"(6!)^2",
"6!7!",
"11!"
] | C | first fix one boy and place other 6 in alt seats so total ways is 6!
now place each girl between a pair of boys... total ways of seating arrangement of girls 7!
total is 6!*7!
ANS C |
AQUA-RAT | AQUA-RAT-38435 | # STRNO - Editorial
Setter: Kritagya Agarwal
Tester: Felipe Mota
Editorialist: Taranpreet Singh
Easy
Number theory
# PROBLEM:
Given two integers X and K, you need to determine whether there exists an integer A with exactly X factors and exactly K of them are prime numbers.
# QUICK EXPLANATION
A valid choice for ... | [
"17",
"18",
"19",
"20"
] | D | First, let's translate the expression 21#39, using the definition given:
21#39 = 21×24×27×30×33×36×39
We need the prime factorization of this product.
Let's factor out 3 from each multiple.
21#39 = 3^7(7×8×9×10×11×12×13)
Now let's replace each consecutive integer with its prime factorization:
21#39 = 3^7(7×2^3×3^2×(2×5... |
AQUA-RAT | AQUA-RAT-38436 | ### 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... | [
"11%",
"15%",
"18%",
"17%"
] | C | C
18%
Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18% |
AQUA-RAT | AQUA-RAT-38437 | s_1 :: Integer -> Integer
s_1 n
| n < 2 = error "s_1: n must be >= 2."
| otherwise = t_0 - t_1 - t_2 - t_3
where x_0 = floor ((fromIntegral n) / phi_r)
ff x = (x * (x + 1) * (x + 2)) div 6
(_, _, t_0) = fast_F m_k m_f x_0
t_1 = 2
t_2 = (sum_of_squares x_0) - (sum_of_squares 1)
t_3 = (ff x_0) - (ff 1)
m_f = M.insert 2 (... | [
"an odd integer",
"an even integer",
"a prime number",
"a composite number"
] | A | Solution:
(2x + 1) times (x + 2) means (2x + 1)(x + 2)
(2x + 1)(x + 2) = 2x^2+5x+2
For 2x^2+5x+2 to be odd, 5x+2 must be odd since 2x^2 is always even.
So 5x must be odd, hence x must be odd.
Therefore x is an odd integer.
Answer: A |
AQUA-RAT | AQUA-RAT-38438 | 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... | [
"10.77 a.m",
"10.85 a.m",
"10.27 a.m",
"10.25 a.m"
] | D | Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer:D |
AQUA-RAT | AQUA-RAT-38439 | # Is there a quicker proof to show that $2^{10^k} \equiv 7 \pmod{9}$ for all positive integers $k$?
I noticed this pattern while playing with digit sums and noticed that the recursive digit sums (until you arrive at a single digit number) of numbers like, $2^{10}$, $2^{100}$, $2^{1000}$ and so on is always $7$. So, I ... | [
"6",
"7",
"5",
"8"
] | D | So, the numbers should be from 10,000,000 to 100,000,000
The following two cases are possible for the sum of the digits to be 2:
1. Two 1's and the rest are 0's:
10,000,001
10,000,010
10,000,100
10,001,000
10,010,000
10,100,000
11,000,000
7 numbers.
2. One 2 and the rest are 0's:
20,000,000
1 number.
Total = 8 numbers.... |
AQUA-RAT | AQUA-RAT-38440 | In layman terms, this means if we assume there is a smallest number X where X>0 but there is no number such that X>Y>0, then X is the difference between 1 and 0.999... As all my opponent's formulas rely on the idea that 0.999... is a real number, he fails the idea when applied to hyperreal numbers.
The following is mu... | [
"5",
"0.05",
"0.5",
"50"
] | B | Explanation :
Required Answer = 0.0005/0.01 = 0.05/1 = 0.05. Answer : Option B |
AQUA-RAT | AQUA-RAT-38441 | 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... | [
"$5.60",
"$7.20",
"$8.80",
"$9.60"
] | B | The lowest price would have to be calculated by finding the price of the $16 product after the initial 40% reduction, then the final price after 25% was taken off of the already-discounted price. So:
A 40% discount on a $16 product would = 60% of the original $16 price: $16 x .60 = $9.6
Next you have to find the price ... |
AQUA-RAT | AQUA-RAT-38442 | the area and volume of a sphere, using simple geometric arguments. The surface area is the surface part of a three-dimensional object. Find out what's the height of the cylinder, for us it's 9 cm. Volume of a cylinder is (to find half, divide by 2): Vcylinder = Abase * height In a cylinder, the base is a circle and the... | [
"725pi sq m",
"1025pi sq m",
"600pi sq m",
"125pi sq m"
] | A | s.a. = h x p + 2 x a
we need to excude the bottom area, so the formula becomes:
s.a. = h x p + a
p = 2 pi x r, so 10 pi = 2 pi x r
r = 5
since we have 5 cylinders with different heights the equation becomes
s.a. = ( 4 + 8 + 12 + 16 + 20 ) x 10pi + 5 x pi x r ^2
60 x 10 pi + 5 pi x 5^2
600 pi + 125 pi = 725 pi sq. m.
An... |
AQUA-RAT | AQUA-RAT-38443 | ## 28.
The Correct Answer is (D) — Graphs for answer choices A and B imply that the area of this rectangle can be 800$\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}... | [
"10",
"12",
"14",
"16"
] | D | perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20
cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 682
62L = 992
L = 16 meters
The answer is D. |
AQUA-RAT | AQUA-RAT-38444 | • I hope that the graphs would not converge on $50\%.$ When the $P_{ai}$ and $P_{bi}$ are independently uniformly distributed between $0$ and $1,$ they should converge to a value very close to $41\%.$ That is due to the fact that (a) both students have equal chances of coming out with a higher score and (b) there is ab... | [
"52%",
"64%",
"72%",
"76%"
] | A | If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midt... |
AQUA-RAT | AQUA-RAT-38445 | SIMPLE
$27^\frac{2}{3}=(3\cdot\ 3\cdot\ 3)^{\frac{2}{3}}=(3^3)^{\frac{2}{3}}=(3)^{3\cdot\frac{2}{3}}=**(3)^{\frac{6}{3}}**=3^2$
ACTUALLY. $27^2$. BECOMES $3^6$
The following is multiple choice question (with options) to answer.
If three eighth of a number is 141. What will be the approximately value of 32.08% of thi... | [
"90",
"120",
"160",
"60"
] | B | x * 3/8 = 141 => x= 376
376 * 32.08/100 = 120
ANSWER:B |
AQUA-RAT | AQUA-RAT-38446 | special-relativity, visible-light, reference-frames, rotational-dynamics, rotation
Title: Light’s Behavior in a Rotating Reference Frame Let’s say there is a laser on one side of a very large rotating table, and it’s beam is shining onto a target on the other side of this table. The target is equipped with a very sens... | [
"1/4",
"1/3",
"1/2",
"2/3"
] | B | 1 revolutions per minute = 1 revolution every 60 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 60 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 20 seconds) = 1 - P (man in dark for max of 20 seconds) = 1 - 20/60 =... |
AQUA-RAT | AQUA-RAT-38447 | $11 + 6.5 = 17.5 \text{ or } 24 - 6.5 = 17.5$.
Therefore, 17.5 is the number in the middle of $11 \mathmr{and} 24.$
• 4 minutes ago
• 5 minutes ago
• 7 minutes ago
• 8 minutes ago
• 37 seconds ago
• A minute ago
• A minute ago
• 2 minutes ago
• 2 minutes ago
• 3 minutes ago
• 4 minutes ago
• 5 minutes ago
• 7 minutes... | [
"330",
"267",
"278",
"160"
] | D | (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D |
AQUA-RAT | AQUA-RAT-38448 | ## anonymous 5 years ago 100 people are present in a party. If each of them must do a handshake with all the other people, how many handshakes should be done? Please explain how to get the answer, thanks!
1. anonymous
you need 2 people for an hand shake and u have 100 people so i think that its C(100,2) but i am not ... | [
"76",
"55",
"44",
"12"
] | D | Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1}
From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12.
Answer:D |
AQUA-RAT | AQUA-RAT-38449 | # If $$(10)^9$$ + $$2(11)^1(10)^8$$ + $$3(11)^2(10)^7$$ + …… + $$10(11)^9$$ = $$K(10)^9$$, then k is equal to
## Solution :
$$K(10)^9$$ = $$(10)^9$$ + $$2(11)^1(10)^8$$ + $$3(11)^2(10)^7$$ + …… + $$10(11)^9$$
K = 1 + 2$$({11\over 10})$$ + 3$$({11\over 10})^2$$ + ….. + 10$$({11\over 10})^9$$ ……(i)
$$({11\over... | [
"I",
"J",
"K",
"L"
] | D | IF
6= I... Second letter of ONE.
7= E.... Second letter of TWO.
8= I
9= I
10= E
THEN 11=L... Second letter of Eleven
ANSWER:D |
AQUA-RAT | AQUA-RAT-38450 | # How to prove $\sqrt {75025} + \sqrt {121393} + \sqrt {196418} + \sqrt{317811} \approx \sqrt {514229} + \sqrt {832040}$?
Let $$a = \sqrt {75025} + \sqrt {121393} + \sqrt {196418} + \sqrt{317811}$$ and $$b = \sqrt {514229} + \sqrt {832040}$$. By using SageMath we can see that $$a - b \approx 2.95301560981898 \cdot 10^... | [
"222222222",
"111111111",
"333333333",
"777777777"
] | B | B
It's a maths magical square root series as :
Square root of number 121 is 11
Square root of number 12321 is 111
Square root of number 1234321 is 1111
Square root of number 123454321 is 11111
Square root of number 12345654321 is 111111
Square root of number 1234567654321 is 1111111
Square root of number 12345678765432... |
AQUA-RAT | AQUA-RAT-38451 | homework-and-exercises, special-relativity, inertial-frames, observers
But how much has John aged, according to Mike?
During t1, John was stationary according to Mike and therefore aged t1. During t2 + t2, John was moving at 0.5c, so aged
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
" 3",
" 3.5",
" 4",
" 4.5"
] | B | 222 - 198 = 24 pounds lost in 3 months
24/3 = 8, so Joe is losing weight at a rate of 8 pounds per month.
...in approximately how many months will he weigh 170 pounds?
A simple approach is to just list the weights.
Now: 198 lbs
In 1 month: 190 lbs
In 2 months: 182 lbs
In 3 months: 174 lbs
In 4 months: 166 lbs
Since 170... |
AQUA-RAT | AQUA-RAT-38452 | Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.
Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.
Back to the problem:
From F.S 1, ... | [
"17",
"199",
"16",
"11"
] | D | Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11
Answer:D |
AQUA-RAT | AQUA-RAT-38453 | # What is the next number in this sequence: $1, 2, 6, 24, 120$? [closed]
I was playing through No Man's Sky when I ran into a series of numbers and was asked what the next number would be.
$$1, 2, 6, 24, 120$$
This is for a terminal assess code in the game no mans sky. The 3 choices they give are; 720, 620, 180
• W... | [
"20",
"26",
"28",
"21"
] | B | In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
23-1 = 22
22+2 = 24
24-1 = 23
23+2 = 25
25-1 = 24
24+2 = 26
Answer is B |
AQUA-RAT | AQUA-RAT-38454 | Let one woman complete the job in $$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}$$ job/day... | [
"12hours",
"10hours",
"6hours",
"8hours"
] | A | A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + B)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
C's 1 hour work = (7/12 - 1/2) = 1/12
C alone will take 12 hours to do the work.
Answer:A |
AQUA-RAT | AQUA-RAT-38455 | $\text{So we have shown:}$
$\setminus q \quad {\text{odd"_1 +"odd"_2 + "odd"_3 +"odd"_4 + "odd"_5 +"odd"_6 \ = "even}}_{5.}$
$\text{So we conclude:}$
$\setminus \quad \text{the sum of any 6 odd numbers (consecutive or not) is even.}$
The following is multiple choice question (with options) to answer.
If the sum of ... | [
"A+3",
"A+9",
"A+18",
"2A + 3"
] | C | In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/3 = Mean = Second Integer
First Integer = A/3 - 2
Second Integer = A/3
Third Integer = A/3 + 2
i.e.
Fourth Integer = A/3 + 4
Fifth Integer = A/3 + 6
Sixth Integer = A/3 + 8
Now Mean of next 3 Integers = Median = A/3 + 6
... |
AQUA-RAT | AQUA-RAT-38456 | For $N = 5$, $2A$ looks like:
$$\begin{array}{ccccc} &0 &1 &0 &0 &1 \\ &1 &0 &1 &0 &0 \\ &0 &1 &0 &1 &0 \\ &0 &0 &1 &0 &1 \\ &1 &0 &0 &1 &0 \end{array}$$
Solving this equation system for $\mathbf{x}$ with $N = 10$ and $\mathbf{b} = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]$ gives
$x_6 = 1$.
6. For her to announce an average ... | [
"125",
"777",
"255",
"199"
] | A | Sum of the 35 numbers = 35 * 25 = 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.Answer: A |
AQUA-RAT | AQUA-RAT-38457 | Since we have $21$ terms taking $20$ possible values, there are some $0 \le i < j \le 20$ such that $S_i = S_j$. It follows that the total number of hours of study between days $i+1$ and $j$ (inclusive) is a multiple of $20$.
If it is not exactly equal to $20$ hours, then it must be at least $40$ hours. However, this ... | [
"25",
"45",
"55",
"70"
] | B | Day 1&2 = 80; Only Day 1&2 (80-20) = 60,
Day 2&3 = 70; Only Day 2&3 (70-20) = 50,
Only Day 1 = 175 - (60+50+20) = 45
Answer:B |
AQUA-RAT | AQUA-RAT-38458 | => 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... | [
"Rs.200",
"Rs.220",
"Rs.250",
"Rs.300"
] | C | Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C |
AQUA-RAT | AQUA-RAT-38459 | 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 ... | [
"Rs. 537600",
"Rs. 180000",
"Rs. 201600",
"Rs. 504000"
] | A | B's monthly income = 16000 * 112/100 = Rs. 17920
B's monthly income = 2 parts ----> Rs. 17920
A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800
A's annual income = Rs. 44800 * 12 = Rs. 537600
ANSWER:A |
AQUA-RAT | AQUA-RAT-38460 | # 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... | [
"15 a.m",
"10 a.m",
"7 a.m",
"02 a.m"
] | C | Suppose they meet x hours after 4 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 7 a.m.
Answer:C |
AQUA-RAT | AQUA-RAT-38461 | # 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... | [
"800 1/7 grams",
"800 grams",
"800 8/3 grams",
"883 1/3 grams"
] | B | If the cost price is Rs.100, then to get a profit of 25%, the selling price should be Rs.125.
If 125kg are to be sold, and the dealer gives only 100kg, to get a profit of 25%.
How many grams he has to give instead of one kilogram(1000 gm).
125 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/125 =800 grams.
Answer:B |
AQUA-RAT | AQUA-RAT-38462 | homework-and-exercises, kinematics, velocity, vectors, relative-motion
I've drawn the man swimming at some arbitrary angle $\theta$ at a speed $v$. The river is flowing at a speed $V$, and the time the man takes to cross is $t$. The distance swum by the man is $d_m$ and the distance the water moves is $d_r$.
The key p... | [
"9.2",
"10.3",
"11.5",
"12.4"
] | D | Man's rate in still water = (21 - 4.3) km/hr = 16.7 km/hr.
Man's rate against the current = (16.7 - 4.3) km/hr = 12.4 km/hr.
Answer:D |
AQUA-RAT | AQUA-RAT-38463 | ### Exercise 23
x+2y=10x+2y=10 size 12{x+2y="10"} {}
(35)
y+z=5y+z=5 size 12{y+z=5} {}
(36)
z+w=3z+w=3 size 12{z+w=3} {}
(37)
x+w=5x+w=5 size 12{x+w=5} {}
(38)
### Exercise 24
x+w=6x+w=6 size 12{x+w=6} {}
(39)
2x+y+w=162x+y+w=16 size 12{2x+y+w="16"} {}
(40)
x2z=0x2z=0 size 12{x - 2z=0} {}
(41)
z+w=5z+w=5 size 12{z+w... | [
"48",
"41",
"46",
"43"
] | D | Let a and b be the two numbers
(a+b)^2=a^2+2ab+b^2
Given (a+b)=21 a^2+b^2=527
So, 21^2=527+2ab
2ab=527-441
2ab=86
ab=43
Ans D |
AQUA-RAT | AQUA-RAT-38464 | ### Show Tags
22 Mar 2017, 01:52
If n is the product of 3 consecutive integers, which of the following must be true?
I. a multiple of 2 II. a multiple of 3 III. a multiple of 4
A. I only
B. II only
C. III only
D. I and II
E. II and III
_________________
The following is multiple choice question (with options) to an... | [
" I only",
" II only",
" I and III only",
" II and III only"
] | C | Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = i... |
AQUA-RAT | AQUA-RAT-38465 | area of that circle click on the calculate button... It is also known as the longest straight line segment which passes the! Segment which passes through the center of the circle demonstration is to use this calculator, by... 3 = 150687.075 mm if we know circumference as the straight line segment which passes through m... | [
"7 meters",
"9 meters",
"4 meters",
"5 meters"
] | C | 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 96,000 m : C is the circumference
C = 4 meters
correct answer C |
AQUA-RAT | AQUA-RAT-38466 | # Problem regarding percentage increases.
#### Strikera
##### New member
Ran into a problem which is driving me nuts and would appreciate any assistance on the problem.
Problem:
A factory increases it's production by 10%. The factory then increases it's production by another 20%. To return to the original productio... | [
"86%",
"64%",
"50%",
"14%"
] | B | Total = n(A) + n(B) - Both + None
None = Total - n(A) - n(B) + Both
Calculate "none" for each case
None(5+ yrs Line) = 200 - 50 - 40 + 30 = 140
None(5+ yrs Staff) = 160 - 40 - 50 + 20 = 90
Employees not taking either workshop/Total number of employees = (140 + 90)/(200 + 160) = 230/360 = About 64%
ANSWER:B |
AQUA-RAT | AQUA-RAT-38467 | 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... | [
"$100",
"$150",
"$300",
"$250"
] | C | C's 1day work = (1/3)-(1/6 + 1/8) = 1/24
A:B:C= 1/6 : 1/8: 1/24 = 4:3:1
A's share = 600*4/8 = $300
Answer is C |
AQUA-RAT | AQUA-RAT-38468 | #### David Harper CFA FRM
##### David Harper CFA FRM
Staff member
Subscriber
That's interesting, Steve (to me, because I write so many questions).
With regard to "An asset is quoted at 12% annually with continuous rate. Interest is paid quarterly." Note three timeframes are invoked:
1. Interest paid quarterly (4 per ... | [
"Rs. 1386",
"Rs. 1764",
"Rs. 1425",
"Rs. 2268"
] | C | Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.171.
∴ x 16 x9/ 12x 1/100}= 171 or x = 1425.
∴ P.W. = Rs. 1425.
Answer C |
AQUA-RAT | AQUA-RAT-38469 | 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 ... | [
"181",
"165",
"121",
"99"
] | A | Since the question asks for the answer that CANNOT be the sum of P and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that P and N are two-digit positive integers and have the SAME DIGITS... |
AQUA-RAT | AQUA-RAT-38470 | Use $\int_a^b f(x)dx=\int_a^nf(a+b-x)dx$ and $\int_0^{2a}f(x)dx=\int_0^a f(x)dx+f(2a-x)dx$
The following is multiple choice question (with options) to answer.
If f(a)=a^2, what is the value of (f(a+b)−f(b))/b ? | [
"2a+a^2",
"b",
"2a",
"2a + b"
] | A | start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2
a^2+2ab+b^2 - b^2/b = (simplify a^2)
2ab+a^2/b = (cancel b's)
= 2a+a^2
Ans : A |
AQUA-RAT | AQUA-RAT-38471 | 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... | [
"120 meter",
"300 meter",
"100 meter",
"200 meter"
] | C | when B runs 25 m, A runs 22.5 m
=> When B runs 1000 metre, A runs 22.5/25 x 1000 = 900m.
=> When B runs 1 kilometre, A runs 900 m
Hence, in a kilometre race, B beats A by
ANSWER:C
(1 kilometre - 900 metre) = (1000 metre - 900 metre) = 100 metre |
AQUA-RAT | AQUA-RAT-38472 | 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... | [
"50",
"64",
"70",
"80"
] | B | A + B = 54, A = 2B
2B + B = 54 => B = 18 then A = 36.
5 years, their ages will be 41 and 23.
Sum of their ages = 41 + 23 = 64.
ANSWER:B |
AQUA-RAT | AQUA-RAT-38473 | 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... | [
"5",
"6",
"7",
"8"
] | C | Explanation:
Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions)
=2+3=5 rounds per hour
Therefore, they cross each other 5 times in 1 hour and 2 times in 12 hour
Time duration from 8 a.m. to 9.30 a.m. =1.5 hour
Hence they cross each other 7 times before 9.30 a.m.
ANSWER IS C |
AQUA-RAT | AQUA-RAT-38474 | => 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... | [
"$120",
"$125",
"$130",
"$135"
] | B | Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 10] + [(1/3)F – 10] + [(1/2)F – 25]
F = (1/4)F + (1/3)F + (1/2)F – 25
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 300
12F = 13 F – 300
–F = ... |
AQUA-RAT | AQUA-RAT-38475 | speed of the car in miles per hour? what dimensions should he use? Custom Solutions. Find the fraction. Find the fraction. Given : This year, the chickens laid 30% less eggs than they did last year and they laid 3500 eggs this year. This was$14 less than twice what she spent for a blouse. So, the chickens laid 5000 egg... | [
"1/3",
"1/5",
"1/4",
"2/3"
] | A | We don't need to get into calculations for solving this question. We can use the concept of weighted averages.
The average time for the entire project is 15 hours; so, she spent a lesser duration of time painting the ship than constructing it.
5---(5---5)
This shows that you can divide the entire project into 3 equal p... |
AQUA-RAT | AQUA-RAT-38476 | # Homework Help: A somewhat simple Probabilty problem
1. Dec 16, 2011
### Whitishcube
1. The problem statement, all variables and given/known data
Suppose two teams are playing a set of 5 matches until one team wins three games (or best of five).
Considering the possible orderings for the winning team, in how many w... | [
" 5040",
" 2520",
" 720",
" 120"
] | B | PRINCETON REVIEW OFFICIAL SOLUTION:
A beats B? Carmelo beats B? No one said anything about specific results, especially not on a question that includes so many people.
Many questions on the GMAT can be overwhelming in appearance so first thing…Relax. This question looks nasty, but it’s pretty straightforward, requiring... |
AQUA-RAT | AQUA-RAT-38477 | 3. 0725. This calculator shows the steps and work to convert a fraction to a decimal number. Write the repeating part as the numerator of the fraction. Okay, so you can use division to see if a fraction has a repeating decimal, but how do you convert a repeating decimal into a fraction? Changing a repeating decimal in ... | [
"5",
"0.5",
"0.05",
"0.015"
] | D | Explanation:
It will be 1/2(3%) = 1/2(3/100) = 3/200 = 0.015
Answer: Option D |
AQUA-RAT | AQUA-RAT-38478 | ## A committee of 2 people is to be selected out of
##### This topic has expert replies
Legendary Member
Posts: 1892
Joined: 14 Oct 2017
Followed by:3 members
### A committee of 2 people is to be selected out of
by VJesus12 » Thu Mar 15, 2018 4:23 am
A committee of 2 people is to be selected out of 3 teachers and 4 ... | [
"12",
"14",
"16",
"18"
] | C | The total number of ways to choose 3 people from 6 is 6C3 = 20.
The number of committees without Jane or Thomas is 4C3 = 4.
There are 20-4 = 16 possible committees which include Jane and/or Thomas.
The answer is C. |
AQUA-RAT | AQUA-RAT-38479 | \begin{align} \dbinom{6}{2} & \longleftrightarrow \dbinom{6}{6-2} \\[8pt] AB & \longleftrightarrow CDEF \\ AC & \longleftrightarrow BDEF \\ AD & \longleftrightarrow BCEF \\ AE & \longleftrightarrow BCDF \\ AF & \longleftrightarrow BCDE \\ BC & \longleftrightarrow ADEF \\ BD & \longleftrightarrow ACEF \\ BE & \longleftr... | [
"6",
"8",
"10",
"12"
] | B | 26 + 20 - 17 = 29
37 - 29 = 8 play neither
Answer is B |
AQUA-RAT | AQUA-RAT-38480 | 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}$$ job/day... | [
"20",
"22",
"25",
"28"
] | D | Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/35
Work done by P, Q and R in 1 day = 1/10 + 1/35 =9/70
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 9/70
=> Work done by P in 1 day = 9/140
=> Work done by Q and R... |
AQUA-RAT | AQUA-RAT-38481 | $$1\\1+1\\ 1+1+1\quad1+2\\ 1+1+1+1\quad1+1+2\\ 1^5\quad1+1+1+2\quad1+2+2\quad1+1+3\\ 1^6\quad1^4+2\quad1^2+2+2\quad1^3+3\quad1+2+3\\ 1^7\quad1^5+2\quad1^3+2+2\quad1+2^3\quad1^4+3\quad1^2+2+3\quad1^3+4\quad1+2+4\\ 1^8\quad1^6+2\quad1^4+2+2\quad1^2+2+2+2\quad1^5+3\quad1^3+2+3\quad1^2+3+3\quad1+2+2+3\quad1^4+4\quad1+1+2+4... | [
" 6^7",
" 6^10",
" 6^12",
" 6^16"
] | A | Let's see that 6 + 12 + 18 is 36 or 6^2, then: 6^2 + 5 x 6^2 becomes 6 x 6^2 that is 6^3. So we follow with the next element: 6^3 + 5 x 6^3 is equal to 6 x 6^3 that is 6^4. Then is assumed right before 5 x 6^6: 6^6 + 5 x 6^6 becomes 6 x 6^6 that is 6^7. Thus, the correct answer is the option A, 6^7. |
AQUA-RAT | AQUA-RAT-38482 | kmph. com/2016/01/01/speed-distance-timeVideos, worksheets, 5-a-day and much more. If a car traveled 50 miles over the course of one hour then its average speed will be 50 mph. Distance, Time and Speed Word Problems | GMAT GRE Maths. Exercise: Problems on Speed Time and Distance. org/time-speed-distanceTime, Speed and ... | [
"50 Kmph",
"20 Kmph",
"65 Kmph",
"70 Kmph"
] | B | Time = 6
Distence = 180
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 180/9 = 60 Kmph
B) |
AQUA-RAT | AQUA-RAT-38483 | I don't see it...
• May 21st 2010, 12:36 PM
wonderboy1953
Hint
Look for cycles.
• May 21st 2010, 03:22 PM
Soroban
Hello, pollardrho06!
Quote:
Find the number of positive integers not exceeding 1000
that are divisible by 3 but not by 4.
Every third number is divisible by 3.
. . There are: . $\left[\frac{1000}{3}\righ... | [
"13",
"24",
"35",
"16"
] | B | 1 also gives the remainder of 1 when divided by 3. So, there are total of 24 numbers.
Answer: B. |
AQUA-RAT | AQUA-RAT-38484 | $$T = \frac {60}{160 + w} + \frac {60}{160-w} = \frac {60(160-w) + 60(160 + w)} {(160 + w)(160 - w)} = \frac {9600 - 60w + 9600 + 60w}{(160 + w)(160 - w)}= \frac {19200}{(160 + w)(160 - w)} = \frac {19200}{25600 +160w-160w-w^2}=\frac {19200}{25600-w^2}$$
For this scenario of finding round trip time where you have 2 is... | [
"205 km/h",
"215 km/h",
"225 km/h",
"235 km/h"
] | C | The speed of the plane in still air = x km/h
The speed of the wind is 15 km/h
Speed with the wind = (x + 15) km/h
Speed against the wind = (x – 15) km/h
Time = Distance/ Speed
720 / (x+15) = 630 / (x-15)
720(x-15) = 630(x+15)
72x - 1080 = 63x + 945
9x = 2025
x = 225
Therefore, the speed of the plane in still air is 2... |
AQUA-RAT | AQUA-RAT-38485 | 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... | [
"328",
"288",
"2800",
"600"
] | D | Distance covered by Amar = 18/4.8 (1.6km)
= 3/8(1600)
= 600 m
Answer:D |
AQUA-RAT | AQUA-RAT-38486 | # Find the least next N-digit number with the same sum of digits.
Given a number of N-digits A, I want to find the next least N-digit number B having the same sum of digits as A, if such a number exists. The original number A can start with a 0. For ex: A-> 111 then B-> 120, A->09999 B-> 18999, A->999 then B-> doesn't... | [
"43",
"34",
"44",
"35"
] | B | Let the original no be 10x+y
Sum of the digits x+y=7
When the digits are reversed then it is 10y+x
Since it is decreased by 9 it is written as (10y+x)-(10x+y)=9 solving this we get y=4
Substitute in x+y=7 we get x=3
so the number is 34 correct ans is B |
AQUA-RAT | AQUA-RAT-38487 | (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 ... | [
"137",
"138",
"135",
"140"
] | B | For lost, use negative. For gain, use positive.
200+-20+-43+1
correct answer is B)138 |
AQUA-RAT | AQUA-RAT-38488 | You can use sample() and select specific probabilities for each integer. If you sum the product of the probabilities and the integers, you get the expected value of the distribution. So, if you have a mean value in mind, say $$k$$, you can solve the following equation: $$k = 1\times P(1) + 2\times P(2) + 3\times P(3) +... | [
"1/4",
"1/8",
"1/2",
"3/8"
] | B | y will only be negative for x=2.
(We can check the values from 1 to 8 to be certain.)
P(y is negative) = 1/8
The answer is B. |
AQUA-RAT | AQUA-RAT-38489 | # 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... | [
"10%",
"40%",
"30%",
"25%"
] | B | cp=50
sp=70
profit=70-50=20
%=20/50*100=40%
ANSWER:B |
AQUA-RAT | AQUA-RAT-38490 | ### Show Tags
05 Sep 2017, 11:01
2
In traveling from city A to city B, John drove for 1 hour at 50 mph and for 3 hoursat 60 mph. What was his average speed for the whole trip?
(A) 50
(B) 53.5
(C) 55
(D) 56
(E) 57.5
The total distance traveled from City A to City B is 50*1 + 60*3 = 230
Since John drove for 4 hours t... | [
"a) 8.33 m/hr",
"b) 9 m/hr",
"c) 10 m/hr",
"d) 20 m/hr"
] | C | Your calculations look perfect, but I think they answer a different question from the one the question designer intended. I don't find the wording of this question to be good at all, but I'm pretty sure what they mean is this: from the point in time at which John and Tom meet, it takes a *further* 3 1/3 hours for John ... |
AQUA-RAT | AQUA-RAT-38491 | life easy!, 456/789 ) thirty seconds fraction converted in to decimals an percent shown! + 1/3 = ( 1×3+1×2 ) / ( 2×3 ) = 5/6 learn to add, subtract,,... Use the calculator provided returns fraction inputs in both cases, fractions are presented their. 'S a division as 1 3/2 easily subtract mixed fractions and mixed frac... | [
"120",
"123",
"124",
"125"
] | D | Explanation:
Let the number = x,
Then, x-(3/5)x = 50,
=> (2/5)x = 50 => 2x = 50*5,
=> x = 125
Answer: Option D |
AQUA-RAT | AQUA-RAT-38492 | Hope it helps.
Hi Bunuel,
Can we say that the sum of the numbers will be 1111 to 4444 ? since the repetition of the digits are allowed. I think this range would cover all the numbers. Then we can simply use the formula for arithmetic mean to calculate the sum ? Please correct my thinking if wrong.
Yes, the numbers r... | [
"1692",
"1792",
"1795",
"1892"
] | B | the number is 1792.
Let the number be represented as 1000x+100y+10z+t
acc to ques,
xyzt=126
x + y + z + t = 10x + z = 19
so, number in thousands and tens place are 1 and 9 respectively.
the remaining factor is 14 which is 7*2
So the number is 1792.
ANSWER:B |
AQUA-RAT | AQUA-RAT-38493 | When we add $10$ red, we end up with $4k+10$ red. The blues remain unchanged at $7k$.
So the new proportion is $(4k+10): 7k$. We are told that the proportion $(4k+10): 7k$ is $6:7$. So $$\frac{4k+10}{7k}=\dfrac{6}{7}.$$ If we multiply through by $7k$, we get $4k+10=6k$, and therefore $k=5$. It follows that there are $... | [
"28",
"42",
"48",
"80"
] | D | Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=115 or 23x=115...here 7x,4x and 12x represent hats of each type
23x=115 so x=5...Blue hats =7*5=35...Not blue will be 115-35=80.
Ans D |
AQUA-RAT | AQUA-RAT-38494 | Example 2
In a large population of adults, 45% have a post secondary degree.
If people are selected at random from this population,
a) what is the probability that the third person selected is the first one that has a post secondary degree?
b) what is the probability that the first person with a post secondary degree i... | [
"39%",
"45%",
"55%",
"65%"
] | A | Setting up a matrix is how I solve this one.
Diploma No Diploma Totals
Job of Choice w/Diploma
Job of Choice w/o Diploma = 10%
Job of Choice Total = 40%
Not Job of Choice with Diploma =.15X
Not Job of Choice w/o Diploma= .85X
Total Not Job of Choice = X
Total with Diploma
Total without Diploma
Total citizen = 100
If 40... |
AQUA-RAT | AQUA-RAT-38495 | ## A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners
##### This topic has expert replies
Legendary Member
Posts: 2898
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:5 members
### A number of people shared a meal, intending to divide the cost evenl... | [
"$1",
"$2",
"$3",
"$4"
] | C | He would need to keep $ 3 to himself so he can give $ 1084 to all 12 people so option C is correct one |
AQUA-RAT | AQUA-RAT-38496 | Quick way
Use Smart Numbers
Give 100 for the initial amount
Then you will have 50-0.25x = 30
x = 80
So % is 80/100 is 80%
Hope it helps
Cheers!
J
SVP
Joined: 06 Sep 2013
Posts: 1647
Concentration: Finance
Re: If a portion of a half water/half alcohol mix is replaced [#permalink]
### Show Tags
29 May 2014, 11:41... | [
"2.5%",
"11%",
"5%",
"15%"
] | B | 50% of (x-y)=40% of(x+y)
(50/100)(x-y)=(40/100)(x+y)
5(x-y)=4(x+y)
x=9y
x=9y
therefore required percentage
=((y/x) X 100)% = ((y/9y) X 100) =11%
Answer is B. |
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