source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38997 | # Difference between revisions of "2017 AMC 10A Problems/Problem 25"
## Problem
How many integers between $100$ and $999$, inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999?$ For example, both $121$ and $211$ have this property.
$\mathrm{\textbf{(A)} \ }226... | [
"4",
"9",
"11",
"12"
] | B | The Question basically asks how many positive odd integers less than 90 are odd multiples of 5
So we have 5,15,25,35,45,55,65,75,85
= 9
Ans B |
AQUA-RAT | AQUA-RAT-38998 | # 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... | [
"150",
"339",
"342",
"359"
] | C | Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer T= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C |
AQUA-RAT | AQUA-RAT-38999 | $24 = 1^3 + 2^3 - 3^3 - 4^3 + 5^3 + 6^3 - 7^3 + 8^3 + 9^3 + 10^3 - 11^3 + 12^3 + 13^3 + 14^3 - 15^3 - 16^3$ (at least 7 other ways)
Each of the above representations is the shortest possible. The algorithm created a sequence of sets $S_n$ with $S_0 = \{0\}$ and $S_n = \{x+n^3, x-n^3 : x \in S_{n-1}\}$ for $n > 0$, so ... | [
"7",
"8",
"9",
"10"
] | C | 27^y> 3^24
Converting into the same bases:
27^y> 27^8
Therefore for the equation to hold true, y> 8 or y= 9
Option C |
AQUA-RAT | AQUA-RAT-39000 | # 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... | [
"120%",
"125%",
"150%",
"100%"
] | B | g% = 50 + 50 + (50*50)/100
= 125%
ANSWER:B |
AQUA-RAT | AQUA-RAT-39001 | # How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?
How would I go about solving this math problem?
if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$?
I got $a/c = 2/5$ but that is not a corr... | [
"10",
"87",
"20",
"72"
] | C | Let the two numbers be 5x and 6x.
Let the number added to both so that their ratio becomes 7:8 be k.
(5x + k)/(6x + k) = 7/8
42x = 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
Answer:C |
AQUA-RAT | AQUA-RAT-39002 | 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... | [
"11",
"16",
"77",
"88"
] | B | Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x => x= 16 days.
Hence, Tanya takes 16 days to complete the work.
Answer: B |
AQUA-RAT | AQUA-RAT-39003 | python, python-3.x
if seniors + carers >= int(40) or seniors <= int(1) or seniors >= int(37) or carers <= int(1) or (seniors >= int(24) and carers <= int(2)):
print("Enter Valid Info Please")
else:
print("Seniors going: " + repr(seniors) + " | Carers going: " + repr(carers))
if seniors >= int(1) and senio... | [
"$336",
"$289",
"$282",
"$274"
] | A | Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*15 = 16*15 = 240 $
Total charge =126 +240 = 366$
Answer A |
AQUA-RAT | AQUA-RAT-39004 | 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... | [
"40",
"54",
"45",
"39"
] | A | Answer
Let number of toys be N.
More hours, More toys (Direct proportion)
2 : 80 : : 1 : N
⇒ N = 80/2 = 40 toys
Correct Option: A |
AQUA-RAT | AQUA-RAT-39005 | Smallest number of children such that, rounding percentages to integers, $51\%$ are boys and $49\%$ are girls [closed]
I faced a very confusing question during my preparation for Mathematics olympiad, here is the question:
The percentage of boys in a gathering, rounded to an integer, is 51 percent. and the percentage... | [
"120",
"125",
"153",
"200"
] | A | 44 + 28 + 10 = 82%
100 – 82 = 18%
850 * 18/100 = 153
ANSWER A |
AQUA-RAT | AQUA-RAT-39006 | # remainder of $a^2+3a+4$ divided by 7
If the remainder of $$a$$ is divided by $$7$$ is $$6$$, find the remainder when $$a^2+3a+4$$ is divided by 7
(A)$$2$$ (B)$$3$$ (C)$$4$$ (D)$$5$$ (E)$$6$$
if $$a = 6$$, then $$6^2 + 3(6) + 4 = 58$$, and $$a^2+3a+4 \equiv 2 \pmod 7$$
if $$a = 13$$, then $$13^2 + 3(13) + 4 = 212$... | [
"2",
"3",
"4",
"5"
] | C | When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?
Putting a value say x = 24 we get remainder as 24 when divided by 61.
When 24 divided by 5 we get 4 as remainder.
C is the answer. |
AQUA-RAT | AQUA-RAT-39007 | ## 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 (2 to the x) - (2 to the (x-2)... | [
"9",
"11",
"13",
"15"
] | C | (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 11)
2^x - 2^(x-2) = 3. 2^11
Hence x = 13.
Answer is C |
AQUA-RAT | AQUA-RAT-39008 | # 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... | [
"2 2 1/8 kmph",
"2 3 1/2 kmph",
"4 2 1/2 kmph",
"2 2 1/2 kmph"
] | D | 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2 kmph
Answer:D |
AQUA-RAT | AQUA-RAT-39009 | # 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... | [
"6400",
"2777",
"2666",
"2888"
] | A | Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.
Answer: A |
AQUA-RAT | AQUA-RAT-39010 | Will give the value for two hits or fewer and two hits exactly respectively.
5. Oct 3, 2016
### RJLiberator
Allright, so now the answer to A is P_12(2)+P_12(1)+P_12(0) = 0.168+0.014+0.071 = 0.253
This makes more reasonable sense to me and I see how it makes sense with the additions of the probabilities as it relate... | [
"0.06",
"0.12",
"0.21",
"0.29"
] | A | The probability that eachdoesn'thit is: 0.1, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities:
.9*.7*.8 = 0.06.
Option: A |
AQUA-RAT | AQUA-RAT-39011 | 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... | [
"8 days",
"5 days",
"6 days",
"7 days"
] | D | 1/5 + (1 + x)/10 = 1 => x = 7 days
Answer: D |
AQUA-RAT | AQUA-RAT-39012 | # arrangement
#### jacks
##### Well-known member
How many permutation of the letters of the words $\bf{"MADHUBANI"}$ do not begin with $\bf{M}$ but end with $\bf{I}$
#### Jameson
Staff member
How many permutation of the letters of the words $\bf{"MADHUBANI"}$ do not begin with $\bf{M}$ but end with $\bf{I}$
I am no... | [
"28",
"21",
"26",
"20"
] | D | The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 5P2
= 5 * 4 = 20.
Answer: D |
AQUA-RAT | AQUA-RAT-39013 | ## 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 ... | [
"70",
"560",
"630",
"1,260"
] | B | Total number of ways to select at least one professor = Number of ways to select 3 people from 10 students and 7 professors - Number of ways to select 3 people from 10 student (i.e. without including any professor)
= 17C3 - 10C3 = 680 - 120 = 560
ANSWER:B |
AQUA-RAT | AQUA-RAT-39014 | This is an A.P. The below workout with step by step calculation shows how to find what is the sum of natural numbers or positive integers from 1 to 250 by applying arithmetic progression. is 56. If n is an integer, then n, n+1, and n+2 would be consecutive integers. If A and G be A.M. and G.M., respectively between two... | [
"14,550",
"18,550",
"22,550",
"26,550"
] | C | 2 + 4 + 6 + 8 +...+ 100 = 2550
402 + 404 + ... + 500 = 50(400) + (2+4+...+100) = 20,000 + 2550 = 22,550
The answer is C. |
AQUA-RAT | AQUA-RAT-39015 | ### 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... | [
"A)2500",
"B)3500",
"C)5000",
"D)6000"
] | B | Interest received by A from B = 10% of half of Rs.5000 = 10% * 2500 = 250.
Amount received by A per annum for being a working partner = 500 * 12 = Rs.1000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (250 + 1000 + P)
Total income of B = only his share from the remaining... |
AQUA-RAT | AQUA-RAT-39016 | The operations above are perfectly reasonable. Let me show you the kind of situation that I think you were worried about, and you'll see why it's different from the situations above:
I take 4 exams and have an average score of 80. Then I take 2 more exams and on those 2, my average is 100. What's my overall average fo... | [
"300",
"350",
"400",
"450"
] | C | total marks:1500 for three exams
60% of 1500=900
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =900
X=400
ANSWER:C |
AQUA-RAT | AQUA-RAT-39017 | The statement
"(the integer referred to by the decimal symbol 1) + (the integer referred to by the decimal symbol 1) = (the integer referred to by the decimal symbol 2)"
is indeed always true. Whether or not this is expressed in symbols as
"1 + 1 = 2"
depends on how you choose to represent integers.
The following ... | [
"12/a",
"3/a",
"8/a",
"9/a"
] | C | 1/a + 3/a + 4/a
=8/a
Answer C |
AQUA-RAT | AQUA-RAT-39018 | 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... | [
"82.1 sec",
"12.1 sec",
"24.2 sec",
"13.1 sec"
] | C | Speed = 36 * 5/18 = 10 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/10 = 24.2 sec.
Answer:C |
AQUA-RAT | AQUA-RAT-39019 | # Ten-digit number that satisfy divisibilty rules for 2,3,4,5,6,7,8,9,10&11
Question: Arrange the digits 1,2,3,4,5,6,7,8,9,0 to make a ten-digit Number that satisfies all of the divisibility rules for 2,3,4,5,6,8,9,10,&11. BONUS: make the number also divisible by 7
• Should I add no-computer tag? – Omega Krypton Oct ... | [
"985",
"970",
"955",
"990"
] | D | Greatest number of 3 digits = 999
LCM of 5, 10, 15 = 30
999 ÷ 30= 33, remainder = 9
Hence, greatest number of four digits which is divisible by 5,10,15
= 999 - 9 = 990
answer : D |
AQUA-RAT | AQUA-RAT-39020 | # In how many ways can 3 distinct teams of 11 players be formed with 33 men?
Problem:
In how many ways can 3 distinct teams of 11 players be formed with 33 men? Note: there are 33 distinct men.
The problem is similar to this one: How many distinct football teams of 11 players can be formed with 33 men?
Fist, I thou... | [
"6^6 ways",
"8^9 ways",
"7^8 ways",
"8^7 ways"
] | A | 6 people can be prized with distinct prizes in 6^6 ways
ANSWER:A |
AQUA-RAT | AQUA-RAT-39021 | ## Wednesday, August 12, 2015
### The angle between the hour and minute hands of a clock.
Q. The time shown in the clock is 7:35 what is the angle between the hour and minute hands of a clock?
A. Consider the simpler problem if the time is 7:00. As there are 12 hours in a complete revolution of the hour hand, one ho... | [
"6:39",
"6:37",
"6:31",
"6:32"
] | D | For hour = 360/12 = 300300/hr
For Minute = full rotation = 36003600/hr
Let the line is 't' , for 6 = 6*30=18001800
then
30 t + 180=360 t
330t = 180
t = 180/330
t = 6/11 hr 6/11*60=360/11=32611611
Ans. D |
AQUA-RAT | AQUA-RAT-39022 | comes up heads. The student will count the coins and write their answer to the right of each problem. The probability of all three tosses is heads: P ( three heads) = 1 × 1 + 99 × 1 8 100. ' 'The coin is just as likely to land heads as tails. Probability measures and quantifies "how likely" an event, related to these t... | [
"37/256",
"56/256",
"65/256",
"70/256"
] | A | More than 5 times tails = 6times +7times+8times = 8C6 + 8C7 + 8C8 = 37
- - - - - - - -
2 2 2 2 2 2 2 2
2^8 times total events and 37 events where tails side up .
So probability = 37/2^8 = 37/256 (Answer A) |
AQUA-RAT | AQUA-RAT-39023 | 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 ... | [
"166",
"213",
"413",
"438"
] | B | Cookies which have both nuts and chocolate chips = 185
Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that
batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x
(185+x)/(450+x) = 6/10
=>1850 + 10x =... |
AQUA-RAT | AQUA-RAT-39024 | ### Show Tags
19 Aug 2015, 01:34
2
KUDOS
1
This post was
BOOKMARKED
Let's assume that the total no. of people is n and the initial average is x.
So we can assume that the total sum of ages would be nx initially.
When the guy aged 39 is added to the total, the new sum of ages would be (nx+39). The new average now wo... | [
"22 years",
"23 years",
"24 years",
"25 years"
] | C | Total age of 12 students=12*20=240
If total age of 4 students=x
Then, (240+x)/(12+4) =(20+1), x=96
So average age of new students=96/4= 24 years
ANSWER:C |
AQUA-RAT | AQUA-RAT-39025 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. .... | [
"28",
"30",
"31",
"32"
] | D | Assume that initial number of men = initial number of women = x
2(x-8) = x
=> 2x - 16 = x
=> x = 16
Total number of men and women = 2x = 2 × 16 = 32
Answer is D. |
AQUA-RAT | AQUA-RAT-39026 | # another probability: number of ways for 4 girls and 4 boys to seat in a row
4 posts / 0 new
Ej-lp ACayabyab
another probability: number of ways for 4 girls and 4 boys to seat in a row
In how many ways can 4 girls and 4 boys be seated in a row containing 8 seats if boys and girls must sit in alternate seats?
The ans... | [
"720",
"6",
"2880",
"5040"
] | B | Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6.
Answer: B. |
AQUA-RAT | AQUA-RAT-39027 | int <- .1/100 # annual interest rate of 0.1%
inf <- 2/100 # annual inflation rate 2%
n <- 10 # number of years
The following is multiple choice question (with options) to answer.
The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven. | [
"0.3d + 1609",
"0.3d + 16089",
"0.3d + 1600",
"0.3d + 1602"
] | C | c = md + b
The cost is $ 4600 for 10 000 km
4600 = m (10 000) + b
10 000 m + b = 4600
b = -10 000 m + 4600 ------- (i)
The cost is $ 9100 for 25 000 km
9100 = m (25 000) + b
9100 = 25 000 m + b
25 000 m + b = 9100
b = -25 000 m + 9100 --------- (ii)
From equation (i) and (ii) we get;
-10 000 m + 4600 = -25 000 m + 9100... |
AQUA-RAT | AQUA-RAT-39028 | => 18x/4=154
x=308/9
TOTAL WAGES PAID WILL BE
(12/11 + 18/7)*309/9
PLEASE TELL ME WHERE I AM WRONG
Lets try -
SW4 wrote:
Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the differe... | [
"1/2 m",
"1/3 m",
"1/4 m",
"1/5 m"
] | A | After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/2.
Answer: A. |
AQUA-RAT | AQUA-RAT-39029 | # Mean and Median in a Classic River Crossing Problem
Consider the following classic problem:
Four people on the west side of a river wish to use their single boat to get to the east side of a river. Each boat ride can hold at most two people, and the time it takes to get across will be the time preferred by the slow... | [
"14",
"15",
"16",
"28"
] | C | Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty cl... |
AQUA-RAT | AQUA-RAT-39030 | # Given an Alphabet, how many words can you make with these restrictions.
I'm trying to understand from a combinatoric point of view why a particular answer is wrong. I'm given the alphabet $\Sigma = \{ 0,1,2 \}$ and the set of 8 letter words made from that alphabet, $\Sigma_8$ . There are $3^8 =6561$ such 8 letter wo... | [
"5040",
"1254",
"4510",
"1203"
] | A | 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
Ans: A |
AQUA-RAT | AQUA-RAT-39031 | (ones digit is $$0$$, because it is the difference of two numbers whose ones digit is $$1$$).
Now if $$3n$$ is divisible by $$10$$, for an integer $$n$$, then $$n$$ is divisible by $$10$$. QED.
The following is multiple choice question (with options) to answer.
If n is a 9-digit positive integer, all of whose digits ... | [
"I and II only",
"I only",
"I and III only",
"II and III only"
] | A | Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.
Rules for divisibility by 9: The sum of the digits should a multiple of 9
Consider no 111... |
AQUA-RAT | AQUA-RAT-39032 | # 2d kinematics
1. Sep 13, 2013
### Jabababa
1. The problem statement, all variables and given/known data
A diver jumps off a 3.00 meter high diving board with an initial velocity of 1.75 m/s vertically upward.
a) What is the diver's veolcity when she reaches the water? (assume the surface of the water is 3.00 mete... | [
"1/5",
"1/15",
"4/25",
"9/64"
] | D | Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.25 = 25/100 = 1/4
i.e. Probability of Non-Perfect dive = 0.75 = 75/100 =3/4
The probability of Janet to dive and get a perfect score depends on that other other previous two dives must... |
AQUA-RAT | AQUA-RAT-39033 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"24",
"25",
"26",
"27"
] | A | Ans. 24 days |
AQUA-RAT | AQUA-RAT-39034 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"50 m",
"72 m",
"80 m",
"82 m"
] | A | Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
ANSWER:A |
AQUA-RAT | AQUA-RAT-39035 | ##### Well-Known Member
Subscriber
Actually, it looks like the discount rate is a risk-free rate not necessarily equal to a LIBOR of the correct period length.
#### Dr. Jayanthi Sankaran
##### Well-Known Member
Hi Brian,
In many countries such as Thailand, the Treasury yield curve is illiquid across maturities. On t... | [
"1 months",
"4 months",
"7 months",
"9 months"
] | B | S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = 100 x 80 year = 1 year = 4 months.
1600 x 15 3
View Answer Discuss in Forum Workspac
Answer:B |
AQUA-RAT | AQUA-RAT-39036 | \, =\, \frac{21}{32}e\, +\, \frac{21}{64}f\, +\, \frac{127}{64} \\\\ 43f\, =\, 42e\, +\, 127 \: \: \: ---(2)$$ Combining these, we obtain
The following is multiple choice question (with options) to answer.
The average weight of D, E and F is 42 kg. If the average weight of D and E be 35 kg and that of E and F be 41 kg... | [
"23 Kg",
"24 Kg",
"25 Kg",
"26 Kg"
] | D | Let the weight of D, E and F are a,b and c respectively.
Average weight of D,E and F = 42
a + b + c = 42 × 3 = 126 --- equation(1)
Average weight of D and E = 35
a + b = 35 × 2 = 70 --- equation(2)
Average weight of E and F = 41
b + c = 41 × 2 = 82 --- equation(3)
equation(2) + equation(3) - equation(1)
=> a + b + b + ... |
AQUA-RAT | AQUA-RAT-39037 | # 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 ... | [
"48 min. past 19",
"48 min. past 12",
"48 min. past 10",
"48 min. past 11"
] | A | Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. af... |
AQUA-RAT | AQUA-RAT-39038 | The second-last digit must be divisible by 4, because the number must be divisible by 4 and 8. The third to last digit must also be even, to make it divisible by 8.
Now
all we have is 11 (and 7 for extra credit). To satisfy this, we have to make it so that when placing alternating signs between the digits so the resu... | [
"1",
"2",
"0",
"4"
] | C | The number 5x4 must be divisible by 8.
x=0 as 504 is divisible by 8.
Correct Option : C |
AQUA-RAT | AQUA-RAT-39039 | • $P_2$ will fly $\big[1-(d+r+y)\big]$ distance away from the airport in the counter-clockwise direction to meet up with $P_3$.
• At this point, $P_2$ will donate $z$ fuel to $P_3$.
• $P_2$ and $P_3$ will then both fly back $z$ distance, arriving at a distance of $1-d-r-y-z$ from the airport with no fuel.
• After refue... | [
"4",
"6",
"5",
"2"
] | D | We need on-time departure rate to be higher than 4/10, so it should be at least 5/11, which means that 5 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 5-3=2 subsequent flights need to depart on-time.
Answer: D |
AQUA-RAT | AQUA-RAT-39040 | There are 3 crates of apples A, B and C. The ratio of the number of apples in crate A to crate B to crate C is 8 : 5 : 3. David removed 42 apples from crate A and placed them into crate C. as such, there are 2 more apples in crate C than crate B. How many apples are there altogether?
2. HINT: 3k + 42 = 5k + 2
4. Orig... | [
"1 to 4",
"1 to 3",
"2 to 6",
"3 to 4"
] | C | Correct Answer: C
Solution: C. We know that when Pam and Stanley were both working, the ratio was 2 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, th... |
AQUA-RAT | AQUA-RAT-39041 | the first question correctly: 1/5 For that 1/5 of the time when the first question has been guessed correctly, the second question could be guessed correctly 1/5 of the time. Instead, Microsoft is adding more questions of new types. It's probably the biggest struggle students have with multiple choice questions. Each q... | [
"60 %",
"55 %",
"70%",
"75%"
] | B | {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 65 - {Both correctly} + 5
{Both correctly} = 55.
Answer: B. |
AQUA-RAT | AQUA-RAT-39042 | # Math Help - Integers
1. ## Integers
Hello,
I am trying to solve this problem:
If j and k are integers and j - k is even, which of the following must be even?
a) k
b) jk
c) j + 2k
d) jk + j
e) jk - 2j
According to the booklet the answer is d, however how would I even go about arriving at this answer? Any help wo... | [
" –5",
" 1",
" 13",
" 17"
] | D | 2x-j=11....j=2x-11
4x+j=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D |
AQUA-RAT | AQUA-RAT-39043 | The correct answer is 4. The chart below shows the remainder calculated vs. the remainder that is the answer (4). The values that don't match up are once again in red. Please note that I removed 3 from the table because it was a root of the equation, so the results weren't useful for my purposes.
In summary, does the ... | [
"12",
"13",
"14",
"15"
] | C | When x is divided by 9, the remainder is 2: So, the possible values of x are: 2, 11, 21, 29, etc.
When x is divided by 7, the remainder is 4: So, the possible values of x are: 4,11,18,... STOP. Since both lists include 11, the smallest possible value of x is 11.
When y is divided by 11, the remainder is 3: So, the poss... |
AQUA-RAT | AQUA-RAT-39044 | Now find the time Rick spends running.
$\displaystyle t_{r,R}=\frac{D}{2v_r}$
Now just add the two times up and you’re done.
$\displaystyle t_R=\frac{D}{2v_w}+\frac{D}{2v_r}=\frac{D}{2v_wv_r}\left(v_w+v_r\right)$
#### PART B. Find Rick’s average speed for covering the distance D.
You were given the total distance ... | [
"1100 meters",
"1200 meters",
"1250 meters",
"1300 meters"
] | B | Let X = Minutes
And Y = Aryan runs speed = 40 meter per X
And Z = Rahul runs speed = 50 meter per X (i.e., 200 + 50x)
And D = Total distance covered by the dog = X* 60meters
Y = Z
40x = 200 + 50x
200 = 10x
x = 200/10
x = 20
So, by 20minutes, both Aryan and Rahul meets.(Rahul reaches Aryan.)
So, dog covered distance, D ... |
AQUA-RAT | AQUA-RAT-39045 | (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 ... | [
"1000",
"1055",
"1428",
"1500"
] | C | Cost of 11 kg grapes = 98 × 11 = 1078.
Cost of 7 kg of mangoes = 50 × 7 = 350.
Total cost he has to pay = 1078 + 350= 1428
C |
AQUA-RAT | AQUA-RAT-39046 | 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
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"12",
"11",
"15",
"16"
] | A | A
12
Let Harsh’s age 6 years back = A
Then, Amith’s age 6 years back = 32.
Then 5/3 (A + 6 + 6) = (3A + 6 + 6)
5(A + 12) = 3 (3A + 12)
4A = 24
A = 6
Harsh’s age today = (A + 6) years
= 12 years. |
AQUA-RAT | AQUA-RAT-39047 | I got y = 1/2
6. Originally Posted by magentarita
You got the right answer. But how did you get y = 1?
I got y = 1/2
Substitute x= -2 into the expression :
2 [ (-2+2)² + 1/2 ] = 2 [ 0+1/2 ] = 1
7. Originally Posted by magentarita
ok but none the choices given for the minimum point is (-2, 1/2).
(2,33)
(2,17)
(-2,... | [
"53/28",
"59/11",
"51/77",
"41/11"
] | A | = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(9/5)^2+1] / [(9/5)^2-1]
= [(81/25)+1] / [(81/25)-1] = 53/28
Answer is A. |
AQUA-RAT | AQUA-RAT-39048 | all three = neither =5 = 10/3 % of 150
working formula :-
Total = AC + sunporch + swimming pool - Exactly two - 2*all three + neither
100 = 60 + 50 + 30- Exactly two - 2*10/3 + 10/3
100 =140 - Exactly two - 10/3
Exactly two = 40 - 10/3 = (120-10)/3 = 110/3 %
110/3 % of 150 = 110*150/300 =55
Ans D
Senior SC Moderator... | [
"45%",
"90%",
"65%",
"55%"
] | A | Trucks = 40% of 300 = 120
Other Vehicles (Excluding Trucks) = 300-120 = 180
Diesel Vehicle = 20% of 300 = 60 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 60-15 = 45
Trucks that are NOT diesel = 120 - 15 = 105
Other Vehicles that are NOT diesel Vehicles = 180-45 = 135
Required % = (135/300)*100 = 45%... |
AQUA-RAT | AQUA-RAT-39049 | It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\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$$.
bunuel, pls help
if i equate time i am n... | [
"16 days",
"17 days",
"19 days",
"12 days"
] | D | P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 9 days, which means Q can do the work in 48 days.
Hence, P can do the work in 12 days.
Answer:D |
AQUA-RAT | AQUA-RAT-39050 | = 1/9, i. Like area, surface area is also expressed in square units. The surface area and the volume of a cylinder have been known since ancient times. As the cube gets bigger, the volume increases much more rapidly than the surface area, because the volume increases as the cube of the linear dimension, but the surface... | [
"54",
"64",
"81",
"288"
] | D | Volume of larger cube = 64 = 4^3
Side of larger cube = 4
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 4^2 = 96
Surface area of 27 smaller cubes = 64 * 6 * 1 = 384
Difference = 384 - 96 = 288
Answer: D |
AQUA-RAT | AQUA-RAT-39051 | ## Digit Problems
1. Use $$3,4,5,6,7,8$$ to make digits between 5,000 & 6,000.
2. 2, 3, 4, 5, 6, 7: 6-digit numbers not divisible by 5
3. 5, 6, 7, 8, 0: Five digit numbers divisible by 4.
4. Make 7-digit numbers using 3, 4, 5, 5, 3, 4, 5, 6, keeping odd digits at odd positions, without using digits more than its frequ... | [
"99111",
"99946",
"99869",
"99792"
] | B | Largest 4 digit number is 99999
After doing 99999 ÷ 77 we get remainder 53
Hence largest 5 digit number exactly divisible by 77 = 99999 - 53 = 99946
B |
AQUA-RAT | AQUA-RAT-39052 | evolution, zoology, anatomy, species
Title: Examples of animals with 12-28 legs? Many commonly known animals' limbs usually number between 0 and 10. For example, a non-exhaustive list:
snakes have 0
Members of Bipedidae have 2 legs. Birds and humans have 2 legs (but 4 limbs)
Most mammals, reptiles, amphibians have 4 ... | [
"17",
"26",
"90",
"27"
] | C | 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C |
AQUA-RAT | AQUA-RAT-39053 | As others have said, one can ask that the girls' chairs, and the block of chairs for the boys, be chosen together (in this way, we treat the group of boys as "another girl", for a total of 5 "girls" choosing among 5 "seats"); thus, we can have the boys choose one of the 5 "seats" (in reality, it is their block of chair... | [
"65",
"50",
"80",
"35"
] | A | The total number of ways to choose 4 children is 8C4 = 70
The number of ways to choose only boys is 5C4 = 5
The number of groups which include at least one girl is 65.
The answer is A. |
AQUA-RAT | AQUA-RAT-39054 | only effective. Share, and after five years it earned you$ 15 in income 2 years or decreases ) in! A certain period of time that an investment over time as a percentage of investment. Zijn bidirectioneel, wat wil zeggen dat je woorden gelijktijdig in beide talen kan.! Are returned to you not reinvest would have $40 per... | [
"Rs. 118",
"Rs. 120",
"Rs. 124.75",
"Rs. 131"
] | C | For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C |
AQUA-RAT | AQUA-RAT-39055 | # How to approach this combinatorics problem?
You have $12$ different flavors of ice-cream. You want to buy $5$ balls of ice-cream, but you want at least one to be made of chocolate and also you don't want more than $2$ balls per flavor. In how many ways can you can choose the $5$ balls?
• Does order matter? – vrugte... | [
"4",
"8",
"12",
"1"
] | D | 1 flavours * 1 choices = 1C1*1C1 = 1*1=1=D |
AQUA-RAT | AQUA-RAT-39056 | 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... | [
"70%",
"15%",
"20%",
"25%"
] | A | price of a coat in a certain store = $500
the price of the coat is to be reduced by $350
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (350)*100 / 500 = 70%
Answer: Option A |
AQUA-RAT | AQUA-RAT-39057 | 5. Originally Posted by Nath
"I have 2 children. One is female. What is the probability the other is also female?"
This puzzle appeared in New Scientist magazine, and a similar one in Scientific American several months back. The consensus among mathematicians (according to the articles in the magazines), including a f... | [
"2/7",
"5/7",
"4/7",
"3/7"
] | C | P(1st b, 2nd g) = 4/7*3/6 = 4/14;
P(1st g, 2nd b) = 3/7*4/6 = 4/14.
P = 4/14 + 4/14 = 4/7.
Answer: C. |
AQUA-RAT | AQUA-RAT-39058 | ### Show Tags
16 Jun 2018, 09:16
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?
1) The average of the prices of all of the shirts and sweaters that the store sold during the sale wa... | [
"50%",
"33.33%",
"25%",
"16.66%"
] | D | Say the original retail price of the item was $200.
The price after the first sale = 3/5 * $200 = $120.
The price after the second sale = 1/2 * $200 = $100.
The percent change from the first sale to the second = (120 - 100) / 120 = 1/3 = 16.66%.
Answer: D. |
AQUA-RAT | AQUA-RAT-39059 | The remainder is $\,2 \,P_6(x^2)\,$, which follows for $\,n=6\,$ from the general identity:
\begin{align} P_{2n}(x^2) = \frac{x^{4n}-1}{x^2-1} &= \frac{x^{2n}-1}{x-1} \, \frac{x^{2n}+1}{x+1} \\[5px] &= \, \frac{x^{2n}-1}{x-1} \, \frac{x^{2n}-1+2}{x+1} \\[5px] &= - \, \frac{x^{2n}-1}{x-1} \, \frac{(-x)^{2n}-1}{(-x)-1} ... | [
"5808",
"5336",
"5343",
"5345"
] | A | Divisor = (5 * 48) = 240
= 10 * Quotient = Divisor
=> Quotient = 240/10 = 24
Dividend = (Divisor * Quotient) + Remainder
Dividend = (240 * 24) + 48 = 5808.
A |
AQUA-RAT | AQUA-RAT-39060 | # 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... | [
"8/21",
"7/11",
"5/27",
"11/32"
] | A | Total number of balls = 8+7+6 = 21
E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
n(E) = 8
P(E) = 8/21
Answer is A |
AQUA-RAT | AQUA-RAT-39061 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"7",
"4",
"6",
"2"
] | C | Explanation:
David and Moore complete half work in 3 days
=> they can complete whole work in 6 days
Answer: Option C |
AQUA-RAT | AQUA-RAT-39062 | 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... | [
"877 m",
"165 m",
"167 m",
"887 m"
] | B | Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 25)m = 375 m. Let the length of the platform be x meters. Then, (x + 375)/36 = 15
==> x + 375 = 540 ==> x
= 165 m.
Answer: B |
AQUA-RAT | AQUA-RAT-39063 | # Number of rectangles with odd area.
We have a $10\times 10$ square.
How many rectangles with odd area are on the picture?
I say lets choose a vertex first, there are $11\cdot11=121$ possibilities.
Now, choose odd width and side (left or right) and odd length and side (up or down). There are $5$ possibilities to eac... | [
"144",
"36",
"72",
"56"
] | C | Length of side 1= 8+1=9
Length of side 2= 7+1= 8
Area of rectangle= 9*8= 72
C is the answer |
AQUA-RAT | AQUA-RAT-39064 | dominion wrote:
1. A bag of 10 marbles contains 3 red marbles and 7 blue marbles. If two marbles are selected at random, what is the probability that at least one marble is blue?
scenario 1: 1 red, 1 blue
scenario 2: 2 blue
total possibility
10C2
(scenario 1 + scenario 2)/total possibilities = (3C1 x 7C1 +7C2)/10C2
... | [
"2/29",
"2/17",
"2/21",
"2/28"
] | C | Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 ... |
AQUA-RAT | AQUA-RAT-39065 | java
Title: Computing quantity-based discounts I'm a CS professor and provided this code as a small piece of a refactoring assignment:
private double getTotalPrice(int quantity, double itemPrice) {
if (quantity == 13) {
return itemPrice * 12; // Baker's dozen
}
else if (quantity >= 6) {
ret... | [
"the same as one 45 percent discount",
"the same as one 40 percent discount",
"the same as one 36 percent discount",
"the same as one 30 percent discount"
] | C | Say initial order = 100
Discount 20% = 20
Value = 100 - 20 = 80
Again discount 20% =80∗20100=16=80∗20100=16
Value = 80-16 = 64
Total discount = 20+16 = 36
Answer = C) the same as one 36 percent discount |
AQUA-RAT | AQUA-RAT-39066 | # A simple riddle related to addition of odd numbers
I'm not sure if this type of question can be asked here, but if it can then here goes:
Is it possible to get to 50 by adding 9 positive odd numbers? The odd numbers can be repeated, but they should all be positive numbers and all 9 numbers should be used.
PS : The... | [
"180",
"245",
"320",
"405"
] | D | reduce 1 - 90
5 - 15 - 25 - 35 - 45--55--65--75--85 are valid multiples. Add them --> 405
D |
AQUA-RAT | AQUA-RAT-39067 | Transcript
TimeTranscript
00:00 - 00:59so this is the question 1 ka manufacture compile data that the indicated mileage decrease in the number of the miles between driven between recommended serving increased the manufacturer use the equation Y is equal to minus one upon 200 X + 35 to model the data based on the infor... | [
"14",
"16",
"21",
"24"
] | D | I treat such problems as work ones.
Work=Rate*Time
Mileage(m)=Rate(mpg)*Gallons(g)
X gallons is a full tank
{462=RX
{336=(R-9)X solve for R, R=33
33-9=24 mpg
D |
AQUA-RAT | AQUA-RAT-39068 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"15 min",
"20 min",
"27.5 min",
"30 min"
] | D | Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min
ANSWER:D |
AQUA-RAT | AQUA-RAT-39069 | but x, y must satisfy the negative Pell equation x2 − 2y2 = −1.
nigiri sushi. and the thrust pressure, )
The original cube (1m sides) has a surface area to volume ratio of 6:1. {\displaystyle x^{3}+(-x)^{3}+n^{3}=n^{3}} The figure above shows a cube. (If I didn't remember, or if I hadn't been certain, I'd have grabbe... | [
"81 : 100",
"9 : 11",
"729 : 1331",
"27 : 121"
] | A | Ratio of the sides = ³√729 : ³√1000 = 9 : 10
Ratio of surface areas = 9^2 : 10^2 = 81 : 100
ANSWER:A |
AQUA-RAT | AQUA-RAT-39070 | 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$$ (from the initial 90... | [
"350 m",
"278 m",
"876 m",
"150 m"
] | A | Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 21) m
= 350 m.
Answer: A |
AQUA-RAT | AQUA-RAT-39071 | MHF Helper
Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.
1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0... | [
"5%",
"10%",
"60%",
"40%"
] | C | The complete round trip consists of driving to the service center and then back home again.
So, once the technician drives to the service center he/she has already competed 50% of the entire trip.
Since the technician completes a portion of the trip back home,the correct answer must be greater than 50%
Only one answer ... |
AQUA-RAT | AQUA-RAT-39072 | # Math Help - Annual Compounding Interest
1. ## Annual Compounding Interest
Jane has $6 and Sarah has$8. Over the next few years, Jane invests her money at 11%. Sarah invests her money at 8%. When they have the same amount of money, how much will they have? Assume annual compounding interest, and round to the nearest... | [
"s. 52500; Rs. 47500",
"s. 59375; Rs. 35625",
"s. 72500; Rs. 27500",
"s. 82500; Rs. 17500"
] | B | Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (95000 - x). Then,
(x * 9 * 1)/100 + [(95000 - x) * 11 * 1]/100 = (95000 * 39/4 * 1/100)
(9x + 1045000 - 11x)/100 = 39000/4 = 18525/2
x = 59375
Sum invested at 9% = Rs. 59375
Sum invested at 11% = Rs. (95000 - 59375) = Rs. 35625.
ANSWER:B |
AQUA-RAT | AQUA-RAT-39073 | Since 1000 = 999 + 1, 100 = 99 + 1, and 10 = 9 + 1, this equation can be rewritten
$$999 d_{1}+d_{1}+99 d_{2}+d_{2}+9 d_{3}+d_{3}+d_{4}=3 k$$
Rearranging gives
$$d_{1}+d_{2}+d_{3}+d_{4}=3 k-999 d_{1}-99 d_{2}-9 d_{3}$$
$$=3 k-3\left(333 d_{1}\right)-3\left(33 d_{2}\right)-3\left(3 d_{3}\right)$$
We can now factor ... | [
"0",
"1",
"2",
"8"
] | A | The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^5+s^4 will have the units digit of 9+1 = 10 as a units digit.
The answer is A. |
AQUA-RAT | AQUA-RAT-39074 | homework-and-exercises, special-relativity, inertial-frames, observers
But how much has John aged, according to Mike?
During t1, John was stationary according to Mike and therefore aged t1. During t2 + t2, John was moving at 0.5c, so aged
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"18",
"20",
"25",
"23"
] | C | Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 5 = 25 => x = 5
Deepak's age = 5x = 25 years.
Answer: C |
AQUA-RAT | AQUA-RAT-39075 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"10%",
"6%",
"15%",
"17%"
] | B | Let me try a simpler one.
Lets assume that candidate got 47% votes and total votes is 100.
Candidate won = 47
Remaining = 53
To get 50%, candidate requires 3 votes from 100 which is 3% and 3 votes from 53.
3/53 = .056= 5.6%
Which is approx 6%. Hence the answer is B. |
AQUA-RAT | AQUA-RAT-39076 | = 0 \\ a^7+ b^7 + c^7 = -7mk^2$$ Then your identity reads $$\left( -\frac{3m}{3} \right) \left( -\frac{7mk^2}{7} \right) = \left( -\frac{5mk}{5} \right)^2 \\ \left( -m \right) \left( -mk^2 \right) = (mk)^2$$
The following is multiple choice question (with options) to answer.
Find the value of c from (8)^3 x 9^3 ÷ 679... | [
"249.7",
"529.7",
"549.7",
"594.7"
] | C | Given Exp. =(8)^3 x 9^3 ÷ 679 = c
= 512 x 729 ÷ 679
= 549.7
C |
AQUA-RAT | AQUA-RAT-39077 | # When will train B catch up with train A?
Printable View
• January 27th 2010, 08:19 PM
bball20
When will train B catch up with train A?
Trains A & B are traveling in the same direction on a parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 5:15 PM. If tra... | [
"72 sec",
"210 sec",
"192 sec",
"252 sec"
] | B | Solution
Relative Speed = (46 - 40 ) Kmph
= 6 kmph
=(6 x 5 / 18)m/sec
= (30 / 18 ) m/sec
Time taken = (350 x 18 / 30) sec
= 210 sec.
Answer B |
AQUA-RAT | AQUA-RAT-39078 | ## Digit Problems
1. Use $$3,4,5,6,7,8$$ to make digits between 5,000 & 6,000.
2. 2, 3, 4, 5, 6, 7: 6-digit numbers not divisible by 5
3. 5, 6, 7, 8, 0: Five digit numbers divisible by 4.
4. Make 7-digit numbers using 3, 4, 5, 5, 3, 4, 5, 6, keeping odd digits at odd positions, without using digits more than its frequ... | [
"305",
"5",
"365",
"405"
] | B | 470, 472, 474, 476, and 478, so total 5. Hence Option B. |
AQUA-RAT | AQUA-RAT-39079 | 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 next number of the following sequence
10, 7, 12, 10, 14, __ ? | [
"13",
"14",
"15",
"16"
] | A | combine two series:
1st series is:10 12 14
10+2=12
12+2=14
14+2=16
2nd series is:7 10
means its 7+3=10
10+3=13
ANSWER:A |
AQUA-RAT | AQUA-RAT-39080 | • #### 1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
1. \begin{aligned} 120m^2 \end{aligned}
2. \begin{aligned} 130m^2 \end{aligned}
3. \begin{aligned} 140m^2 \end{aligned}
4. \begin{aligned} 150m^2 \end{aligned}
Explanation:
\begin{aligned}
\text... | [
"1350",
"277",
"299",
"266"
] | A | Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer:A |
AQUA-RAT | AQUA-RAT-39081 | permutations around a round table with labelled seats
Two men, Adam and Charles, and two women, Beth and Diana, sit at a table where there are seven places for them to sit down. Two people are sitting next to each other if they occupy consecutive chairs. A non-trivial rotation defines a different seating arrangement, ... | [
"A)160",
"B)170",
"C)190",
"D)15120"
] | D | 9p5 = 9 x 8 x 7 × 6 × 5 = 15120
Option 'D' |
AQUA-RAT | AQUA-RAT-39082 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"16 2/3%",
"16 2/8%",
"16 7/3%",
"16 5/3%"
] | A | 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A |
AQUA-RAT | AQUA-RAT-39083 | 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{... | [
"23",
"28",
"48",
"25"
] | D | Explanation:
H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.
Answer: D |
AQUA-RAT | AQUA-RAT-39084 | # If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n. Also find that term. - Mathematics
Sum
If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n. Also find that term.
#### Solution
Let the first term, common difference
A... | [
"2",
"9",
"1.8",
"1.7"
] | A | Explanation :
Jan 1 – S1 and S2 has n members. Till july 2nd, there are 6 more months, and hence 6 more additions.
In S1, b members are added each month. So after 6 months, S1 has n + 6b.
In S2, r members are multiplied each month. So after 6 months, S2 has n * r6.
After 6 months, both are same, hence
=> n + 6b = nr6. ... |
AQUA-RAT | AQUA-RAT-39085 | ### 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... | [
"1999",
"1900",
"19077",
"19055"
] | B | 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B |
AQUA-RAT | AQUA-RAT-39086 | # Placing m books on n shelves such that there is at least one book on each shelf
Given $m \ge n \ge 1$, how many ways are there to place m books on n shelves, such that there is at least one book on each shelf?
Placing the books on the shelves means that:
• we specify for each book the shelf on which this book is pl... | [
"4!",
"15!",
"16!",
"28!"
] | A | Solution
Since books A,B and C are arranged first and second, only books D, E,F and G will change order. Therefore it an arrangement problem involving 4 items and the number of different order is given by
4!
Answer A |
AQUA-RAT | AQUA-RAT-39087 | 18. freckles
so... notice that every term on top has a common factor of h and the denominator also has a common factor h
19. freckles
$f'(x)=\lim_{h \rightarrow 0} \frac{h(2ax+ah+b)}{h(1)}$
20. haleyelizabeth2017
Oh!
21. freckles
we can write as: $f'(x)=\lim_{h \rightarrow 0} \frac{h}{h} \cdot \frac{2ax+ah+b}{1}... | [
"270",
"300",
"299",
"322"
] | A | the numbers are (18 x 11) and (18 x 15).
Larger number = (18 x 15) = 270.
ANSWER :A |
AQUA-RAT | AQUA-RAT-39088 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"19:00",
"17:00",
"16:00",
"18:00"
] | A | Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 9:00 a.m and Pipe B at 10:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 10:00 a.m
Pool filled after 1 hour with both ... |
AQUA-RAT | AQUA-RAT-39089 | EZ as pi
Featured 5 months ago
$\text{males : females } = 6 : 5$
#### Explanation:
When working with averages (means), remember that we can add sums and numbers, but we cannot add averages.
(An exception would be if there were the same number of males and females - in this case we may add the averages and divide by... | [
"15 years, 17 years",
"11 years, 14 years",
"16 years, 20 years",
"10 years, 16 years"
] | B | 11,14
ANSWER:B |
AQUA-RAT | AQUA-RAT-39090 | Example $$\PageIndex{6}$$:
A student’s grade point average is the average of his grades in 30 courses. The grades are based on 100 possible points and are recorded as integers. Assume that, in each course, the instructor makes an error in grading of $$k$$ with probability $$|p/k|$$, where $$k = \pm1$$$$\pm2$$, $$\pm3$... | [
"A)78",
"B)82",
"C)96",
"D)91"
] | C | correct avg marks = 100+(10-50)/10
avg = 100-4 = 96
Answer is C |
AQUA-RAT | AQUA-RAT-39091 | Hello Matty R!
No, that doesn't mean anything, does it?
Hint: what will Bea's age be when Claire is as old as Dawn is now?
3. Feb 27, 2010
### HallsofIvy
Staff Emeritus
"When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea."
Claire will be as old as Dawn is no... | [
"25 years",
"30 years",
"35 years",
"40 years"
] | C | Sol.
Let their ages of x years and (x + 10) years respectively.
Then, (x + 10) - 15 = 2(x - 15)
⇔ x - 5 = 2x - 30
⇔ x = 25.
∴ Present age of the elder person = (x + 10)
= 35 years.
Answer C |
AQUA-RAT | AQUA-RAT-39092 | Thus the hands have been coincident 118 times after the starting position.
Counting the starting position, the answer is 119. But let's discount this, which is what I'm guessing is intended. Thus the answer is 118.
Assuming you want to include both 2pm and 4pm as times when the two hands line up, the answer is $119$.... | [
"21",
"20",
"12",
"26"
] | C | C
12
period = 65 minutes/60 minutes = 1.08.
The number of cycles per hour then = 1/period = 1/1.08 = .923.
The number of cycles in 24 hours, then = (0.923)(24) = 22.153. That's how you compute how many times the minute hand catches up the hour hand in 24 hours (round to 22) |
AQUA-RAT | AQUA-RAT-39093 | (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 $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"$ 40.",
"$ 50.",
"$ 60.",
"$ 70."
] | B | Solution:
Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
Answer B |
AQUA-RAT | AQUA-RAT-39094 | Lets assume like finding a pair for each man,
for the 1st guy -- can choose 1 from 5 women
for the 2nd guy -- can choose 1 from 4 women
.
.
for the 5th guy -- can choose 1 from 1 woman
so 5!
The following is multiple choice question (with options) to answer.
A committee has 3 men and 6 women. What are the number... | [
"127",
"60",
"882",
"272"
] | B | The number of ways to select two men and three women
= 3C₂ * ⁶C₃
= (3 *2 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 60
Answer: B |
AQUA-RAT | AQUA-RAT-39095 | # 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... | [
"200",
"2000",
"1500",
"400"
] | D | Total money after selling articles = 200*12 = 2400
cost price = 200*10 = 2000
profit = 400
correct option is D |
AQUA-RAT | AQUA-RAT-39096 | Originally Posted by dumluck
That's facinating so $1 + 3 + 5 + 7 + 9 + 11 = 6^2?$
• Mar 5th 2011, 10:31 AM
dumluck
Quote:
Originally Posted by HallsofIvy
The sum of all integers from 1 to n is, as you noted in your first post, $\frac{n(n+1)}{2}$. Notice that the sum of even numbers, 2+ 4+ 6+ 8+ ...= 2(1+ 2+ 3+ 4+ ...... | [
" 1.8",
" 4",
" 6",
" 18"
] | B | CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then
Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(18) = [(6+18)/2]*7 = 84
h(10) = (6+10)/2]*3 = 24
h(18)/h(10) = (84) / (24) ~ 4
Answer : B |
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