source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-39397 | (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 ... | [
"20",
"22",
"24",
"26"
] | B | Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what... |
AQUA-RAT | AQUA-RAT-39398 | 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... | [
"Rs. 700",
"Rs. 690",
"Rs. 650",
"Rs. 698"
] | D | Explanation:
Simple Interest (SI) for 1 year = 854-815 = 39
Simple Interest (SI) for 3 years = 39 × 3 = 117
Principal = 815 - 117 = Rs.698
Answer: Option D |
AQUA-RAT | AQUA-RAT-39399 | 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... | [
"270 m",
"245 m",
"235 m",
"220 m"
] | C | Explanation:
Assume the length of the bridge = x meter
Total distance covered = 140+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (140+x)/30 m/s
=> 45 × (10/36) = (140+x)/30
=> 45 × 10 × 30 /36 = 140+x
=> 45 × 10 × 10 / 12 = 140+x
=> 15 × 10 × 10 / 4 = 140+x
=> 15 × 25 = 140+... |
AQUA-RAT | AQUA-RAT-39400 | Lastly, the area of $$\triangle ABC$$ gives us the following identity:
$24 = \frac{1}{2} \cdot (3y) \cdot [ 2x\cdot \sin(A) ]$
which implies the area of $$\triangle ADE$$ is
$\frac{1}{2}\cdot x\cdot y \cdot \sin(A) = 4$
It should be fairly straightforward to deduce that the area of $$\triangle DEF$$ is
$24 - (4+4+9) = ... | [
" 1/9",
" 1/8",
" 1/6",
" 1/5"
] | A | If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore
Area of ABC is 1/2*12*12 (Height of ABC is the y coordinate of the third point (8,12))
similarly Area of XYZ is 1/2*4*4
dividing area of XYZ with that of ABC gives C= 1/9.A |
AQUA-RAT | AQUA-RAT-39401 | 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, ... | [
"1250",
"1640",
"1240",
"1680"
] | D | 8p4 = 8 x 7 x 6 × 5 = 1680
D) |
AQUA-RAT | AQUA-RAT-39402 | 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... | [
"228",
"267",
"200",
"750"
] | D | Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750 .Answer: D |
AQUA-RAT | AQUA-RAT-39403 | # Remainder on division with $22$
What is the remainder obtained when $$14^{16}$$ is divided with $$22$$?
Is there a general method for this, without using number theory? I wish to solve this question using binomial theorem only - maybe expressing the numerator as a summation in which most terms are divisible by $$22... | [
"6",
"7",
"8",
"9"
] | A | L 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A |
AQUA-RAT | AQUA-RAT-39404 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"1/8",
"1/3",
"3/6",
"3/8"
] | D | A's one day's work = 1/20
B's one day's work = 1/40
(A + B)'s one day's work = 1/20 + 1/40 = 3/40
The part of the work completed in 5 days = 5 (3/40) = 3/8.
Answer:D |
AQUA-RAT | AQUA-RAT-39405 | # Remainder on division with $22$
What is the remainder obtained when $$14^{16}$$ is divided with $$22$$?
Is there a general method for this, without using number theory? I wish to solve this question using binomial theorem only - maybe expressing the numerator as a summation in which most terms are divisible by $$22... | [
"797",
"254",
"597",
"997"
] | B | According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 18* 14 + 2 = 254 correc answer B |
AQUA-RAT | AQUA-RAT-39406 | pressure, vacuum, air
Title: How to understand air pressure against a hand pump? Imagine this little though experiment with me for a moment.
A piston sort-of contraption - like a bicycle pump, but without any nozzle to push air out of. One foot tall, one inch width/depth. Lets say the pump is completely bottomed out. ... | [
" 2",
" 3",
" 4",
" 5"
] | D | My approach is to find more or less good number and plug in. Lets take 90 as the total volume of an air, and the question asks after how many stokes there will be less than 0,9 air in a tank, if each stroke takes 2/3 of an air.
So after he1 strokethe volume will be 30 (90-60=30), and so on
2 stroke- 30-20=10
3 stroke- ... |
AQUA-RAT | AQUA-RAT-39407 | 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... | [
"50 yards per minute",
"40 yards per minute",
"60 yards per minute",
"55 yards per minute"
] | A | Suppose x is the distance travelled by the man in 10 min upstream.
Then
x/(v-u) = 10 where v is man's speed and u is river speed)
total time taken to swim by the man upstream and down stream is equal to the time taken by the hat to travel 1000 yards with the speed of river
1000/u = 10 + (x+1000)/(u+v)
now substitute x ... |
AQUA-RAT | AQUA-RAT-39408 | Suppose the slower car stands still for one hour. How often will the faster car pass it? Then stop the faster car and start the slower car for another hour. How often will the slow car pass the stopped car? Add.
Consider alternative case when cars complete exactly $4$ and $8$ rounds. It's easily seen that the number o... | [
"87",
"138",
"192",
"83"
] | C | Explanation:
48(x + 1) = 64x
X = 3
48 * 4 = 192 km
Answer: Option C |
AQUA-RAT | AQUA-RAT-39409 | ## A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners
##### This topic has expert replies
Legendary Member
Posts: 2898
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:5 members
### A number of people shared a meal, intending to divide the cost evenl... | [
"32.84",
"22.84",
"30.58",
"24.84"
] | C | dinner bill of 5 person = 139 + 10% tip
so,
10% of 139 = (139*10)/100 = 13.9
So, the actual total amount = 139+13.9 = $ 152.9
so per head bill = 152.9/5 = $ 30.58
ANSWER:C |
AQUA-RAT | AQUA-RAT-39410 | So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed.
• it means that if they are covering 135km each our then they would be meet together in 135x... | [
"10.50 a.m.",
"11.20 a.m.",
"10.30 a.m.",
"11.40 a.m."
] | B | D = 170 – 20 = 150
RS = 20 + 25 = 45
T = 150/45 = 3 1/3 hours
8 a.m. + 3 hrs 20 min = 11.20 a.m.
ANSWER:B |
AQUA-RAT | AQUA-RAT-39411 | 321
a) f(x)=abs(x), g(x)=-x
b) f(x)=cos(x), g(x)=x+2pi
6. ### csprof2000
287
Good point.
I guess then that my argument only works for functions which don't have an inverse where Domain(inv f) = Range(f). This, naturally, precludes functions such as abs(x) and cos(x)...
So I guess more though will have to be put int... | [
"30x^3-12x+52",
"11x^2-12x+44",
"8x^3-8x+32",
"30x^3+4x+4"
] | A | g(f(x)) = 6(f(x)) +4 = 6(5x^3- 2x+8) + 4 = 30x^3-12x+52 =>A |
AQUA-RAT | AQUA-RAT-39412 | Difference in angular distance travelled by the minute hand and the hour hand in one minute is thus $6-\dfrac{1}{2} = \dfrac{11}{2}$ degrees. So, on a full rotation $(360^\circ)$, any similar event between them will be repeated every $\dfrac{360}{(11/2} = 65 \dfrac{5}{11}$ minutes.
In twenty four hours, i.e. $24 \time... | [
"5.30 a.m",
"6.42 a.m",
"7.55 a.m",
"7.42 a.m"
] | D | Sol.
Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two
Relative speed of A and B = (6-1) = 5 rounds per hour.
Time taken to complete one round at this speed = 1/5 hr = 12 min.
Answer D |
AQUA-RAT | AQUA-RAT-39413 | \begin{align*} a_1&=1+b_0\\ a_2&=1+b_0+b_1\\ a_3&=1+b_0+b_1+b_2\\ a_4&=1+b_0+b_1+b_2+b_3 \end{align*}
(We don’t need $b_4$ to reconstruct $A$; it’s there to make the sum a known constant.)
Thus, there is a bijection between $4$-element subsets $A$ of $\{1,\dots,10\}$ satisfying the condition that no two members are c... | [
"35",
"48",
"69",
"70"
] | D | 5*a1 + 7*b1 = t
5*a2 + 7*b2 = t
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding ... |
AQUA-RAT | AQUA-RAT-39414 | => 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... | [
"13x /15",
"15x/15",
"7x/15",
"2x/30"
] | A | 30 days- X lines
80% of 30
24 days; 0.2X lines
Remaining 6 days:
0.8X lines
Need to find out for last 14 days;
We know the number of lines for last 6 days: 0.8X
How about 8 days before that;
24 days- 0.2X
1 day - 0.2X/24 lines
8 days - (0.2X/24)*8 lines = (1/15)X lines
Total number of lines in last 14 days
(1/15)x + 0.... |
AQUA-RAT | AQUA-RAT-39415 | 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} ... | [
"74",
"78",
"86",
"126"
] | D | Divisor = (6 * 3) + 12 = 30
5 * Quotient = 30
Quotient = 6.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 6) + 6 = 126.
D) |
AQUA-RAT | AQUA-RAT-39416 | python, beginner, python-3.x
Title: Flooring cost calculator I've made a small program that calculates the cost of flooring for a given area based on the price per sqft and total sqft. I have only been programming for a few days now so I am sure that there are some things I could be doing better.
from decimal import *... | [
"Rs. 15000",
"Rs. 15550",
"Rs. 15600",
"Rs. 20625"
] | D | Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1000 × 20.625) = 20625. Answer D |
AQUA-RAT | AQUA-RAT-39417 | When we add $10$ red, we end up with $4k+10$ red. The blues remain unchanged at $7k$.
So the new proportion is $(4k+10): 7k$. We are told that the proportion $(4k+10): 7k$ is $6:7$. So $$\frac{4k+10}{7k}=\dfrac{6}{7}.$$ If we multiply through by $7k$, we get $4k+10=6k$, and therefore $k=5$. It follows that there are $... | [
"8",
"7.5",
"6.5",
"5"
] | D | Solution: Let x be added to each term.
According to question,
(7+x)/(11+x) = 3/4;
Or, 33+3x = 28+4x;
Or, x = 5.
Answer: Option D |
AQUA-RAT | AQUA-RAT-39418 | For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.
Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.
We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, ... | [
"270",
"250",
"245",
"320"
] | A | Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
ANSWER A |
AQUA-RAT | AQUA-RAT-39419 | homework-and-exercises, statics
My way to solve this:
since ladder is not moving
Torque on the ladder
$$ -\frac{mgL}{2}\sin\theta-\mu N_{f}L\cos\theta+N_{f}L\sin\theta=0$$
Horizontal forces
$$ N_{w}-f_{f}=0$$
Vertical forces
$$ N_{f}+f_{w}-mg=0$$
where $N_{f}$ and $N_{w}$ is normal forcé due to floor and Wall, $f_{w... | [
"4",
"10",
"18",
"19"
] | B | 14^2-9^2=115
it means that the height is equal to 10.72.
since the top of the ladder slips down 1 feet, then the height of the wall =10.72-1=9.72
the bottom =sqrt(14^2-9.72^2)=sqrt(196-94.47)=10.07~=10
ans is B |
AQUA-RAT | AQUA-RAT-39420 | 2. World War 1 started July 28, 1914. What day of the week was it?
3. Little Boy is the name of the atomic bomb dropped in Hiroshima, Japan on August 6, 1945. What day of the week that happened?
4. Marie Skłodowska-Curie is the real name of Polish Marie Curie, the first woman who won Nobel Prize in both Chemistry and... | [
"Monday",
"Tuesday",
"Saturday",
"Friday"
] | B | Explanation:
1 Jan 1901 = (1900 years + 1st Jan 1901)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601-1900
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
(As we can reduce perfect multiple... |
AQUA-RAT | AQUA-RAT-39421 | x 0.6
=
y 2.6
Could somebody check these please?
Thanks!
they don't work, show us the work that you did c00ky and we can show you where you went wrong
note: rather than using latex, you can show us matrixes like this:
|2 3 5|
|3 4 5|
11. I mixed the 3 and 4 the wrong way around earlier on.
I now have x = -2 and y... | [
"-0.71",
"-2.13",
"1.07",
"1.71"
] | B | Dove straight into calculation
((-1.9)(0.6) – (2.6)(1.2))/2.0 = -2.13
Answer B |
AQUA-RAT | AQUA-RAT-39422 | # 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. 27,000",
"Rs. 26,000",
"Rs. 30,000",
"Rs. 36,000"
] | B | 30,000 *12=45,000*8
1:1
Madhu's share=1/2*52,000
i.e. Rs. 26,000
ANSWER:B |
AQUA-RAT | AQUA-RAT-39423 | # 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... | [
"56",
"37",
"38",
"39"
] | A | ratio of 36% profit cars to 9% profit cars = 8:19
so no. of cars sold at 36% profit = 189*8/27= 56 cars
ANSWER:A |
AQUA-RAT | AQUA-RAT-39424 | 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... | [
"1/3",
"1/2",
"1/4",
"1/5"
] | B | Let the time when all three were working together be t hours. Then:
Tom worked for t+4 hour and has done 1/10*(t+4) part of the job;
Peter worked for t+2 hour and has done 1/5*(t+2) part of the job;
John worked for t hours and has done 1/2*t part of the job:
1/10*(t+4)+1/5*(t+2)+1/2*t=1 --> multiply by 10 --> (t+4)+(2t... |
AQUA-RAT | AQUA-RAT-39425 | 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 group consists of 5 men, 5 women and 3 children. In ... | [
"300 ways",
"400 ways",
"500 ways",
"360 ways"
] | A | Two men, two women and one child can be selected in 5C₂ * 5C2 * 3C₁ ways
5*4/2*1*5*4/2*1*3
= 300 ways
Answer : A |
AQUA-RAT | AQUA-RAT-39426 | # 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... | [
"22",
"98",
"92",
"72"
] | C | Explanation:
Let be the price of cloak is = x
According to the Question he should get 7/12th of 100 and 7/12th of cloak.
712(100)+712(x)=20+x712(100)+712(x)=20+x
⇒ x = 92.
Answer: C |
AQUA-RAT | AQUA-RAT-39427 | physical-chemistry, thermodynamics, phase, gas-phase-chemistry, liquids
Title: Liquification of ideal solution of two liquids from vapor phase A and B form an ideal solution. In a cylinder piston arrangement, $\pu{2.0 mol}$ of vapor of liquid A and $\pu{3 mol}$ of vapor of liquid B are taken at $\pu{300 torr}$ and $T~... | [
"4/3",
"5/3",
"7/3",
"8/3"
] | D | An alternate to the alligation method is the more direct/algebraic method:
Let x be the amount of turpentine to be added.
New total amount of turpentine = 4+x
Total amount of paint = 4
New total = 4+4+x=8+x
Final ratio required (for turpentine) = 5/(5+3)=5/8
Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.
D ... |
AQUA-RAT | AQUA-RAT-39428 | per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. What is its speed? 4) A car goes 250 km in 4 hours. The total time is 5 seconds, so t = 5. 4. Aptitude Questions and Answers. Learn how teachers can make BrainPOP-style assessments by ... | [
"125 km/hr",
"678 km/hr",
"782 km/hr",
"789 km/hr"
] | A | Distance = (50 x 5) =250 km.
Speed = Distance/Time
Speed = 250/2 = 125 kmph
Answer : A |
AQUA-RAT | AQUA-RAT-39429 | python, python-3.x, calculator
Title: Taxi fare calculator, trip recorder, and fuel calculator I solved this practice problem in preparation for school exams.
The owner of a taxi company wants a system that calculates how much money his taxis take in one day.
Write and test a program for the owner.
Your program must... | [
"$3.15",
"$4.5",
"$4.80",
"$5.05"
] | B | Let the fixed charge of Jim’s Taxi Service = 2.25 $
and charge per 2/5 mile(.4 mile) = .25$
Total charge for a trip of 3.6 miles = 2.25 + (3.6/.4) * .25
= 2.25 + 9*.25
= 4.5 $
Answer B |
AQUA-RAT | AQUA-RAT-39430 | ## 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... | [
"7:22",
"7:24",
"7:27",
"7:30"
] | D | 7:27minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is D.
Answer: D. |
AQUA-RAT | AQUA-RAT-39431 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"5 km/h",
"8 km/h",
"10 km/h",
"15 km/h"
] | D | Let A's speed be X km/hr.
Then, 90/x - 90/2x = 3
6x = 90
x = 15 km/hr.
Answer : D. |
AQUA-RAT | AQUA-RAT-39432 | +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... | [
"84",
"92",
"94",
"98"
] | C | 1
1 × 2 + 2 = 4
4 × 2 + 2 = 10
10 × 2 + 2 = 22
22 × 2 + 2 = 46
46 × 2 + 2 = 94 C |
AQUA-RAT | AQUA-RAT-39433 | newtonian-mechanics, rotational-dynamics, estimation, stability
Title: Human Lean Equation For a medical experiment I am doing, I need an equation to find the angle at which someone will lean before falling. I am not mathematically inclined in terms of advanced stuff, I am more so of a trigonometry person.
I assume fa... | [
"13",
"20",
"30",
"43"
] | A | His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.20-1) = 13
A |
AQUA-RAT | AQUA-RAT-39434 | 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 ... | [
"8.2",
"4.2",
"6.1",
"7.2"
] | D | Distance =600 metre =0.6 km
Time = 5 min = 1/12 hr
speed = dist/time = 0.6/(1/2) = 7.2 km/hr
ANSWER D |
AQUA-RAT | AQUA-RAT-39435 | Sum the two parts gives $\pi/3$.
• Can you explain to why the bound of $\rho$ is between $0 \: \text{and} \:1$ in this case..? – misheekoh Apr 5 '17 at 4:41
• @misheekoh because you are integrating over the (half) unit sphere's volume, to cover this volume the radius has to change from $0$ to $1$. – Taozi Apr 5 '17 at... | [
"50%",
"60%",
"75%",
"80%"
] | C | Let the volume of sphere PP be 64 parts.
Therefore volume of sphere QQ
=64−3764%=64−3764% of 6464
=64−37=27=64−37=27 parts.
The volume of RR
=27−1927×27=27−1927×27
=27−19=8=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2=P:Q:R=4:3:2
The surface area will be 16:9:516:9:5
Surface area... |
AQUA-RAT | AQUA-RAT-39436 | Question
# In measuring the length and breadth of a rectangle, errors of 5% and 3% in excess, respectively, are made. The error percent in the calculated area is
A
7.15%
B
6.25%
C
8.15%
D
8.35%
Solution
## The correct option is C 8.15% Let actual length and breadth of the rectangle be 'l' and 'b' respectivel... | [
"4.04%",
"4.14%",
"4.16%",
"4.20%"
] | A | 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
A) |
AQUA-RAT | AQUA-RAT-39437 | homework-and-exercises, pressure, fluid-statics
Title: Which tank fills up first? Which tank would fill first. My first guess was 3 and 4 simultaneously due to Pascal's Law of pressure distribution. Then tank 2 and then 1. Could you please help? This is my first question ever on Stack Exchange. Tank 1 will to the lev... | [
"42 minutes",
"14 minutes",
"39 minutes",
"40 minutes 20 seconds"
] | A | In one cycle they fill 40+30-20 = 50 liters
700 = 50*n => n = 14
here n = number of cycles.
total time = 14*3 = 42 as in one cycle there are 3 minutes.
thus 42 minutes
ANSWER:A |
AQUA-RAT | AQUA-RAT-39438 | # 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... | [
"I,II only",
"I,III only",
"I only",
"III only"
] | D | If x is divisible by 2,7 means it will be = or > 14, 28,42 etc...
That are not divisible by 60, 32.
So, the answer is D |
AQUA-RAT | AQUA-RAT-39439 | # 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... | [
"17%",
"19%",
"18%",
"21.6%"
] | D | Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 66900
Profit(%) = (66900 - 55000)/55000 * 100
= 21.6%
Answer: D |
AQUA-RAT | AQUA-RAT-39440 | 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... | [
"4:5",
"4:3",
"4:6",
"4:9"
] | C | Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √36 = 4:6
Answer:C |
AQUA-RAT | AQUA-RAT-39441 | (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 ... | [
"190",
"200",
"210",
"220"
] | B | Let x be the amount of pears that she sold.
Then she poached 0.9x.
Then she canned 1.3*0.9x=1.17x.
The total amount of pears is x+0.9x+1.17x=3.07x
The fraction of pears that she sold is 1/3.07=100/307.
The number of pears she sold is (100/307)*614=200.
The answer is B. |
AQUA-RAT | AQUA-RAT-39442 | the largest and smallest integers in the group. This method should take three decimal arguments, and return the smallest of the three. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. It is similar to modulus – ‘%’ operator of C/C++ language. Note that this is not... | [
"67",
"71",
"73",
"21"
] | A | The second smallest prime number is 67.
A) |
AQUA-RAT | AQUA-RAT-39443 | 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... | [
"1/32",
"1/16",
"1/8",
"1/64"
] | D | The length of cube N = 1;
The length of cube M = 4;
The ratio of the volume of cube N to the volume of cube M = 1^3/4^3 = 1/64
Answer : D |
AQUA-RAT | AQUA-RAT-39444 | For some reason I find it easier to think in terms of letters of a word being rearranged, and your problem is equivalent to asking how many permutations there are of the word YYYYBBBBB.
The formula for counting permutations of words with repeated letters (whose reasoning has been described by Noldorin) gives us the co... | [
"7!/(2!)2 3!",
"8!/(2!)2 8!",
"8!/(8!)2 3!",
"8!/(2!)2 3!"
] | D | n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'REMEMBER' consists of 8 letters of which there are 2R's, 3E's, 2M's and 1B.
Number of arrangements = 8!/(2!)2 3!
Answer: D |
AQUA-RAT | AQUA-RAT-39445 | 80&4352803871250866057941284067804134&18,17,27,27,29,30\\ 81&11395788481298729007027429355459050&18,17,27,29,29,30\\ 82&29834561572649264127826347038980028&18,17,29,29,29,30\\ 83&78107896236653244353987095675034922&18,17,29,29,29,32\\ 84&204489127137313012297066889013936544&18,17,29,29,31,32\\ 85&5353594851752965663947... | [
"divisible by 3 but not by 11",
"divisible by 11 but not by3",
"divisible by both 3 and 11",
"neither divisible by 3 nor by 11."
] | D | Sum of digits= 35 and so it is not divisible by 3.
(Sum of digits at odd places)- (Sum of digits at even places)= 19-16=3, not divisible by 11.
So, the given number is neither divided by 3 nor by 11.
ANSWER:D |
AQUA-RAT | AQUA-RAT-39446 | ### Show Tags
18 Feb 2015, 07:51
1
Using smart numbers:
Jennifer Purchases watches for $5: B=5 Markup of 100%; now selling for$10: x=10
She sells 5 watches: N=5
Her total profit will be (N*x)-(B*N)
(5*10)-(5*5)= 25
T=25
Now using the variables we must look at the answer choices that will solve for the % markup of t... | [
"0.945x",
"0.985x",
"0.995x",
"1.05x"
] | A | The price at the end is 0.9(1.05x)=0.945x
The answer is A. |
AQUA-RAT | AQUA-RAT-39447 | # 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... | [
"8% and 8 years",
"6% and 6 years",
"10% and 10 years",
"6 % and 6 years"
] | D | 9â„25 P = P×R×R/100
⇒ R2 = 900â„25 ⇒ R^2 = 36 R= 6
Also, time = 6 years
Answer D |
AQUA-RAT | AQUA-RAT-39448 | Then, in any case $(a-b)^2=8$
• -1.This is a low grade method. – N.S.JOHN Apr 17 '16 at 10:42
$$a+b=2$$
$$\implies(a+b)^2=4$$
$$\implies a^2+b^2+2ab=4$$
$$\implies2ab=-2$$
Also,
$$(a-b)^2=a^2+b^2-2ab$$
$$6-(-2)=6+2=8$$(by substituting $a^2+b^2=6$ and $2ab=-2$)
The following is multiple choice question (with op... | [
"A is larger than B by 2^64 times",
"B is larger than A by 1",
"A is larger than B by 1",
"A is equal to B"
] | C | lets say A : 2^4=16 , B: 2^3+2^2+2^1+2^0 = 15 so A is larger than B by 1 always
ANSWER:C |
AQUA-RAT | AQUA-RAT-39449 | 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 ... | [
"Rs.10000",
"Rs.10800",
"Rs.10500",
"Rs.11000"
] | A | Let Z share be ‘a’ then
Y = a + Rs.6000 [as X investment is Rs.10000 more than Z, and Rs.4000 more than Y, then Y share more than Z by Rs.10000 – Rs.4000 = Rs.6000]
X = a + Rs.10000.
X + Y + Z = 3a + 16000 = Rs.106000.
3a = 106000 – 16000 = Rs.90000.
a = 90000 / 3 = Rs.30000.
therefore Z investment = Rs.30000.
Y = Rs.3... |
AQUA-RAT | AQUA-RAT-39450 | Notice carefully, the sign of the net increase is negative, clearly indicating the after the successive decrease the value of the original number, decreased instead of increasing. And what was the magnitude??? Right 28%. The net decrease is 28%.
So, before we use this approach to give you an official answer for the ab... | [
"no change",
"decreases by 12.5%",
"increases by 12.5%",
"increases by 10%"
] | C | Explanation :
Reduction of price = (100 -10)% = 90% = 0.9
Increase of sale = (100+25)% = 125% = 1.25
Total effect = 0.90X 1.25 = 112.5%, Increases by 12.5%
Answer : C |
AQUA-RAT | AQUA-RAT-39451 | Spoiler:
The middle number is the average of the other two.
$\frac{47+63}{2} \:=\:55,\quad \frac{85+99}{2} \:=\:92,\quad \frac{73+25}{2} \:=\:{\color{red}49}$
3. ## Re: Math puzzles questions?
Originally Posted by amrithaa
1. What number should replace the question mark?
Each row is 8 times the immediate row above.... | [
"34",
"27",
"25",
"46"
] | C | C
25
There are two alternate sequences: start at 10 and add 3, 5, 7;
start at 50 and deduct 5, 7, 9. |
AQUA-RAT | AQUA-RAT-39452 | 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... | [
"42",
"36",
"108",
"120"
] | C | Explanation:
Distance covered = 120+120 = 240 m
Time = 4 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/4 = 60 m/s
Speed of each train = v = 60/2 = 30 m/s
= 30×36/10 km/hr = 108 km/hr
Answer: Option C |
AQUA-RAT | AQUA-RAT-39453 | Examveda
# In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver... | [
"322",
"340",
"333",
"327"
] | D | locals from Arts = 50% of 400 = 200
locals from Science = 25% of 100 = 25
locals from Commerce = 85% of 120 = 102
total locals = 200+25+102 = 327
D |
AQUA-RAT | AQUA-RAT-39454 | # Probability based on a percentage
We have a group of 15 people, 7 men and 8 women.
Randomly selecting 5 people, what's the probability to pick 3 men and 2 women? What's the probability to pick at least 1 man?
I tried solving the first question like this: $${7 \choose 3} = \frac{7!}{(7-3)!3!} = 35$$ and $${8 \choos... | [
"1/3",
"2/5",
"1/2",
"3/5"
] | D | probability = Desired Outcomes/Total Outcomes
Event = Selection of 3 employees to assign office from 5 such that 2 are men and 1 is woman
Total Outcomes = Selection of any 3 employees from 5 employees = 5 C 3 = 10
Desired Outcomes = Selection of 2 Men from 3 Men AND selection of 1 woman from 2 Women. = (3 C 2) * (2 C 1... |
AQUA-RAT | AQUA-RAT-39455 | ## 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... | [
"4/9",
"2/3",
"3/4",
"5/6"
] | A | 2/3 ---- 12
? ----- 8 ==> 4/9
ANSWER A |
AQUA-RAT | AQUA-RAT-39456 | 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... | [
"2%",
"4%",
"5%",
"8%"
] | D | Let List price of an item = 100
Discount on each item = 10%
Discounted price of an item = .9*100 = 90
If they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%
Originally if 10 items were sold in a month , with the new discount 12 items wi... |
AQUA-RAT | AQUA-RAT-39457 | # 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... | [
"13000",
"27767",
"16688",
"26678"
] | A | Let the CP be Rs. x.
Had he offered 22% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 22/100(18000) = Rs. 14040
=> 1.08x = 14040
=> x = 13000
\Answer: A |
AQUA-RAT | AQUA-RAT-39458 | Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have
48(35) = 22(38) + 26x
1680 = 836 + 26x
26x = 844
x = 844/26
x = 32 12/26 ≈ 32.5
_________________
Scott Woodbury-Stewart
Founder and CEO
GMAT Quant Self-Study Course
50... | [
"9 years",
"12 years",
"60 years",
"70 years"
] | D | Explanation:
Let the age of three persons be x, 5x, 7x
= 13x/3 = 52
x= 12 years
Answer: Option D |
AQUA-RAT | AQUA-RAT-39459 | 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... | [
"777.4",
"877.4",
"577.4",
"477.4"
] | B | Let the costs of each kg of apples and each kg of rice be Rs.a and Rs.r respectively.
10a = 24r and 6 * 20.50 = 2r
a = 12/5 r and r = 61.5
a = 147.6
Required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5
= 590.4 + 184.5 + 102.5 = Rs.877.40
Answer: B |
AQUA-RAT | AQUA-RAT-39460 | Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day... | [
"36",
"42",
"28",
"54"
] | C | A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/21
= 3+1/3x = 4/3x = 1/21
x = 21*4/3 = 28
ANSWER:C |
AQUA-RAT | AQUA-RAT-39461 | "Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4959 Location: Canada GMAT 1: 770 Q49 V46 When a positive integer n is divided by 5... | [
"0",
"1",
"2",
"3"
] | B | n = 5x+3, for some integer x
(n+3)^2=(5x+6)^2=5y+36, for some integer y
When we divide this by 5, the remainder is 1.
The answer is B. |
AQUA-RAT | AQUA-RAT-39462 | # In how many ways can 3 distinct teams of 11 players be formed with 33 men?
Problem:
In how many ways can 3 distinct teams of 11 players be formed with 33 men? Note: there are 33 distinct men.
The problem is similar to this one: How many distinct football teams of 11 players can be formed with 33 men?
Fist, I thou... | [
"A)6",
"B)7",
"C)8",
"D)9"
] | D | 126/14=9 plus remainder.
The answer is D. |
AQUA-RAT | AQUA-RAT-39463 | ### Show Tags
16 Jun 2018, 09:16
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?
1) The average of the prices of all of the shirts and sweaters that the store sold during the sale wa... | [
"297",
"272",
"342",
"762"
] | B | 400*(80/100)*(85/100)
= 272
Answer: B |
AQUA-RAT | AQUA-RAT-39464 | the number of committees that exist where the man and women serve together is given by,
$$\begin{pmatrix} 1 \\ 1 \end{pmatrix} \begin{pmatrix} 5 \\ 2 \end{pmatrix} \begin{pmatrix} 1 \\ 1 \end{pmatrix} \begin{pmatrix} 7 \\ 2 \end{pmatrix} = 210$$
so the total number of committees in this case amounts to,
$$1120 - 210... | [
"11760",
"266",
"5040",
"3000"
] | A | Req no of ways = 8C5 * 10C6
=11760
ANSWER A |
AQUA-RAT | AQUA-RAT-39465 | 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... | [
"18 1/2 days",
"17 1/2 days",
"19 1/2 days",
"14 1/4 days"
] | A | P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 14 days, which means Q can do the work in 48 days.
Hence, P can do the work in 18 1/2 days.
Answer:A |
AQUA-RAT | AQUA-RAT-39466 | # 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... | [
"$878",
"$880",
"$882",
"$884"
] | C | 1.05*1.05*800=$882
The answer is C. |
AQUA-RAT | AQUA-RAT-39467 | 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... | [
"648",
"432",
"23",
"2 to the power(23)-1"
] | C | Since bags are different so it should be 9+8+6=23
ANSWER:C |
AQUA-RAT | AQUA-RAT-39468 | ## 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... | [
"152",
"125",
"225",
"325"
] | B | Here the repetition of digits allowed. The unit place of the number can be filled in by any of the given numbers in 5 ways. Simillarly each one of the ten's and the hundred's place can be filled in 5 ways. Therefor the total number of required numbers =5*5*5 =125 Answer : B |
AQUA-RAT | AQUA-RAT-39469 | # 2010 AMC 10B Problems/Problem 25
## Problem
Let $a > 0$, and let $P(x)$ be a polynomial with integer coefficients such that
$P(1) = P(3) = P(5) = P(7) = a$, and
$P(2) = P(4) = P(6) = P(8) = -a$.
What is the smallest possible value of $a$?
$\textbf{(A)}\ 105 \qquad \textbf{(B)}\ 315 \qquad \textbf{(C)}\ 945 \qqua... | [
"5",
"0",
"-8",
"-3"
] | C | #p# = ap^3 + bp - 1
#-5# = 6
putting p = -5 in above equation
-125a -(5b +1) = 6 or
#-5# = (125a+5b+1) = -6
therefore 125a+5b = -7 .....(1
now putting p = 5
#5# = 125 a+5b - 1
using equation 1(125a+5b = -7)
#5# = -7-1 = -8
hence C |
AQUA-RAT | AQUA-RAT-39470 | # 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... | [
"81.6",
"81.7",
"81.0",
"281.6"
] | A | SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6.Answer: A |
AQUA-RAT | AQUA-RAT-39471 | of a circle and therefore its area is a fraction of the area of the whole circle. com Area and Perimeter of Circle and Semi-Circle Perimeter. 1) A circle has a radius of 5 cm. Area of rectangle = 4 × 8 = 32 m² A circle of radius 8 cm is cut into 6 parts of equal size, as shown in the diagram. A button is made in the sh... | [
"3.34 sq m",
"3.38 sq m",
"3.24 sq m",
"3.36 sq m"
] | A | Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4)
= 53.38/16
= 3.34 sq m
Answer:A |
AQUA-RAT | AQUA-RAT-39472 | How do you solve this?
There is this kind of question in our test and I don't know how will I do it.
You're working in a company. Your starting income is 5000. Every year, the income will increase by 5%. What is your total income on your 25th year in the company?
Related Precalculus Mathematics Homework Help News on ... | [
"15 years",
"16 years",
"17 years",
"18 years"
] | D | if initial annual gross salary = Rs. 450000/-
check when
450000+25000*n = 450*(1+4/100)^n
After 18 years
ANSWER:D |
AQUA-RAT | AQUA-RAT-39473 | $7|61$ gives $61=7\cdot 8 +5$
He would have 5 cows left over. So 61 can't be an answer
5. Hello, swimalot!
A cowboy was asked how many cows were on the ranch.
He replied that he was unsure, but he knew that when he counted them
by twos, threes, fours, fives, or sixes, he always had one left over.
When counted by sev... | [
"33",
"37",
"41",
"45"
] | D | 5/7*P are ponies with horseshoes, so P is a multiple of 7.
2/3*5/7*P = 10/21*P are Icelandic ponies with horseshoes, so P is a multiple of 21.
The minimum value of P is 21. Then H = P+3 = 24.
The minimum number of horses and ponies is 45.
The answer is D. |
AQUA-RAT | AQUA-RAT-39474 | # 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... | [
"16 2/3 %",
"25 %",
"33 1/3 %",
"50%"
] | B | 1986; 2/3
1988; 1/2
% decrease = change/original*100
2/3−1/2 / 2/3∗100
1/6∗3/2∗100=14∗100=25
Answer: "B" |
AQUA-RAT | AQUA-RAT-39475 | thanks in advance.
2. Originally Posted by Simo
Dear all,
I need to know if is it possible to find the mean of a normal distribution knowing the ratio of the area under the "bell" curve on the left and on the right of a given point.
To be more precise I need to solve the following equation
$\frac{1}{\sigma \sqrt{2\pi ... | [
"0",
"1",
"3",
"6"
] | B | Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.B |
AQUA-RAT | AQUA-RAT-39476 | in the comments section. At what speed does the second train B travel if the first train travels at 120 km/h. You can approach this as if you were solving for an unknown in math class or you can use the speed triangle. Time, Speed and Distance: Key Learnings. ) Since the distances are the same, I set the distance expre... | [
"70 km/hr",
"75 km/hr",
"80 km/hr",
"87.5 km/hr."
] | D | Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
Let the speed of two trains be 7x and 8x km/hr.
x = 100/8 = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer : D. |
AQUA-RAT | AQUA-RAT-39477 | 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... | [
"5",
"6",
"7",
"8"
] | A | Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 75 = 45.
He would have to answer 45 - 40 = 5
Answer: Option A |
AQUA-RAT | AQUA-RAT-39478 | 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... | [
"49",
"4",
"12",
"14"
] | D | Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
9 : 6 :: 21 : x 9 * x = 6 x 21
x = (6 x 21)/9
x = 14.
Answer is D. |
AQUA-RAT | AQUA-RAT-39479 | (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 ... | [
"60",
"80",
"90",
"115"
] | C | b+c=250_______(1)
1.5b+0.75c=315
2b+c=420_______(2)
(2)-(1)
b=170
c=80
b-c=170-80=90
ANSWER:C |
AQUA-RAT | AQUA-RAT-39480 | # Probability: If I have a friend that likes half of the food he tries, what is the probability that he likes three of five foods that he's given?
I was thinking 1*1*1*2*2 = 4 out of 32, with LLLDD, LLLLL, LLLDL, LLLLD, with L as like and D as dislike. But if I can do LLLLD and LLLDL, why couldn't I do LDLLL or DLLLD?... | [
"0.009",
"0.015",
"0.027",
"0.036"
] | C | One case is: candy - candy - no candy
The probability is 1/10*1/10*9/10 = 9/1000
There are 3 such cases, so we should multiply this probability by 3.
P(exactly 2 buy candy) = 9/1000 * 3 = 27/1000 = 0.027
The answer is C. |
AQUA-RAT | AQUA-RAT-39481 | # Sort of a challenge
#### topsquark
##### Well-known member
MHB Math Helper
This isn't so much a challenge problem as much as it has a startling (at least I think so) answer.
Say we tie a rope around the Earth. Now we are going to cut it and add another 6 meters to it. If we pull the new rope tight (in a circle) ho... | [
"1222",
"1289",
"1210",
"1129"
] | C | π (232 – 122)
= 1210
Answer:C |
AQUA-RAT | AQUA-RAT-39482 | ### Show Tags
19 May 2015, 12:37
we have here 4 (4 years) successive increases of 25% or *1,25 --> 1,25^4 * X = 6250, X = 2560
See MGMAT (Percents) for detailed explanation of such question types.....
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
8... | [
"1680",
"1600",
"1200",
"1500"
] | C | Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 40 % = 140 %
140 % -------> 1680 (140 × 12= 1680)
100 % -------> 1200 (100 × 12 = 1200)
Option 'C' |
AQUA-RAT | AQUA-RAT-39483 | # 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... | [
"714 1/7 grams",
"714 2/7 grams",
"714 8/3 grams",
"714 1/3 grams"
] | B | If the cost price is Rs.100, then to get a profit of 40%, the selling price should be Rs.140.
If 140kg are to be sold, and the dealer gives only 100kg, to get a profit of 40%.
How many grams he has to give instead of one kilogram(1000 gm).
140 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/140 = 714 2/7 grams.
Answer:B |
AQUA-RAT | AQUA-RAT-39484 | Another answer that use almost the same idea: the sum or subtraction of two even or odd number is an even number. How many odd number we have?
Replacing 100 with $n$ and using Brian M. Scott's solution, we want a partition of $\{1, 2, ..., n+1\}$ into two sets with equal sums.
The sum is $\frac{(n+1)(n+2)}{2}$, and i... | [
"1500",
"3100",
"4400",
"6200"
] | A | Each term in set B is 60 more than the corresponding term in set A.
The difference of the sums = 25 * 60 = 1500.
The answer is A. |
AQUA-RAT | AQUA-RAT-39485 | # 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",
"5",
"6",
"7"
] | A | Let x be the number of shelves.
12x - 21 = 8(x-1) + 3
4x = 16
x= 4
The answer is A. |
AQUA-RAT | AQUA-RAT-39486 | # computing probability that at least one letter matches with envelope
Four letters to different insurers are prepared along with accompanying envelopes. The letters are put into the envelopes randomly. Calculate the probability that at least one letter ends up in its accompanying envelope.
### Attempt
Since this is... | [
"1/24",
"1/8",
"1/4",
"1/3"
] | D | Total Lanya# of ways - 4! = 24.
Desired:
A-Mapped to the only correct address----------x 1 way only
B-Mapped to other two incorrect addresses - x 2 ways
C-Mapped to other two incorrect addresses - x 2 ways
D-Mapped to other two incorrect addresses - x 2 ways
Therefore, 1*2*2*2/24 = 1/3.? |
AQUA-RAT | AQUA-RAT-39487 | evolution, population-dynamics
Title: How many humans have been in my lineage? Is it almost the same for every human currently living? If I were to count my father, my grandfather, my great-grandfather, and so on up till, say chimps, or the most common ancestor, or whatever that suits the more accurate answer, how man... | [
"1",
"7",
"3",
"9"
] | C | Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be years.
Then, age of the elder child ... |
AQUA-RAT | AQUA-RAT-39488 | 1. ## Having Trouble
Hi all,
I am just new to this site and it looks like such an awesome resource.
Can anyone help me with this???
If x + y = 1 and x³ + y³ = 19, find the value of x² + y²
2. Originally Posted by Joel
Hi all,
I am just new to this site and it looks like such an awesome resource.
Can anyone help ... | [
"1",
"2",
"3",
"4"
] | A | xy=1
As x+y=25
x2y3+y2x3=25
x2y2(y+x)=25
Substituting x+y
x2y2=1
xy=1
ANSWER:A |
AQUA-RAT | AQUA-RAT-39489 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"79.4",
"79.0",
"79.5",
"79.2"
] | D | Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D |
AQUA-RAT | AQUA-RAT-39490 | +0
# At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
0
2788
3
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Feb 25, 2015
#3
+99377
+5
At a party, everyone shook hands with everyb... | [
" 10•9•8•7•6•5•4•3•2•1",
" 10•10",
" 10•9",
" 66"
] | D | We got #12 people who shake each other's hands once ==> a pair of 2
12!/10!2! = 12*11 / 2*1 = 66.
Hence answer D. |
AQUA-RAT | AQUA-RAT-39491 | 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... | [
"30",
"80",
"20",
"68"
] | D | Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (79 - 45)
=> X/2 = 34
=> X = 68.
ANSWER:D |
AQUA-RAT | AQUA-RAT-39492 | Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day... | [
"days",
"days",
"days",
"1/2 days"
] | A | Explanation:
10/40 + 10/30 + 10/x = 1
x = 24 days
Answer: A |
AQUA-RAT | AQUA-RAT-39493 | java, xml, swing
<lastWeekSolution>I'm Going to get this</lastWeekSolution>
</week>
<week>
<date>2012/03/12 00:00:00</date>
<riddle>ipso lorem 7</riddle>
<lastWeekSolution>I'm Going to get this</lastWeekSolution>
</week>
<week>
<date>2012/03/19 00:00:00</date>
... | [
"Sunday",
"Monday",
"Tuesday",
"Thursday"
] | A | 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + ... |
AQUA-RAT | AQUA-RAT-39494 | of$5$, and$-2=5\pmod{7}$. – joriki Jun 10 '11 at 0:20 Regarding divisibility by 7 I created an algorithm that must be applied repetitively to each period of a large number. If the last sum results in a multiple of 7 then the tested number is also a multiple of 7, otherwise it is not. The sum of each period must be adde... | [
"3",
"5",
"4",
"-3"
] | D | Let X be the required number, then
(7 + X) : (11 + X) :: (11 +X) : (19 + X)
(7 + X) (19 + X) = (11 + X)2
X2 + 26X + 133 = X2 + 22X + 121
4X = - 12 or X = - 3
ANSWER:D |
AQUA-RAT | AQUA-RAT-39495 | Decide the seating order of the people, starting from one of the brothers, say Ivan. Then position the other brother, Alexei, in one of the two slots (fourth and fifth) that fulfill the "separated by two others" condition - $2$ options. Then with Ivan and Alexei resolved, order the remaining five people in one of $5!=1... | [
" 20%",
" 30%",
" 40%",
" 50%"
] | C | The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be An... |
AQUA-RAT | AQUA-RAT-39496 | in n yrs and A 2 in (n+1) yrs, then Rate of compound interest =(A 2 - A 1)/A 1 *100% Sum = A 1 (A 1 /A 2) n. 596 APPENDIXC:COMPOUNDINTERESTTABLES 1/2% CompoundInterestFactors 1/2% SinglePayment UniformPaymentSeries ArithmeticGradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund ... | [
"277",
"270",
"291",
"266"
] | C | I = (520*7*8)/100 = 291
Answer: C |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.