source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38797 | c#, beginner
public static void AskForBookPage(int bookNumber_in)
{
Console.Write($"{bookNumber_in + 1}. book - How many pages does the book have? --> ");
}
}
static class BookList
{
public const int MAX_SIZE = 100;
public static string option;
... | [
"0",
"4",
"840",
"90"
] | B | Remaining pages = 512 – 302 = 210
Let average printing error in remaining pages = x
Then, 1208+210×x /512=4
⇒ 210x = 840 ⇒ x = 4
Answer B |
AQUA-RAT | AQUA-RAT-38798 | 5. Why we can't solve it by 100+15/2=125
6. Why we can't solve it by 100+15/2=125
7. nice
8. The speed of the train going from Nagpur to Allahabad is 100 km/h while when coming back from Allahabad to Nagpur, its speed is 150 km/h and again going to the same way Nagpur to Allahabad at a speed of 120km/hr.Find the ave... | [
"45",
"43",
"40",
"38"
] | A | Solution: Average speed = 2XY / X+Y
= 2*60*36 / 60+36
= 45
Answer : A |
AQUA-RAT | AQUA-RAT-38799 | Nice observation! Something else you might notice, which turns out to imply your observation, is that all of the odd prime factors of your numbers are $$1 \bmod 4$$: $$\{ 5, 13, 17, 29, \dots \}$$. And a final thing you might notice is that all of your numbers are themselves congruent to $$2 \bmod 4$$, or equivalently ... | [
"a−b",
"a−2b",
"2c−2d",
"2c/2d"
] | C | The answer is C. Let's assume that a is an even prime integer and b is an odd prime integer, their subtraction results in an odd integer and an odd integer multiplied by an even integer yields an even integer.
Answer C |
AQUA-RAT | AQUA-RAT-38800 | "Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4959 Location: Canada GMAT 1: 770 Q49 V46 When a positive integer n is divided by 5... | [
" 12",
" 24",
" 35",
" 16"
] | C | If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5c + 3
n = 7d + 4
I will need to check for the smallest such number.
I put d= 1. n = 11. Is it of the form 5c + 3? No.
Put d= 2. n = 18. Is it of the form 5c + 3? Yes.
When 18 is di... |
AQUA-RAT | AQUA-RAT-38801 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest be... | [
"$2.04",
"$3.06",
"$4.80",
"$8.30"
] | A | A.
$. 2.04
B.
$. 3.06
C.
$. 4.80
D.
$. 8.30
Answer: Option A
Explanation:
C.I. when interest
compounded yearly = $ 5000 x 1 + 4 x 1 + x 4
100 100
= $. 5000 x 26 x 51
25 50
= $. 5304.
C.I. when interest is
compounded half-yearly = $ 5000 x 1 + 2 3
100
= $ 5000 x 51 x 51 x 51
50 50 50
= $5306.04
Difference = $. (5306.04 ... |
AQUA-RAT | AQUA-RAT-38802 | 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... | [
"18",
"19",
"27",
"29"
] | C | Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C |
AQUA-RAT | AQUA-RAT-38803 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"4 hours",
"5 hours",
"6 hours",
"7 hours"
] | D | Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = ... |
AQUA-RAT | AQUA-RAT-38804 | # Making Friends around a Circular Table
I have $n$ people seated around a circular table, initially in arbitrary order. At each step, I choose two people and switch their seats. What is the minimum number of steps required such that every person has sat either to the right or to the left of everyone else?
To be spec... | [
"5!",
"8!",
"11!",
"12!"
] | A | Ans.(A)
Sol. Total number of persons = 6 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 5 places => 5! Ways ... The number of required arrangements = 5! x 1= 5! = 5! ways |
AQUA-RAT | AQUA-RAT-38805 | # whole numbers and division
Consider the whole number with one thousand digits that can be formed by writing the digits 2772 two hundred and fifty time in succession. Is it divisible by 9? Is it divisible by 11?
-
I answered yes to both because 2772 is divisible by 9 and 11. I am just trying to make sure this is cor... | [
"3",
"5",
"9",
"11"
] | D | Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
ANSWER : D |
AQUA-RAT | AQUA-RAT-38806 | mass, newtonian-gravity, statics
Title: How do you weigh a box on a scale whose limit is too low? As you will see I know nothing about physics and after being asked to solve a physics problem in a recent interview wanted to ask it of professionals and see what the response would be:
I have a set of domestic scales (a... | [
"3",
"4",
"5",
"6"
] | D | The weights of the items in the suitcase are 7k, 5k, and 3k.
If removing 5 pounds of clothes doubles the ratio of books to clothes, then 5 pounds represents half the weight of the clothes.
2.5k = 5 pounds and then k = 2 pounds.
The electronics weigh 3(2) = 6 pounds.
The answer is D. |
AQUA-RAT | AQUA-RAT-38807 | 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... | [
"22",
"88",
"48",
"99"
] | C | Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C |
AQUA-RAT | AQUA-RAT-38808 | # Math Help - Permutation Help!
1. ## Permutation Help!
Problem:
---------
There are 120 five-digit numbers that can be formed by permuting the digits 1,2,3,4 and 5 (for example, 12345, 13254, 52431). What is the sum of all of these numbers?
--------
399 960
I can't get this question...I don't know what to do...
Al... | [
"A)3",
"B)5",
"C)7",
"D)9"
] | A | x/2 – x/3 = 5 => x =30
3 + 0 = 3
ANSWER:A |
AQUA-RAT | AQUA-RAT-38809 | Let us take another mixture problem:
Question 2:
Two types of rice costing $60 per kg and$40 per kg are mixed in a ratio 2: 3. What will be the cost per kg of mixed rice?
Solution:
• Can we apply alligation to this question?
• Can we assume the price of the mixed rice to be $x per kg and make this diagram? • Now do... | [
"15%",
"20%",
"23%",
"30%"
] | C | Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 13 = x = 77 kg.
∴ Reduction in consumption = 23%.
Answer C |
AQUA-RAT | AQUA-RAT-38810 | ### Show Tags
09 Oct 2015, 14:30
jimjohn wrote:
If x, y, and z are integers greater than 1, and (3^27)(35^10)(z) = (5^8)(7^10)(9^14)(x^y), then what is the value of x?
(1) z is prime
(2) x is prime
I found an almost identical question with the same question stem, but different statements.
Here it is: if-x-y-and-z-a... | [
"I only",
"II only",
"II,III only",
"III only"
] | C | Answer : C |
AQUA-RAT | AQUA-RAT-38811 | The only possible answer is E i.e 12 hrs.
Yes, your approach is very good. The only thing I have an issue with is the approximation used.
Their combined time is 4.8 hrs and hence we know that Jack will take more than 9.6 hrs. 10 hrs is a possible candidate for the correct option in that case. Though I would say that i... | [
"16 days",
"10 days",
"8 days",
"6 days"
] | B | Number of days taken by Ram to complete task = 30
Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days
If total work done by Ram in 30 days is 30w
Amount of work done by Ram in 1 day = w
Amount of work done by Krish in 1 day = 2w
Total amount of work don... |
AQUA-RAT | AQUA-RAT-38812 | 2. Mike says:
of course i meant 5 buckets, one for each student ;).
3. meichenl says:
Let there be $c$ cookies and $n$ students. Denote the number of ways to distribute $c$ cookies between $n$ students by $S_n(c)$. This is claiming that for a given number of students, the number of ways to distribute the cookies is ... | [
"6",
"0",
"4",
"3"
] | B | trisha made 6*6 cookies = 36 cookies. 4 friends eat 3 cookies, leaving 24 remaining for 2 friends.
24 is divisible by 2. The 2 friends ate a cumulative number of cookies divisible by 2, because the number is the same.
24-24=0;
B is the correct answer |
AQUA-RAT | AQUA-RAT-38813 | 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... | [
"5days",
"6days",
"7.5days",
"8.5days"
] | B | Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =12∗1/2= 6 days
Option B |
AQUA-RAT | AQUA-RAT-38814 | # Math Help - Finding the values of a and b
1. ## Finding the values of a and b
Hello everyone. This question is apparently unsolvable:
If $x = 3$ or $-4$ are the solutions of the equation $x^2+ax+b=0$, find the values of $a$ and $b$.
The keyword in this irksome question would be the word 'or'. So it denotes that t... | [
"0",
"2",
"4",
"5"
] | B | (x − 1)(x − 2)
x = 1 or 2.
B |
AQUA-RAT | AQUA-RAT-38815 | # 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... | [
"1 ≤ n ≤23",
"7 ≤ n ≤17",
"5 ≤ n ≤19",
"6 ≤ n ≤18"
] | B | ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-4+3=17 for the maximum, and 12-6+4-3=7 for the minimum, so B is the answer |
AQUA-RAT | AQUA-RAT-38816 | 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 ... | [
"24",
"27",
"29",
"32"
] | A | The total of seven numbers = 5X18 = 90
The total of first 2 and last 2 numbers is = 2 X 14+2 X 19 = 66
So, the middle number is (90 - 66 ) = 24
A |
AQUA-RAT | AQUA-RAT-38817 | Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers.
When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3.
## Related Chapters
### Preparation Products
##### JEE Main Rank Booster 2021
This course wi... | [
"only one such pair exists",
"no paid is exists",
"many such pairs exist",
"pair exists"
] | B | Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option:B |
AQUA-RAT | AQUA-RAT-38818 | It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.
3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.
Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.
bunuel, pls help
if i equate time i am n... | [
"16 days",
"12 days",
"8 days",
"6 days"
] | C | Answer
Ram takes 24 days to complete the task, if he works alone.
Krish is twice as efficient as Ram is. So, working alone, Krish will take half the time to complete the task.i.e., 12 days.
Ram will complete 1/24th of the task in a day.
Krish will complete 1/12th of the task in a day.
When they work together, they will... |
AQUA-RAT | AQUA-RAT-38819 | x = 25/324
Guest Mar 13, 2017
#6
+223
+5
This one seems to work! Thanks!
#5
+7153
+6
$$(20\frac{1}{4})x + 5\frac{1}{2} = 7\frac{1}{16} \\~\\ (\frac{81}{4})x + \frac{11}{2} = \frac{113}{16} \\~\\ (\frac{81}{4})x = \frac{113}{16} - \frac{11}{2} \\~\\ (\frac{81}{4})x = \frac{113}{16} - \frac{11(8)}{2(8)} \\~\\ (\frac{... | [
"110/1547",
"120/1547",
"140/1547",
"160/1547"
] | B | P : 1/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 1/13 * 5/34
P*7/48 = 5/442
P = 240/3094 => P = 120/1547
ANSWER:B |
AQUA-RAT | AQUA-RAT-38820 | your kids. The volume formula for a rectangular box is height x width x length, as seen in the figure below: To calculate the volume of a box or rectangular tank you need three dimensions: width, length, and height. Find the dimensions of the box that minimize the amount of material used. The calculated volume for the ... | [
"50,000",
"40,000",
"45,000",
"50,000"
] | B | The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*100*150 = 15,000 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 100*1*150 = 15,000 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 100*1... |
AQUA-RAT | AQUA-RAT-38821 | So total sales for the year, 30000, cash sales 6000. Thus the yearly proportion of cash sales is $\dfrac{6000}{30000}=20\%$. This is the correct percentage.
Now let's compute the monthly averages. For January through October, they are $50\%$. For each of November and December, they are $5\%$.
To find the average of t... | [
"10%",
"25%",
"33%",
"50%"
] | D | When you say Senior is 1/30, what do you mean by it? It is the rate of visit. The time of visit is 30 days. The rate is 1/30. Similarly, the rate of visit for junior is 1/20.
The 2 yrs has no significance in this case. The rate stays the same for every time interval.
{1/20} - {1/30}/ {1/30} * 100 = 50%
ANSWER:D |
AQUA-RAT | AQUA-RAT-38822 | # Permutations of the word $\text{TRIANGLE}$ with no vowels together.
First of all, $$\text{TRIANGLE}$$ has $$8$$ distinct letters, $$3$$ of which are vowels($$\text{I, A, E}$$) and rest are consonants($$\text{T, R, N, G, L}$$).
While attempting this, I came up with the idea of putting alternate vowels and consonants... | [
"12",
"14",
"36",
"38"
] | C | There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6)
Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = 3P3 = 3! = 6.
Also, the 3 consonants can be arrang... |
AQUA-RAT | AQUA-RAT-38823 | electricity, batteries
A battery's capacity is the amount of electric charge it can deliver
at the rated voltage. The more electrode material contained in the
cell the greater its capacity. A small cell has less capacity than a
larger cell with the same chemistry, although they develop the same
open-circuit vo... | [
"145",
"150",
"175",
"180"
] | D | 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 60 percent 180 min.Answer:D |
AQUA-RAT | AQUA-RAT-38824 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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... | [
"10sec",
"20sec",
"25sec",
"30sec"
] | B | Distance = length of train + length of bridge = 250+150 = 400
speed = 72km/hr = 72*5/18 = 20m/s
Required time = 400/20 = 20 seconds
Answer is B |
AQUA-RAT | AQUA-RAT-38825 | # Average length of the longest segment
This post is related to a previous SE post If a 1 meter rope …. concerning average length of a smallest segment.
A rope of 1m is divided into three pieces by two random points. Find the average length of the largest segment. My answer is 11/18. Here is how I do it:
Here we hav... | [
"75.",
"85.",
"90.",
"94."
] | B | Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third strings is 70. That means out 6 / 3 = 2 strings.
let the avg length of two strings be ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 ... |
AQUA-RAT | AQUA-RAT-38826 | => 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... | [
"$1500",
"$150",
"$375",
"$200"
] | C | Let the shares of w,x,y,z are 1a,6a,2a,4a
6a-2a = 1500
4a = $1500, A=375
W's share = 1a = $375
Answer is C |
AQUA-RAT | AQUA-RAT-38827 | A. $28.50 B.$27.00
C. $19.00 D.$18.50
E. $18.00 Let's plug in some NICE VALUES that satisfy the given information... Last year the manufacturer sold twice as many units of Q as P. So, let's say the manufacturer sold 1 P and 2 Q's There were 3 units sold. So, average price =$54/3 = $18 Answer: E GMATPrepNow how do we de... | [
" Between $15,000 and $25,000",
" Between $30,000 and $50,000",
" Between $75,000 and $125,000",
" Between $150,000 and $250,000"
] | C | Number of defective units is between = .3 % of 10000 and .5% of 10000
= 30 and 50
Retail Price per unit = 2500 $
Expected price of refund is between = 2500 x 30 and 2500 x 50
=75,000 and 125,000 dollars
Answer C |
AQUA-RAT | AQUA-RAT-38828 | 1) Show that the tangent line to the parabola y=Ax^2, A not equal to 0, at the point x=c will intersect the x-axis at the point (c/2, 0)
2) Determine where this line intersects the y-axis
Originally Posted by erimat89
Maybe I'm just confused but the question wasn't asking where it intersected the x-axis the x-axis int... | [
"I only",
"II only",
"III only",
"I and III"
] | D | Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 1, y = 3 lies on the parabola, so (1, 2) will be enclosed by the parabola and x axis.
When x = 2, y = 4 lies on the parabola, so ... |
AQUA-RAT | AQUA-RAT-38829 | # Show that $\prod_{k=1}^n (n+k) = 2^n \prod_{k=1}^n (2k-1)$ for all $n\in Z^+$
Show that $$\prod_{k=1}^n (n+k) = 2^n \prod_{k=1}^n (2k-1)$$ for all $$n\in Z^+$$.
I think I'm supposed to use induction to prove this, but I can't seem to figure out how. Any help would be appreciated, thanks in advance!
• The proof bas... | [
"10",
"12",
"15",
"18"
] | D | 20! = 1*2*3*4*5...*19*20 (This is 20 factorial written as 20!)
n = 1*2*3*4*5*6*7.....*19*20
How many 2s are there in n?
One 2 from 2
Two 2s from 4
One two from 6
Three 2s from 8
and so on...
When you count them all, you get 18.
ANSWER:D |
AQUA-RAT | AQUA-RAT-38830 | the beginning of the 4 year period". then it would have been difficult to solve. Thanks Say the number of trees at the beginning of the 4 year period was x, then: At the end of the 1st year the number of trees would be $$x+\frac{1}{4}x=\frac{5}{4}*x$$; At the end of the 2nd year the number of trees would be $$(\frac{5}... | [
"4",
"8",
"10",
"6"
] | D | Explanation:
Let the interval is x .The youngest child's age is 4. Each of the other 3 children will then be 4+x, 4+2x, 4+3x
We know that the sum of their ages is 52 .
so, 4+(4+x)+(4+2x)+(4+3x) = 52
x= 6
Answer: D |
AQUA-RAT | AQUA-RAT-38831 | # 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... | [
"20 m",
"10 m",
"40 m",
"30 m"
] | A | To reach the winning point , A will have to cover a distance of 500 - 140= 360 metre
ratio of the speeds of two contestants A and B is 3 : 4
i.e., when A covers 3 metre, B covers 4 metre.
When A covers 360 metre, B covers 4/3×360 = 480 metre.
Remaining distance B have to cover = 500-480= 20 metre
A wins by 20 metre
Ans... |
AQUA-RAT | AQUA-RAT-38832 | homework-and-exercises, kinematics
Title: Train problem question in kinematics engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last
compartment with velocity v. The middle point of the train passes past the same pole with a velocity of.
My thinking:
Q1 Will the values... | [
"5 seconds",
"2.8 seconds",
"3.5 seconds",
"2.5 seconds"
] | A | First convert speed into m/sec
Speed = 72*(5/18) = 20 m/sec
Time = Distance/speed
= 100/20 = 5 seconds
Answer: A |
AQUA-RAT | AQUA-RAT-38833 | newtonian-mechanics, buoyancy, weight
Title: What is the sensation by man carrying a water bucker with an object floating in it? A man is carrying a bucket with water. If a object is kept in it which floats in water, man will feel
1) heavier
2) lighter
3) none
I think when the body floats its weight is balanced by upt... | [
"7 kg",
"6 kg",
"5 kg",
"8 kg"
] | C | Say Iron = 6 kg EMPTY so filled with 50% water you have a 1/3*6 = 2 kg water weight. so adding the rest of the bucket with water will naturally increase it by another 2kg so you have 2+2+6 = 10 thus 50% of 10 = 5.
ANSWER:C |
AQUA-RAT | AQUA-RAT-38834 | 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... | [
"a) 10",
"b) 24",
"c) 40",
"d) 55"
] | B | Total Score of 16 students is 16*61.50 = 984
Total Score of 15 students is 15*64 = 960
So, the score of the person who left is 24 ( 984 - 960 )
Answer will be (B) |
AQUA-RAT | AQUA-RAT-38835 | d=18: (3,-3), (-3,-3), (-3,3), (3,3)
d=20: (4,2), (4,-2), (-4,-2), (2,-4), (-4,2), (-2,-4), (-2,4), (2,4)
d=25: (-3,-4), (-5,0), (5,0), (4,3), (-3,4), (-4,3), (0,-5), (4,-3), (-4,-3), (3,-4), (3,4), (0,5)
The following is multiple choice question (with options) to answer.
18! is equal to which of the following? | [
"6,402,373,705,728,125",
"6,402,373,705,728,216",
"6,402,373,705,728,624",
"6,402,373,705,728,000"
] | D | After 4!, the units digit of every factorial is 0.
5!=120
6!=720
etc...
The answer is D. |
AQUA-RAT | AQUA-RAT-38836 | # The division of a fraction - Whole or Part?
My example is 1/2 divide by 8.
The correct answer given : 1/16
However, in my mind this answer is 1 divide by 16, which to me is not what the question is asking.
When I construct the argument, it seems it should equal 1/8 as the question is asking "What is the division ... | [
" 1/6 and 1/3 only",
" 1/4 and 1/3 only",
" 1/6, 1/4, and 1/3",
" 1/12, 1/6 and 1/4"
] | A | Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 3rd : 0/3, 1/3, 2/3, 3/3
Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 2... |
AQUA-RAT | AQUA-RAT-38837 | # 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... | [
"33.33%",
"30%",
"23%",
"28%"
] | A | Cost price =500×100/120= 416.67
S.P. at no discount = 500×100/90 = 555.55
∴ % profit = 138.88×100/416.67 = 33.33 %
Answer A |
AQUA-RAT | AQUA-RAT-38838 | ### Question 3
Multiple choice!
The decimal $0.23$ equals:
(A) $\dfrac {23}{10}$
(B) $\dfrac {23}{100}$
(C) $\dfrac {23}{1000}$
(D) $\dfrac {23}{10000}$
### Question 4
The decimal $0.0409$ equals:
(A) $\dfrac {409}{100}$
(B) $\dfrac {409}{1000}$
(C) $\dfrac {409}{10000}$
(D) $\dfrac {409}{100000}$
## SIMPL... | [
"1/5",
"1/3",
"1/4",
"1/9"
] | C | 1/5 = 0.2, 1/3 = 0.33, 1/9= 0.11, 1/8= 0.125, 4/5= 0.8, 1/4= 0.25.
Clearly, 0.25 lies between 0.20 and 0.33.
Therefore, 1/4 Lies between 1/5 and 1/3.
Answer is C. |
AQUA-RAT | AQUA-RAT-38839 | "Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4959 Location: Canada GMAT 1: 770 Q49 V46 When a positive integer n is divided by 5... | [
"96",
"75",
"36",
"25"
] | C | Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 96.25 and remainder is 9
So .25 X y = 9
hence y= 36
Ans C |
AQUA-RAT | AQUA-RAT-38840 | And, sure enough: . $8 + 2\sqrt{15} \;=\;(\sqrt{3} + \sqrt{5})^2$
The following is multiple choice question (with options) to answer.
Which is the middle even number between 5 and 15? | [
"5",
"10",
"25",
"30"
] | B | 5+x = 15-x
2 x = 10
X = 5
Now 5+x = 10
ANSWER:B |
AQUA-RAT | AQUA-RAT-38841 | # 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... | [
"650",
"400",
"1350",
"1800"
] | D | Total cost of Items : 5200/-
amount Paid : 7000/-
Balance receivable : 6000 - 7000= 1800/-
Answer is D |
AQUA-RAT | AQUA-RAT-38842 | 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 ... | [
"25",
"75",
"27",
"25"
] | B | S = (90 + 60)/2
= 75 kmph
Answer: B |
AQUA-RAT | AQUA-RAT-38843 | # 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 ... | [
"13",
"12",
"14",
"11"
] | C | factors : 2,7
2*7 =14
Answer : C |
AQUA-RAT | AQUA-RAT-38844 | software
9.0175 11.2135 2.3156 H 0
8.0176 9.4560 2.2492 C 0
6.3410 11.0331 3.1948 C 0
6.8195 11.7005 2.6977 H 0
6.1061 11.3837 4.0569 H 0
5.5420 10.7916 2.7197 H 0
6.8948 4.6534 2.5072 C 0
7.5354 3.9263 2.4577 H ... | [
"0.19",
"0.1",
"0.06",
"0.11"
] | C | Explanation:
Given numbers are 1.2 , 0.36 and 0.90
H.C.F of 120, 36 and 90 is 6 [ because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.06
Answer: C) |
AQUA-RAT | AQUA-RAT-38845 | Back
## A Test Question
Today, Pearl’s $9$ grandchildren are coming to visit! She loves to spoil them, so she opens her purse and finds $13$ dollar bills.
In how many different ways can Pearl distribute those dollars amongst her grandchildren? Keep reading to find out, or skip to today’s challenge for a similar prob... | [
"39",
"40",
"41",
"75"
] | D | Solution
Start with 25 pens.
Mike gives you 22 pens: 25 + 22 = 47 pens.
Cindy doubles the number of pens you have: 47 × 2 = 94 pens.
Sharon takes 19 pens from you: 94 - 19 = 75 pens.
So you have 75 at the end.
Correct answer: D |
AQUA-RAT | AQUA-RAT-38846 | 7. wayki says:
Here you said there is a 2.9 thousandths of an inch curvature for each 100 feet of horizontal distance.....(heheh).
I hate imperial so please allow me to convert it to metric.
0.07366 mm = 30.480m
Multiply all of this up by 1000 =
73mm fall for every 30,000km. Are you mad? One would have nearly gone... | [
"174.2",
"212",
"288.1",
"296"
] | D | 1.5 inch = 2.54*1.5 cm.
So, 2.54*1.5 represents 24 miles.
So for 47 cm.:
47/(2.54*1.5) = x / 24 ---> x = 24*47/(4.81) = 296
Answer will be D. |
AQUA-RAT | AQUA-RAT-38847 | homework-and-exercises, kinematics
Title: rectlinear motion with constant acceleration Friends, this is a numerical homework problem. I tried my best to solve it but my answer is not matching with the one given at the back of the text book. Please help me out:
A motor car moving at a speed of 72 km/h can come to a sto... | [
"225",
"90",
"45",
"37.5"
] | C | total length will be 330+66=396
time=6 secs
speed=396/6=66 feet/sec
conversion to miles per hour=66*3600/5280=45.
Answer C |
AQUA-RAT | AQUA-RAT-38848 | Example: Take $k=2002$, then $n=63$ and hence $2002$ lies in $(T_{63}-2002+1,63+2002-T_{63})=(15,49)$.
መለሰ
The following is multiple choice question (with options) to answer.
What will be the reminder when (1234567890123456789)^24 is divided by 6561 ? | [
"0",
"1",
"2",
"3"
] | A | The digital sum of number is
(1+2+3+4+5+6+7+8+9+0+1+2+3+4+5+6+7+8+9)=90=(9+0)=9
So it is divisible by 3 or 9
The given divisor 6561 = 9^4
So
9^24/9^4 Reminder is 0
ANSWER:A |
AQUA-RAT | AQUA-RAT-38849 | # Given a bag of 3 red marbles, 5 black, and 8 green, what is the probability that?
A bag has:
$3$ red
$5$ black
$8$ green
marbles.
Total of 16 marbles.
You select a marble, and then another one right after. (without replacement).
What is the probability that $both$ are red?
Probability that first pick is red:... | [
"1/35",
"1/9",
"1/10",
"1/20"
] | A | first, total ways to select for all boys and girls, i.e 8!/(4!*4!) = 8*7*6*5*4*3*2*1/4*3*2*1*4*3*2*1=70
then there are one two way girls can have all same colors, either white or black.
The number of ways in which 4 girls can select 4 white balls = 4C4 = 1
The number of ways in which 4 girls can select 4 black balls = ... |
AQUA-RAT | AQUA-RAT-38850 | ## anonymous one year ago Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out a... | [
"8",
"12",
"18",
"24"
] | B | In: we have: 1,000/2min = 500 litres per minute
Out: we have: 1,000/4 + 1,000/6
Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (1,000 by that net inflow to get the minutes) - 12 min. Answer B. |
AQUA-RAT | AQUA-RAT-38851 | 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 5/7",
"2 1/5",
"1 5/7"
] | D | Work hrs=AB/(A+B)= 12/7 =1 5/7
Answer is D |
AQUA-RAT | AQUA-RAT-38852 | 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 ... | [
"89 kmph",
"92 kmph",
"75 kmph",
"102.5 kmph"
] | D | S = (145 + 60)/2 = 102.5 kmph
D |
AQUA-RAT | AQUA-RAT-38853 | Similar Questions
1). How many different signals , can be made by 5 flags from 8 flags of different colors?
A). 6270 B). 1680 C). 20160 D). 6720
-- View Answer
2). A child has four pockets and three marbles. In how many ways, the child can put the marbles in the pockets?
A). 12 B). 64 C). 256 D). 60
-- View Answer
3)... | [
"128",
"130",
"132",
"143"
] | C | To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C |
AQUA-RAT | AQUA-RAT-38854 | 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... | [
"320",
"340",
"360",
"380"
] | D | Relative speed = (144 - 72) * 5/18 = 4 * 5
= 20 mps.
Distance covered in 19 sec
= 19 * 20
= 380 m.
The length of the faster train
= 380 m.
Answer:D |
AQUA-RAT | AQUA-RAT-38855 | graph-theory, co.combinatorics
9 meals are given by slopes $a = 0,1,\ldots,8$. The intersections with the 4 empty degenerate lines reduce the table size to 9-4=5.
An additional meal is given by the remaining degenerate lines $\{(b,x) | x \in F\}$ for every $b = 4,5,6,7,8$. Here the table size is 9. However (in any ... | [
"16",
"15",
"18",
"20"
] | B | Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer B |
AQUA-RAT | AQUA-RAT-38856 | Goal: 25 KUDOZ and higher scores for everyone!
Senior Manager
Joined: 13 May 2013
Posts: 429
Re: Susan drove an average speed of 30 miles per hour for the [#permalink]
### Show Tags
30 Jul 2013, 16:45
1
Susan drove an average speed of 30 miles per hour for the first 30 miles of a trip & then at a average speed of 6... | [
"The average speed is 40 miles per hour.",
"The average speed is 45 miles per hour.",
"The average speed is 48 miles per hour.",
"The average speed is 50 miles per hour."
] | B | Here, time for which Myra traveled at the two speeds is same.
Average Speed = (a + b)/2 = (30 + 60)/2 = 45 miles per hour
Answer (B) |
AQUA-RAT | AQUA-RAT-38857 | We see that: $b^2-1 \text{ is even }\quad\Rightarrow\quad b^2\text{ is odd }\quad\Rightarrow\quad b\text{ is odd}$
Let: $b \:=\:2c+1$
Then [1] becomes: . $k \:=\:\frac{(2c+1)^2-1}{4} \:=\:c^2 + c \quad\Rightarrow\quad k \:=\:c(c+1)$
Hence, $k$ must be the product of two consecutive integers.
Then: . $x \;=\;\frac{1... | [
"21",
"79",
"143",
"231"
] | C | Since a,b and c are consecutive positive integers and a>b>c, we can write them as (x + 1), x and (x - 1) respectively
(a^2-b^2)(b^2-c^2) can be simplified into (2x + 1)(2x - 1) = 4x^2 - 1
using the options to find the product,
only C. 143 satisfactorily gives us x as an integer
ANSWER:C |
AQUA-RAT | AQUA-RAT-38858 | Maybe the examiner didn't think through your method.
From 10,000 to 99,999 the numbers divisible by 5 end in 0 or 5.
The first (most significant) digit can be any of nine from 1 to 9.
The 2nd digit can be any of 10.
The 3rd digit can be any of 10.
The 4th digit can be any of 10.
The 5th digit can be either of 2.
That... | [
"1",
"3",
"8",
"7"
] | C | Integer is divisible by 9 - Sum of digits is divisible by 9
Answer: C |
AQUA-RAT | AQUA-RAT-38859 | homework-and-exercises, newtonian-mechanics, rotational-kinematics
Now your doubt is that why (2) holds it might happen that $\alpha$ can be positive or negative and thus $\omega_i$ can be greater than or less than $\omega_f$.
In the above problem it is given that wheel covers 90 revolutions in 15 sec. So on averge it... | [
"4",
"9",
"12",
"21"
] | B | More cogs less revolution,..
so
6:14::x:21
(21*6)/14=9
ANSWER:B |
AQUA-RAT | AQUA-RAT-38860 | Or, 1 = $154/4 And Total pay = 154/4*18 =>$ 693
Hence answer will be (E) $693 The wage difference is not with respect to time , correct approach will be with respect to work done.. ( Errorr is highlighted in red ) Further explanation as provide to you via PM Wages/Salary can be of 2 types ( Something You will certainl... | [
"46",
"40",
"44",
"48"
] | A | For 40 hrs = 40*20=800
Excess = 1000-800=200
For extra hours =.75(20)=15+20=35
Number of extra hrs =200/35=5.71=6 approx.
Total hrs =40+6=46
Answer A 46 |
AQUA-RAT | AQUA-RAT-38861 | Hint: Start your proof like this:
Let $k$ be any arbitrary odd integer. Then by the definition of an odd integer, we have $k=2a+1$ for some integer $a$. Thus...
Then consider $-k=-(2a+1)$ and perform some algebraic manipulations. Your final step should look something like:
...hence, since $-k=2b+1$ where $b$ is an i... | [
"2ab+a",
"2ab-b",
"2ab+a+b",
"2ab+2a+b"
] | C | 2ab+a+b=even+odd+odd=even
The answer is C. |
AQUA-RAT | AQUA-RAT-38862 | design-patterns, bash, plugin
validateNumeric() {
BOOKLENGTH=$1
reg='^[0-9]+$'
if ! [[ $BOOKLENGTH =~ $reg ]] ; then
echo "Error: Argument not a number, try again:" >&2;
read BOOKLENGTH
validateNumeric $BOOKLENGTH
else
validateEven $BOOKLENGTH
fi
}
validateEven() {
BOOKLENGTH=$1
echo "Te... | [
"784",
"672",
"492",
"372"
] | B | 9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
260-(90+9)=161 pages will require 161*3=483 digits.
The total number of digits is 9+180+483=672.
The answer is B. |
AQUA-RAT | AQUA-RAT-38863 | Note: Accept $$\frac{{15 – 14}}{{\sqrt {\frac{{3.03}}{{20}}} }}$$.
$$= – 2.569 \ldots$$ (A1)
Note: Accept $$2.569 \ldots$$
$$p{\text{ – value}} = 0.009392 \ldots \times 2 = 0.0188$$ A1
Note: Accept any answer that rounds to 0.019.
Note: Award (M1)(A1)A0 for any answer that rounds to 0.0094.
insufficient e... | [
"10",
"20",
"30",
"43"
] | B | His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20
B |
AQUA-RAT | AQUA-RAT-38864 | 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... | [
"188 m",
"876 m",
"251 m",
"100 m"
] | D | Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 40 = x / 15
x = 100 m.
Answer: D |
AQUA-RAT | AQUA-RAT-38865 | In a bag there are 10 Black balls, 8 White balls and 5 Red balls.
Three balls are chosen at random and one is found to be Black.
Find the probability that remaining two are white.
. $(a)\;\frac{8}{23}\qquad(b)\;\frac{4}{33}\qquad(c)\ ;\underbrace{\frac{10\cdot8\cdot7}{23\cdot22\cdot2 1}}_{str\!ange!} \qquad(d)\;\frac{... | [
"31/145",
"36/145",
"32/145",
"36/147"
] | B | The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B |
AQUA-RAT | AQUA-RAT-38866 | => 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... | [
" 4y",
" 5y",
" 6y",
" 17y"
] | D | Let $x be the advance that both receive = 2x
Amount earned per hour by John and Mary = x/9 and x/8
Mary gives $y to John to make the wages earned equal
Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/8
Solve (x+y)9 = (x-y)/8
8x + 8y = 9x -9y
x = 17y
Ans. D |
AQUA-RAT | AQUA-RAT-38867 | 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... | [
"1 kmph",
"3.2 kmph",
"1.5 kmph",
"2 kmph"
] | C | Explanation:
72 --- 9
? ---- 1
=> Down Stream = 8
45 ---- 9
? ---- 1
=> Up Stream = 5
Speed od current S = ?
S = (8 - 5)/2 = 1.5 kmph.
ANSWER IS C |
AQUA-RAT | AQUA-RAT-38868 | Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?
Total number of pencils Ramesh had = 20
Number o... | [
"24.5",
"14",
"24.21",
"27"
] | B | Explanation:
If Rahul age is x, then Sachin age is x - 7,
so,
9x - 63 = 6x
3x = 63
x = 21
So Sachin age is 21 - 7 = 14
Answer: B) 14 |
AQUA-RAT | AQUA-RAT-38869 | ### Show Tags
29 May 2017, 10:14
1
60*3 = 180
+
24*5= 120
120+180 =300
Speed= Distance/Time = 300/8 = 150/4=75/2=37.5
Manager
Joined: 03 Aug 2017
Posts: 103
Re: Jim travels the first 3 hours of his journey at 60 mph speed and the [#permalink]
### Show Tags
09 Dec 2019, 07:43
Bunuel wrote:
Jim travels the first 3 h... | [
"7hours 75 mins",
"7 hours",
"8 hours",
"5 hours"
] | A | Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time h... |
AQUA-RAT | AQUA-RAT-38870 | 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... | [
"22 sec",
"81.6 sec",
"48 sec",
"18.3 sec"
] | B | Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 850 + 850 = 1700 m.
Required time = 1700 * 6/125 = 81.6 sec.
Answer:B |
AQUA-RAT | AQUA-RAT-38871 | # 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.5725/-",
"Rs.5080/-",
"Rs.6250/-",
"Rs.7000/-"
] | D | Explanation:
45% loss means SP of Rs.3850/- is 55% of CP
:. CP = 3850x100/55 = Rs.7000/-
Answer: Option D |
AQUA-RAT | AQUA-RAT-38872 | Within a class of$M=30$children, knowing that the year counts$A=365$days... The probability that at least$n=2$children have their birthday the same day is: $$P(365,30,2)\simeq 70,6\%$$ The probability that at least$n=3$children have their birthday the same day is: $$P(365,30,3)\simeq 2,85\%$$ The probability that at le... | [
"22",
"18",
"4.5",
"99"
] | C | Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9
We know that the sum of their ages is 36
so, x+(x+3)+(x+6)+(x+9)= 36
therefore The youngest child is 4.5 years old
Answer: C |
AQUA-RAT | AQUA-RAT-38873 | Option A, your future value will be$10,000 plus any interest acquired over the three years. Let's take a look. Discounting or Present Value Concept Compound Value Concept Vn=Vo*(1+k) ^n. Let’s take a look at a couple of examples. (Also, with future money, there is the additional risk that the … The amount of interest d... | [
"1655",
"2888",
"2776",
"2997"
] | A | A = 5000(11/10)^3
= 6655
= 5000
----------
1655
Answer: A |
AQUA-RAT | AQUA-RAT-38874 | Let P=[$(\sqrt{n}+0.7)^2$]
Second Hint
given $n \geq 1$, put n=1 gives P=2
n=2 gives P=4
n=3 gives P=5
n=4 gives P=7
n-5 gives P=8
n=6 gives P=9
n=7 gives P=11
Final Step
here missing number are
1,3,6,10,… which is following a certain pattern
1, 1+2, 3+3, 6+4, 10+5, 15+6, 21+7, 28+8, 36+9, 45+10, 55+11, 66+... | [
"25",
"23",
"20",
"27"
] | D | Let's break the given series as below:
10 18 26
11 19 ?
12 20 28
13 21 29
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 27
Answer : D |
AQUA-RAT | AQUA-RAT-38875 | $(120,34)\simeq S_{5}$
$(120,36)\simeq S_{3}\times(\mathbb{Z}_{5}\rtimes\mathbb{Z}_{4})$
$(144,182)\simeq((\mathbb{Z}_{3}\times\mathbb{Z}_{3})\rtimes\mathbb{Z}_{8})\rtimes\mathbb{Z}_{2}$
$(144,183)\simeq S_{3}\times S_{4}$
$(156,7)\simeq(\mathbb{Z}_{13}\rtimes\mathbb{Z}_{4})\rtimes\mathbb{Z}_{3}$
$(168,43)\simeq((... | [
"210",
"211",
"213",
"214"
] | C | 12= 5*2+2
31= 12*2+5+2
81= 31*2+12+5+2
Similarly 81*2+31+12+5+2 = 162+50=212
ANSWER:C |
AQUA-RAT | AQUA-RAT-38876 | ### Explanation of the last step
This is a property all rectangles in the coordinate plane have.
For a proof, note that for any rectangle $ABCD$ its center can be computed as $(A+C)/2$ and at the same time as $(B+D)/2$. In our case, we can compute that the center is $\left(\frac{2+8}2,\frac{5+3}2\right)=(5,4)$, there... | [
"The closest pair of points among the six given points cannot be (F, C)",
"Distance between A and B is greater than that between F and C.",
"The closest pair of points among the six given points is (C, D), (D, E), or (C, E).",
"none of the above"
] | D | Explanation :
We have not been given the distances between any two points.
Answer : D |
AQUA-RAT | AQUA-RAT-38877 | ## 1 Answer
Case 2:
3 < x < 6
|x-3|= (x-3)
|x-6|= -(x-6)
(x-3)-(x-6)<5
3<5
3<5 is true, so 3 < x < 6 is also solution for |x − 3| + |x − 6| < 5
Finally we have |x − 3| + |x − 6| < 5 $\Leftrightarrow$ 2 < x < 7
The following is multiple choice question (with options) to answer.
If |x + 2| = 10, what is the sum ... | [
"-16",
"-13",
"-4",
"-2"
] | C | There will be two cases
x+2 = 10 or x+2 = -10
=> x = 8 or x= -12
sum of both the values will be -12 + 8 = -4
Answer: C |
AQUA-RAT | AQUA-RAT-38878 | Case 1: (3,1,1) First choose which of the 3 pockets will get three marbles. There are 3C1 =3 ways to do this. Then, choose the number of ways we can place 3 marbles into that box from 5 marbles. There are 5C3 = 10 ways to do this. Next we must place a marble in the next to the last box. There are 2C1 = 2 ways to do thi... | [
"6C4",
"6P4",
"4^6",
"6^4"
] | C | Each marble has 4 options, so there are total of Q= 4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1). |
AQUA-RAT | AQUA-RAT-38879 | - 2 years, 3 months ago
- 2 years, 3 months ago
I was getting the answer as 36.
My cases were similar to that of Deeparaj.
Case 1: When (4,8) is one of the selected pair.
Among the remaining 6 numbers only (2,6) have GCD=2. We can select any 3 pairs from the remaining 6 numbers in ((6C2)(4C2)(2C2)/3!)=15 ways( Not... | [
"14",
"15",
"20",
"22"
] | B | Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 26 => x = 5
So Deepak age is = 3(5) = 15
Answer: Option B |
AQUA-RAT | AQUA-RAT-38880 | # Clock losing time puzzle
The question goes as:
A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. The table clock loses 5 minutes in the 1st hour, 10 minutes in the second hour and ... | [
"55 5⁄61 minutes past 5",
"5 minutes past 6",
"5 minutes to 6",
"59 1⁄64 minutes past 5"
] | A | Time interval indicated by incorrect clock
= 6 p.m – 1 p.m = 5hrs.
Time gained by incorrect clock in one hour
= + 1 min. = +1⁄60 hr.
Using the formula, True time interval /Time interval in incorrect clock
= 1 /1+hour gained in 1 hour by incorrect clock
⇒ Truetimeinterval/5=1/1+1/60
⇒ True time interval = 5×60/61=4 56/6... |
AQUA-RAT | AQUA-RAT-38881 | 7,7),(1,8,7),(2,9,7),(8,0,8),(7,1,8),(9,1,8),(6,2,8),(5,3,8),(4,4,8),(3,5,8),(2,6,8),(1,7,8),(0,8,8),(1,9,8),(9,0,9),(8,1,9)
The following is multiple choice question (with options) to answer.
what is the smallest integer that is multiple of 5,7,8 | [
"A)70",
"B)35",
"C)200",
"D)280"
] | D | It is the lcm of 5, 7 and 8 which is 280.
The answer is D. |
AQUA-RAT | AQUA-RAT-38882 | 0.00698 acre1 acre = 43560 square feet304 sq ft * 1 acre/43560 sq ft = 0.00698 acre
### Number of sq ft per acre?
1 sq mi=5280ft x 5280ft = 27878400 sq ft/sq mi/ 27,878,400 sq ft/sq mi divided by 640acres/sq mi = 43,560 sq ft /acre 1 acre = 43,560 sq ft
### How many square feet are in 1.8 acre?
1 acre = 43,560 sq f... | [
"Rs.2091",
"Rs.1891",
"Rs.1981",
"Rs.1991"
] | B | Explanation:
25% = ¼
:. Cost of total area = Rs.132370x4
Rate per sq.ft = 132370x4/280 = Rs.1891/-
Answer: Option B |
AQUA-RAT | AQUA-RAT-38883 | 2. Mike says:
of course i meant 5 buckets, one for each student ;).
3. meichenl says:
Let there be $c$ cookies and $n$ students. Denote the number of ways to distribute $c$ cookies between $n$ students by $S_n(c)$. This is claiming that for a given number of students, the number of ways to distribute the cookies is ... | [
"0.125%",
"1.25%",
"31.7%",
"125%"
] | C | 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, Ingrid baked 9*5.17 cookies or 47 cookies (approx)
% share = 47/148 = 31.7 approx
Hence, answer is C. |
AQUA-RAT | AQUA-RAT-38884 | If stock price is $$X = (0,30)$$; we use the 7 puts (A) for profit = 7(40 - X); 9 (B) puts are used giving a loss = 9(30 - X). Total earning = 7(40-X) -9(30-X) + 2$= 2X + 12$ > 0
- 3 years, 2 months ago
Assume that the $40 put is still priced at$10.
What would be the price of the $30 put option, where there will be ... | [
"3:2",
"9:2",
"5 : 4",
"1:4"
] | C | X:Y = 50000 : 40000 = 5 : 4
ANSWER:C |
AQUA-RAT | AQUA-RAT-38885 | Overcounting cricketer combinations
Following this, Navneet had a new problem:
I am stuck on another problem:
A team of 11 is to be selected out of 10 batsmen, 5 bowlers, and 2 keepers such that in the team at least 4 bowlers should be included. Find the number of possible ways of selection.
I tried to solve this q... | [
"173",
"174",
"175",
"176"
] | C | 12.4*x+26=(8+x)12
solve equation x=175
ANSWER:C |
AQUA-RAT | AQUA-RAT-38886 | # 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... | [
"6 %",
"8 %",
"5 5/11%",
"11 %"
] | C | Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % =(300/5500 x 100)%= 5 5/11%
Answer:C |
AQUA-RAT | AQUA-RAT-38887 | WAIT!
S=11!
Because we have 11! ways of arranging the 11 items.
Sorry about that.
5. Hello, sweeetcaroline!
Edit: Plato is absolutely right . . . *blush*
6 red beads, 4 white beads, and 1 blue bead are placed in a line in random order.
What is the probability that no two neighboring beads are the same color?
There... | [
"18",
"22",
"42",
"41"
] | D | The correct answer should not take the form: 4x + 2. Hence, it is D |
AQUA-RAT | AQUA-RAT-38888 | substitute our 3rd conclusion:
$1 = x \oplus y \oplus w = 0 \oplus y \oplus 0 = 0 \oplus y = y \Longrightarrow y = 1$
-
The following is multiple choice question (with options) to answer.
If x/|y| = 1 which of the following must be true? | [
"x = -y",
"x = y",
"x = y^2",
"x^2 = y^2"
] | D | x/|y| = 1
x= 1 |y|
Squaring both sides
x^2= (1 |y|) ^2= y^2
D is the answer |
AQUA-RAT | AQUA-RAT-38889 | Let us take another mixture problem:
Question 2:
Two types of rice costing $60 per kg and$40 per kg are mixed in a ratio 2: 3. What will be the cost per kg of mixed rice?
Solution:
• Can we apply alligation to this question?
• Can we assume the price of the mixed rice to be $x per kg and make this diagram? • Now do... | [
"4",
"6",
"8",
"10"
] | C | Say the weight of the second sack after change is x kilograms, then the weight of the first sack after change would be 0.6x. Since the total weight of sugar in both sacks remained the same then x+0.6x=40, which gives x=25.
Now, if the weight of the second sack after change is 25 kilograms then initially it was 25−1=24 ... |
AQUA-RAT | AQUA-RAT-38890 | # 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... | [
"$10,000",
"$26,400",
"$12,000",
"$12,800"
] | B | 1 machine of type B will cost: 20% down payment of 60,000 = 12,000plusremaining sum (50,000-12,000=48,000) with 40% of finance charges 48,000*1.4=67,200 --> 12,000+67,200=79,200;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000... |
AQUA-RAT | AQUA-RAT-38891 | +0
# SOS!!!
0
230
7
+223
I cannot get the right answer for this problem for the life of me. If somebody would solve it I'd give them 5 stars.
THE PROBLEM:
(20+(1/4))x +(5+(1/2)) = (7+(1/16))
(solve for x)
#1
+10
(20+(1/4))x + (5+(1/2)) = (7+(1/16))
(20(1/4))x = (7+(1/16)) - (5+(1/2))
x = ( (7+(1/16)) - (5+(1... | [
"1",
"-2",
"12",
"-3"
] | C | |5x-30| = 100
5x-30 = 100 or 5x-30 = -100
5x = 130 or 5x = -70
x = 26 or x = -14
sum = 26-14 = 12
Answer is C |
AQUA-RAT | AQUA-RAT-38892 | 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... | [
"8am",
"6am",
"7am",
"10am"
] | A | Time of meeting = distance / relative speed = 36/8 + 4 = 36/12 = 3 hrs after 5am = 8am
Answer is A |
AQUA-RAT | AQUA-RAT-38893 | In this case, you have the digits $3$ and $2$, each of them $25$ times, so the remainder when dividing by $8$ is the same as the remainder of $(2+3)\times 25 = 125$ when divided by $8$, which is $5$.
(More generally, the remainder of dividing the number $(b_1b_2\cdots b_k)_b$ by $b-1$ is the same as the remainder of d... | [
"5",
"7",
"9",
"10"
] | A | add 44+17=61
now 61 divided by 8 so we get 5 as reaminder
ANSWER:A |
AQUA-RAT | AQUA-RAT-38894 | $\text{ }$
$\displaystyle (9) \ \ \ \ \ E(X \wedge u)=\int_{-\infty}^u x \ f_X(x) \ dx+u \ S_X(u)$
$\displaystyle (10) \ \ \ \ \ E(X \wedge u)=\biggl(\sum \limits_{x < u} x \ P(X=x)\biggr)+u \ S_X(u)$
$\text{ }$
Interestingly, we have the following relation.
$\text{ }$
$\displaystyle (X-d)_+ + (X \wedge d)=X \ \ ... | [
"$600",
"$1000",
"$3800",
"$5300"
] | B | 0.5 * 600 = 300 where Q = B |
AQUA-RAT | AQUA-RAT-38895 | 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... | [
"310 meter",
"335 meter",
"345 meter",
"350 meter"
] | D | Explanation:
Speed = Distance/Ɵme = 300/18 = 50/3 m/sec
Let the length of the plaƞorm be x meters
then
Distance=Speed
∗
Timex+300=503
∗
39=>3(x+300)=1950=>x=350 meters
Answer: D |
AQUA-RAT | AQUA-RAT-38896 | # Proof for divisibility by $7$
One very classic story about divisibility is something like this.
A number is divisible by $2^n$ if the last $n$-digit of the number is divisible by $2^n$. A number is divisible by 3 (resp., by 9) if the sum of its digit is divisible by 3 (resp., by 9). A number $\overline{a_1a_2\ldots... | [
"16^2+1",
"12",
"(2^96+1)",
"24"
] | C | Explanation:
Let 2^32 = x. Then, (2^32 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(2^32)3 + 1] = (x^3 + 1) = (x + 1)(x^2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
C |
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