source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38697 | The following is an example of a method that you could use to figure this out. The method is called bisection. It is not the fastest, but it is clear how to extract digits from it because it has explicit error bounds.
You know $1^2<2$. You know $2^2>2$. So $1<\sqrt{2}<2$ so its first decimal digit is $1$.
You check $... | [
"1.004",
"1.006",
"1.008",
"1.012"
] | A | As compared to 1, 0.001 is a very small quantity. Thus, we can write (1+0.001)^4 is nearly equal to (1+4*0.001) = 1.004.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.
A |
AQUA-RAT | AQUA-RAT-38698 | sum(res==0)/B
[1] 0.120614
So the probability is around 12%. Some ideas for an analytical solution (or approximation) would be nice! A similar question (without a complete answer).
The following is multiple choice question (with options) to answer.
If 40% of a certain number is 160, then what is 90% of that number? | [
"270",
"380",
"260",
"360"
] | D | Explanation:
40% = 40*4 = 160
90% = 90*4 = 360
Answer: Option D |
AQUA-RAT | AQUA-RAT-38699 | ## 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 hours",
"12hours",
"8hours",
"5hours"
] | A | Work done by the leak in 1 hour = 1/3 - 1/12 = 1/4
The leak will empty the tank in 4hours
Answer is A |
AQUA-RAT | AQUA-RAT-38700 | 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 ... | [
"100",
"120",
"140",
"160"
] | B | 18 km/hr = 18000 m / 3600 s = 5 m/s
time = 600 / 5 = 120 seconds
The answer is B. |
AQUA-RAT | AQUA-RAT-38701 | 2. When you add one component to a solution, the amount of other component does not change. In milk and water solution, if you add water, amount of milk is the same (not percentage but amount)
3.
Amount of A = Concentration of A * Volume of mixture
Amount = C*V
( e.g. In a 10 lt mixture of milk and water, if milk is 5... | [
" 2/3",
" 7/9",
" 24/9",
" 8/3"
] | C | Let x be the # of cups going into the 6 cup bottle.
so.... x/6 = ((4-x)/3)
24 - 6x = 3x
24 = 9x
x = 24/9.
Answer : C |
AQUA-RAT | AQUA-RAT-38702 | c#, formatting
/// <summary>
/// Calculates and returns the general discount
/// based on the <see cref="AccountStatus"/>
/// </summary>
/// <param name="accountStatus"></param>
/// <returns></returns>
private static decimal GetDiscountPercentage(AccountStatus accountStatus)
{
swi... | [
"31.7",
"31.1",
"31.6",
"31.4"
] | C | 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4
= 31.6
Answer: C |
AQUA-RAT | AQUA-RAT-38703 | Define y = 2^{2x}. Then
y^2 - y - 2 = 0
(y - 2)(y + 1) = 0
Thus y = 2 or y = -1.
So
2^{2x} = 2 ==> 2x = 1 ==> x = 1/2
or
2^{2x} = -1, which is impossible.
Thus x = 1/2.
-Dan
5. Originally Posted by erika
Additionally, if both sides of the equation cannot be expressed as the same base, how do we solve for x?
In ge... | [
"65",
"130",
"141",
"142"
] | A | m^2 = 81 => m=9
9= 5x+4 => x=1
y= 2*9+1^2 = 19
2y+3m = 2*19+3*9 = 65
Answer : A |
AQUA-RAT | AQUA-RAT-38704 | 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... | [
"27",
"48",
"45",
"72"
] | B | Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=146
x=3
Difference if ages of Pa and Mo=25x-9x=16x=16*3=48
Answer B |
AQUA-RAT | AQUA-RAT-38705 | 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.
. .... | [
"7",
"9",
"12",
"15"
] | C | 150=51+90+65-32-2x
x=12
C. 12 |
AQUA-RAT | AQUA-RAT-38706 | # How many numbers made out of 5 distinct digits contain 4 and are even
This is an exercise from a book on combinatorics and I can't seem to wrap my head around it: How many numbers are there, made out of 5 distinct digits, which contain '4' and are even. The answer according to the book is 7686.
I distinguished some... | [
"36",
"60",
"84",
"72"
] | B | DETAILED SOLUTION
Any multiple of 12 should be a multiple of 4 and 3. First, let us look at the constraint for a number being a multiple of 3. Sum of the digits should be a multiple of 3. Sum of all numbers from 2 to 7 is 27. So, if we have to drop a digit and still retain a multiple of 3, we should drop either 3 or 6.... |
AQUA-RAT | AQUA-RAT-38707 | ### 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... | [
"5000",
"5007",
"5006",
"5003"
] | A | Let x, y and z be the amount invested in schemes A, B and C respectively. Then,
(x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200
10x + 12y + 15z = 320000
Now, z = 240% of y = 12/5 y
And, z = 150% of x = 3/2 x
x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y
16y + 12y + 36y = 320000
y = 5000
Sum invested in scheme B = R... |
AQUA-RAT | AQUA-RAT-38708 | # 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... | [
"1218",
"1212",
"1210",
"277"
] | C | π (232 – 122) = 1210
Answer: C |
AQUA-RAT | AQUA-RAT-38709 | Since these 6 possibilities are exhaustive, we have $$(1+2+3+4+5+6)q/6 = 1 \implies q = {6 \over 21} = {1 \over 3.5}$$ as I originally suspected; in particular, this implies that $$P(X_\tau = M + j) = (6-j)q/6 = (6-j)/21,$$ agreeing with Mike's answer.
The following is multiple choice question (with options) to answer... | [
" 9/4",
" 12/5",
" 16/5",
" 30/7"
] | D | there are two ways to calculate area of PQS. area remains same, so both are equal.
5*6/2 = PR*7/2
PR = 30/7
D |
AQUA-RAT | AQUA-RAT-38710 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"12",
"15",
"18",
"20"
] | A | Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 12 days = 12 × (1/16) = 12/16 = ... |
AQUA-RAT | AQUA-RAT-38711 | Some part of the 50% solution of acid was replaced with the equal amount of 30% solution of acid. As a result, 40% solution of acid was obtained. What part of the original solution was replaced?
(A) 1/5
(B) 1/4
(C) 1/2 *correct answer
(D) 3/4
(E) 4/5
Original Acid : Total ratio = 50:100 . let us say you replaced x pa... | [
"1/2",
"2/3",
"3/4",
"3/5"
] | C | Let x be the fraction of the original solution that was replaced.
0.5*(1-x)+0.1(x)=0.2
0.4x=0.3
x=3/4
The answer is C. |
AQUA-RAT | AQUA-RAT-38712 | # Formulation and computation of “the” unique median of an even-sized list
Consider an even-sized set of numbers $X = \{x_k\}$, such as $X = \{1, 2, 7, 10\}$.
The median $m$ is defined as:
$$m = \mathrm{arg \min_x} \sum_k \lvert x_k - x\rvert^1$$
Any $m \in [2, 7]$ is a minimizer of this function, and is therefore "... | [
"5",
"6",
"7",
"1"
] | D | Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the v... |
AQUA-RAT | AQUA-RAT-38713 | Time needed for both machine to produce 1500 units is given.
1/8 + 1/12
= 5/24
I hrs work done by both machine.
24/5 = 4.8.
Time needed to complete the entire work.
******* 1500 units must be considered as a single work. units are same for both machine. Therefore we don't need to do anything with units.
C is the... | [
"10 pm",
"1 pm",
"12 pm",
"2 pm"
] | B | Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work comple... |
AQUA-RAT | AQUA-RAT-38714 | java
Any help will be welcomed. Thanks
EDIT:
Keypad format:
The problem statement:
We are given two inputs:
A phone number in string format.
A list of strings.
The output is the list containing only those strings which correspond to any substring of the given phone number when converted to the corresponding letter... | [
"998",
"1000",
"1092 times",
"1100"
] | C | 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
C |
AQUA-RAT | AQUA-RAT-38715 | 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... | [
"70,15,15",
"50,25,25",
"60,20,20",
"40,30,30"
] | B | given quantities of b and c are equal .
therefore instead of considering them as a different quantities take average of both and consider it as a single entity .
so the cost of the mixture "D" (equal quantities of "B" and "C") is 170/2=85rs/kg
now the tea contains only "A" of 95 rs/per and "D" of 85 rs/kg.
it is clearl... |
AQUA-RAT | AQUA-RAT-38716 | => 18x/4=154
x=308/9
TOTAL WAGES PAID WILL BE
(12/11 + 18/7)*309/9
PLEASE TELL ME WHERE I AM WRONG
Lets try -
SW4 wrote:
Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the differe... | [
"Rs. 10000",
"Rs. 11000",
"Rs. 12000",
"Rs. 9000"
] | B | EXPLANATION
Total income of 3 members = Rs. (8000 + 15000 + 6000) = Rs. 29000.
Required income = Rs. [ (10000 x 4) – 29000 ]
= Rs. (40000 – 29000)
= Rs. 11000.
Answer B |
AQUA-RAT | AQUA-RAT-38717 | # 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... | [
"18 2/91%",
"36 4/11%",
"18 9/11%",
"18 2/91%"
] | B | 15 CP = 11 SP
11 --- 2 CP
100 --- ? =>36 4/11%
Answer:B |
AQUA-RAT | AQUA-RAT-38718 | java, performance
Title: The car plate problem: generate from AAA0001 to ZZZ9999 skipping the 0000 I was given the problem (called "car plate problem") to write all the values that go from AAA0001 to ZZZ9999 with the following premises:
Create all the possibilities from AAA0001 to ZZZ9999;
Skip all the 0000, ie: AAB0... | [
"131040",
"116700",
"142369",
"147225"
] | A | we want 4 digit of cars and repetition is not allowed
1st digit can be fill with 0 to 9 i.e = 10
2nd digit can be fill with 0 to 9 except earlier selected i.e = 9
3rd digit can be fill with 0 to 9 except earlier selected i.e = 8
4th digit can be fill with 0 to 9 except earlier selected i.e = 7
No of ways = 10 * 9 * 8 *... |
AQUA-RAT | AQUA-RAT-38719 | homework-and-exercises, fluid-dynamics
Title: Time needed to empty a syringe A) a syringe is filled with 10mL water.
The diameter of the barrel of the syringe is 15.9 mm and the diameter of the tip is 1.2mm. With how much force do we need to push on the plunger to empty the syringe from water in 10 seconds? Neglect fr... | [
"18",
"17",
"16",
"19"
] | A | 1/10 + 1/15 - 1/x = 1/9
x = 18
Answer:A |
AQUA-RAT | AQUA-RAT-38720 | (1) The first $$n$$ people donated $$\dfrac1{16}$$ of the total amount donated.
(2) The total amount donated was $$\120,000.$$
Source: GMAT Prep
Target question: What was the value of n?
When I scan the two statements, it seems that statement 2 is easier, so I'll start with that one first...
Statement 2: The total a... | [
"$100",
"$150",
"$200",
"$250"
] | B | Cavg = average contribution before John
Cavg*1.5 = 75, therefore the average cont is $50 before John.
If he needs to increase the average contribution by $25, he must put in $25 for each of the 3 people.
so $75.
But, he also has to put in the average for himself (the fourth person), so add $75.
So $150 is your answer.
... |
AQUA-RAT | AQUA-RAT-38721 | 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.
. .... | [
"12 kg",
"10 kg",
"20 kg",
"72 kg"
] | A | Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 12 kg
=> (72-x)/5 = 12
=> x = 12
Answer : A |
AQUA-RAT | AQUA-RAT-38722 | (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 ... | [
"8(257/525) gallons",
"8(346/625) gallons",
"8.192 gallons",
"8.25 gallons"
] | C | There is a direct formula to calculate such repetition:
Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:
Left QTY / 20 = (20 -4)^4 / 20^4
Left QTY = 20 (16/20)^4
Left QTY = 20 ( 4/5 )^4
Left QTY = 8.192
Answer is C |
AQUA-RAT | AQUA-RAT-38723 | ## 28.
The Correct Answer is (D) — Graphs for answer choices A and B imply that the area of this rectangle can be 800$\small&space;ft^{2}$ or greater. These values are not possible with only 40ft of fencing material. Similarly, the graph for answer choice C says that the area can be as large as 400$\small&space;ft^{2}... | [
"289",
"132",
"279",
"277"
] | B | 2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer: B |
AQUA-RAT | AQUA-RAT-38724 | The price then decreased by 12% during 2013
A 12% DECREASE is the same a multiplying the price by 0.88
So, the new price = ($100)(1 + p/100)(0.88) The price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012 If the original price was$100, then the price at the end of 2013 was $110 So,... | [
"1% loss",
"1% gain",
"No loss or no gain",
"Cannot be determined"
] | C | M. F 1 = 100-100/9/100 =800/900 = 8/9
M. F 2 = 100+25/2/100 =225/200 =9/8
Total M. F =8/9*9/8 = 1
Overall % change = ( M. F – 1 ) * 100 = ( 1 – 1 ) * 100 = 0
ANSWER:C |
AQUA-RAT | AQUA-RAT-38725 | 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... | [
"12 sec",
"15 sec",
"16 sec",
"20 sec"
] | C | Sol.
Speed = (63 x 5/18) m/sec.
= 35 /2 m / sec.
Time taken = (280 x 2/35) sec = 16 sec
Answer C |
AQUA-RAT | AQUA-RAT-38726 | 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 ... | [
"10km/hr",
"15km/hr",
"20km/hr",
"30km/hr"
] | A | Time required = 2 hrs 30 min - 50 min = 1 hr 40 min = 1 2/3 hrs
Required speed = 50*3/5 = 30km/hr
Original speed = 50*2/5 = 20 km/hr
Difference = 30-20 = 10 km/hr
Answer is A |
AQUA-RAT | AQUA-RAT-38727 | doesn't rule out anything and thus it could be either coin with equal probability. to bet you even money that it is the two headed coin. One coin has been specially made and has a head. He selects a coin at random and flips it twice. One coin is chosen at random and flipped, coming up heads. Perform the following exper... | [
"0.5",
"0.55",
"0.6",
"0.65"
] | A | The probability is exactly same as the cion landed tail up once. That is 2*(1/2)^2 = 2/4 =0.5.
The answer is, therefore, (A). |
AQUA-RAT | AQUA-RAT-38728 | computational-chemistry
( 5 0 | 4 0) = 0.000862792421254
( 5 2 | 1 0) = 0.000000000000000
( 5 3 | 1 0) = 0.049151047350638
( 5 4 | 1 0) = 0.041228155506758
( 5 1 | 2 0) = 0.000000000000000
( 5 1 | 3 0) = 0.005091750233326
( 5 1 | 4 0) = 0.004270986718219
( 5 0 | 2 1) = 0... | [
"0.0001",
"0.001",
"0.01",
"0.1"
] | B | 2 x 5 = 10.
Sum of decimal places = 4
0.002 x 0.5 = 0.001
Answer: Option B |
AQUA-RAT | AQUA-RAT-38729 | 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... | [
"6 days",
"8 days",
"9 days",
"10 days"
] | B | If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
B |
AQUA-RAT | AQUA-RAT-38730 | The price then decreased by 12% during 2013
A 12% DECREASE is the same a multiplying the price by 0.88
So, the new price = ($100)(1 + p/100)(0.88) The price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012 If the original price was$100, then the price at the end of 2013 was $110 So,... | [
"2010",
"2011",
"2012",
"2013"
] | B | EXPLANATION
Suppose commodity X will cost 40 paise more than Y after z years.
Then, (4.20 + 0.40z) – (6.30 + 0.15z) = 0.40
0.25z = 0.40 + 2.10
x =2.50/ 0.25 =250/25 =10
X will cost 40 paise more than Y 10 years after 2001 i.e., 2011.
Answer B |
AQUA-RAT | AQUA-RAT-38731 | Let P=[$(\sqrt{n}+0.7)^2$]
Second Hint
given $n \geq 1$, put n=1 gives P=2
n=2 gives P=4
n=3 gives P=5
n=4 gives P=7
n-5 gives P=8
n=6 gives P=9
n=7 gives P=11
Final Step
here missing number are
1,3,6,10,… which is following a certain pattern
1, 1+2, 3+3, 6+4, 10+5, 15+6, 21+7, 28+8, 36+9, 45+10, 55+11, 66+... | [
"281 and 930.",
"282 and 930.",
"283 and 930.",
"None"
] | B | Solution:
If you look closely, you will find a sequence in every alternating number.
192, 222 and 252 form one series where 30 is added each time.
021, 324 and 627 form one series where 303 is added each time.
Thus the next two numbers will be 282 and 930.
Answer B |
AQUA-RAT | AQUA-RAT-38732 | Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION
Algebraic Solution: If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x ... | [
"560",
"882",
"799",
"778"
] | A | 79%
104%
--------
25% ---- 140
100% ---- ? => Rs.560
Answer: A |
AQUA-RAT | AQUA-RAT-38733 | distance from a given point called centre. You can use the formula for the volume of a cylinder to find that amount! In this tutorial, see how to use that formula and the radius and height of the cylinder to find the volume. As you can imagine, as the discs become thinner, the volume of the sphere gets more accurate. (... | [
"2200",
"2614.9",
"3300",
"1100"
] | B | Cylinder volume = πr(power2)h
= 22/7 × 8 × 8 × 13
= 2614.9 m(power3)
Answer is B. |
AQUA-RAT | AQUA-RAT-38734 | ### 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)14500",
"B)14000",
"C)12000",
"D)13007"
] | C | Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 26000
Share of B = 6/13 (26000)
= Rs. 12000
Answer:C |
AQUA-RAT | AQUA-RAT-38735 | # If $(a+b)(a+c)(b+c)=8abc$ prove $a=b=c$
For positive numbers $$a,b,c$$ we have $$(a+b)(a+c)(b+c)=8abc$$. Prove $$a=b=c$$
I tried expanding the expression. after simplifying we have,
$$a^2b+ab^2+b^2c+ca^2+ac^2+bc^2=6abc$$ But not sure how to continue.
I also noticed that we have,
$$(a+b)(a+c)(b+c)=(2a)(2b)(2c)$$ ... | [
"50",
"60",
"69",
"75"
] | A | (a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER A 50 |
AQUA-RAT | AQUA-RAT-38736 | ### Show Tags
13 Mar 2015, 20:17
MitDavidDv wrote:
If two integers are chosen at random out of the set {2, 5, 7, 8}, what is the probability that their product will be of the form a^2 – b^2, where a and b are both positive integers?
A. 2/3
B. 1/2
C. 1/3
D. 1/4
E. 1/6
Shalom! I am currently studying the probability c... | [
"5/8",
"1/3",
"2/5",
"1/2"
] | A | Answer A.
Total # of outcomes: 5*8= 40
# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 25
Probability: 25/40 = 5/8 |
AQUA-RAT | AQUA-RAT-38737 | # 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... | [
"3.6",
"3",
"18",
"24"
] | B | Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 108
12R2 = 108
R2 =9
R = 3.
Answer: Option B |
AQUA-RAT | AQUA-RAT-38738 | Just need to verify if this one needs to be subtracted or no.
jaytheseer
New member
Mr. Gates owns 3/8 of Macrohard. After selling 1/3 of his share, how much more of Macrohard does Mr. Gates still own?
MarkFL
Staff member
Yes, I would view the subtraction in the form:
If Mr. Gates sold 1/3 of his share, how much o... | [
"2778",
"2679",
"2000",
"2699"
] | C | Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000 = Rs.2000.
Answer:C |
AQUA-RAT | AQUA-RAT-38739 | java, performance
Title: The car plate problem: generate from AAA0001 to ZZZ9999 skipping the 0000 I was given the problem (called "car plate problem") to write all the values that go from AAA0001 to ZZZ9999 with the following premises:
Create all the possibilities from AAA0001 to ZZZ9999;
Skip all the 0000, ie: AAB0... | [
"10966",
"10968",
"10967",
"10966"
] | B | 5 differ numbers can be read upside down same are 0 , 1 , 6 , 8 , 9
try with these no.s
number is 10968.
10968
78633
-------
89601
--------
ANSWER:B |
AQUA-RAT | AQUA-RAT-38740 | • The first remark makes me more confident that the first approach is the correct one. Thanks for that. However, I do not think I forgot the possibility to have a six. My probability is $\frac{4}{6}$ so I am considering the four cases in which the third number is greater than $2$. Maybe also look at my edit. – AndreasS... | [
"4/8",
"5/8",
"6/8",
"7/8"
] | B | total possible combinations=(2,2)(2,4)(2,6)(4,2)(4,4)(4,6)(3,3)(6,2)(6,4)(6,6)=10
so probability=10/16=5/8
ANSWER:B |
AQUA-RAT | AQUA-RAT-38741 | "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... | [
"300",
"320",
"370",
"400"
] | B | When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 127.05
Here 127 is the quotient.
Given that Remainder = 16
So, 127.05 = 127 + 16/J
So, J = 320
Answer: B |
AQUA-RAT | AQUA-RAT-38742 | algorithms, graphs, optimization
There is one final component of your problem we have not addressed, i.e., there is a set of books $S_1$ that MUST go into box 1 and a set $S_2$ that MUST go into box 2.
Off the top of my head, I do not see a way to fix this without incorporating a source and sink $s$ and $t$ (for box... | [
"$255",
"$275",
"$510",
"$612"
] | D | Total no. Of boxes = 3060000/(20×20×15) = 510
Total cost = 510×$1.20=$612
Answer D |
AQUA-RAT | AQUA-RAT-38743 | Once you have $9\ge x^2$, I would recommend first solving the associated equation. That is, $9= x^2$ which does, in fact, have x= 3 and x= -3 as solutions. That divides the number line into 3 intervals, $(-\infty, -3)$, $(-3, 3)$, and $(3, \infty)$ on each interval of which the inequality is either true for every point... | [
" x >= 1",
" x <= –1",
" -3 <= x <= 3",
" x <= –1 or x >= 1"
] | C | 9 - x^2 >=0
means x^2 - 9 <=0
=> (x-3)(x+3) <= 0
=> -3 <= x <= 3
Answer - C |
AQUA-RAT | AQUA-RAT-38744 | 2. ### math
list all the 3 digit numbers that fit these clues. the hundreds digits is less than 3. the tens digit is less than 2. the ones digit is greater than 7
3. ### Math
Think of a five-digit number composed of odd numbers. The thousands digit is two less than the ten thousands digit but two more than the hundr... | [
"1339",
"2300",
"4200",
"1340"
] | A | There is one number in hundred with 2 in th tens digit and 1 in the units digit: 21, 121, 221, 321, ...
The difference between 324,700 and 458,600 is 458,600-324,700=133,900 - one number per each hundred gives 133,900/100=1,339 numbers.
Answer: 1,339 A |
AQUA-RAT | AQUA-RAT-38745 | ### 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... | [
"13333",
"26758",
"45896",
"14639"
] | A | Explanation:
A:B = 4:1 = 4:1
=> A:C = 4:2 = 4:2
=> A:B:C = 4:1:2
A share = (4/6)*20000
= 13333
Option A |
AQUA-RAT | AQUA-RAT-38746 | 3 , 10 , 12 , 5 , 18 , 6 = { x1 , x2 , x3 , x4 , x5 , x6 }
n = 6 , μ = 9
σ = $\dpi{80}&space;\fn_jvn&space;\sqrt{\frac{3^{2}+10^{2}+12^{2}+5^{2}+18^{2}+6^{2}}{6}\:&space;-\:&space;9^{2}}$ = $\dpi{80}&space;\fn_jvn&space;\sqrt{\frac{638}{6}\:&space;-\:&space;81}$ = $\dpi{80}&space;\fn_jvn&space;\... | [
"10.5",
"11",
"11.1",
"12"
] | C | Mean = 14.5
Two standard deviations is 1.7 + 1.7 = 3.4
There could be two calues for this.
Mean + two standard deviations = 17.9
Mean - Two standard deviations = 11.1
Answer choice has 11.1 and so C is the answer. |
AQUA-RAT | AQUA-RAT-38747 | 27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14... | [
"113",
"231",
"245",
"548"
] | D | D
548
The numbers 48269375 are being repeated in the same sequence. |
AQUA-RAT | AQUA-RAT-38748 | logic, first-order-logic, propositional-logic
Title: Relations between statements involving universal quantifier, conditional and biconditional If we consider two predicates:
$b(x)$: x is a boy
$c(x)$: x is clever
Then, there are four statements involving $∀, b(x), c(x), →$ and $↔$ . These are below along with my int... | [
"Chauffeur",
"Steering",
"Mechanic",
"Brake"
] | A | Explanation:
Horse is driven by a jockey .
Similarly,car is driven by a chauffeur
Answer: A) |
AQUA-RAT | AQUA-RAT-38749 | ### 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... | [
"2882",
"2672",
"2288",
"2500"
] | D | Let's Anil's salary be Rs. 100.
Money spent on Rent = 40% of 100 = Rs. 40.
Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.
Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40
Anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60
for 33.6 ---> 100 ; 840 ---> ?
Required salary = 840/33.... |
AQUA-RAT | AQUA-RAT-38750 | Below is another solution which is a little bit faster.
It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times
Let one woman... | [
"60",
"20",
"19",
"29"
] | A | Let 1Man does 1unit/hr of work
15M in 21 days of 8hrs will do (15*21*8) units
3W = 2M
1W=(2/3)units/hr
21W with 3hrs a day will take (15*21*8)/(21*3*(2/3)) days
=> 60 Days
ANSWER:A |
AQUA-RAT | AQUA-RAT-38751 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"0.215%",
"1.215%",
"3.215%",
"6.215%"
] | A | Let d initial price be 100
31 % rise
now price = 131/100*100 = 131
10% discount
Then price = 131 * 90/100 = 117.9
15 % discount
Then price = 117.9 * 85/100 = 100.215
So Gain = 100.215 - 100 = 0.215
Gain % = Gain * 100 /CP
==> 0.215 * 100 /100 = 0.215%
ANSWER:A |
AQUA-RAT | AQUA-RAT-38752 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"2 hours 30 minutes",
"3 hours",
"2 hours",
"1 hour 45 minutes"
] | A | Answer
Let Jane travel 'x' at 60 miles per hour.
As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.
Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles.
Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x mi... |
AQUA-RAT | AQUA-RAT-38753 | 1^{10}\quad1^8+2\quad1^6+2^2\quad1^4+2^3\quad1^2+2^4\quad1^7+3\quad1^5+2+3\quad1^3+2^2+3\quad1+2^3+3\quad1^4+3^2\quad1^2+2+3^2\quad1^6+4\quad1^4+2+4\quad1^2+2^2+4\quad1^3+3+4\quad1+2+3+4\quad1^5+5\quad1^3+2+5\quad1+2^2+5\quad1+1+3+5$$
The following is multiple choice question (with options) to answer.
1^2 – 2^2 + 3^2 ... | [
"-21",
"-53",
"-35",
"-55"
] | D | 1-4+9-16+25-36+49-64+81-100= -55
ANSWER:D |
AQUA-RAT | AQUA-RAT-38754 | +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... | [
"650",
"640",
"630",
"620"
] | A | a = 4
d = 7 – 4 = 3
Sum of first 20 terms, S20
ANSWER IS A |
AQUA-RAT | AQUA-RAT-38755 | ### 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... | [
"125",
"40",
"48",
"35"
] | C | Assuming that face value of the first stock = Rs.100 as it is not given in the question
Since it is a 5% stock, we can take the dividend per stock = Rs.5
Market Value of the first stock = Rs.104
Investment on the first stock = Rs.26000
Number of stocks purchases = 26000/104 = 250
His total income from all these stocks ... |
AQUA-RAT | AQUA-RAT-38756 | binary, numeral-representations
= \sum_{i=0}^{N-1} 2^i - \sum_{i=0}^{N-1} b_i 2^i + 1 = 2^N - b$$
since the two's complement is defined as the complement of the representation $b_{N-1} \cdots b_0$, plus one, and $\sum_{i=0}^{N-1}2^i = 2^N - 1$. Since $a$ is negative, $a_{N-1} = 1$ and then:
$$a = -b
= -2^N + \sum_{i=... | [
"2",
"7",
"9",
"11"
] | D | Adding the digits in unit's place , 5+ 6 + b = 16 (Since a and b are positive single digits )
=> b = 5
Now adding the digits in ten's place , 5+a + 2 + 1= 9 (1 has been carried over from unit's place addition)
=> a= 1
a+2b = 1+2*5
=11
Answer D |
AQUA-RAT | AQUA-RAT-38757 | 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",
"77",
"12",
"99"
] | C | A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer: C |
AQUA-RAT | AQUA-RAT-38758 | ### 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... | [
"66%",
"75%",
"86%",
"116%"
] | C | Let the price of Company A's assets be 100
Price of assets of KW is 50% more than company A's assets which is 150
Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 75
A+B = 175
KW = 150
KW/(A+B)*100 = 150/175*100 = 85.7% or 86%
ANSWER:C |
AQUA-RAT | AQUA-RAT-38759 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"$65,625",
"$105,000",
"$150,000",
"$93,750"
] | D | .04*7 = .28
26250/.28 = $93,750
Answer: D |
AQUA-RAT | AQUA-RAT-38760 | \begin{align} \dbinom{6}{2} & \longleftrightarrow \dbinom{6}{6-2} \\[8pt] AB & \longleftrightarrow CDEF \\ AC & \longleftrightarrow BDEF \\ AD & \longleftrightarrow BCEF \\ AE & \longleftrightarrow BCDF \\ AF & \longleftrightarrow BCDE \\ BC & \longleftrightarrow ADEF \\ BD & \longleftrightarrow ACEF \\ BE & \longleftr... | [
"6",
"8",
"9",
"12"
] | C | 26 + 20 - 17 = 29
38 - 29 = 9 play neither
Answer is C |
AQUA-RAT | AQUA-RAT-38761 | ### Show Tags
26 May 2017, 05:36
1
Which of the following equals the ratio of 3 $$\frac{1}{3}$$to 1 $$\frac{1}{3}$$?
3$$\frac{1}{3}$$ = $$\frac{10}{3}$$
1 $$\frac{1}{3}$$ = $$\frac{4}{3}$$
Required ratio = (10/3) / (4/3) = $$\frac{10}{4}$$ = $$\frac{5}{2}$$
Director
Joined: 13 Mar 2017
Posts: 703
Location: India
Conc... | [
"s. 2890",
"s. 4046",
"s. 1190",
"s. 1620"
] | B | Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 686 : N
&there N = 289 x 686 / 49
= Rs. 4046
Answer :B |
AQUA-RAT | AQUA-RAT-38762 | # 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... | [
"2%",
"4%",
"6%",
"9%"
] | B | 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer:B |
AQUA-RAT | AQUA-RAT-38763 | => 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... | [
" 90",
" 110",
" 105",
" 115"
] | B | First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 34000 - 30000 = 4000
So 10 more machines..
Total = 110 machines
IMO B.. |
AQUA-RAT | AQUA-RAT-38764 | physical-chemistry, density
Title: Find the number of copper spheres in a box
A box contains a mixture of small copper spheres and small lead spheres. The total volume of both metals is measured by the displacement of water to be $\pu{420 cm^3}$ and the total mass is $\pu{5.4 kg}$. What percentage of the spheres are ... | [
"40",
"50",
"60",
"70"
] | C | An alloy of 60oz which is 20% copper means there is 12 oz of gold. To get to an alloy that is 60% copper, let's use this expression: (12 + x)/(60 + x) = 0.60 with x representing the amount of pure copper that must be added to get to 60%. The expression we are using represents the new total weight of pure copper over th... |
AQUA-RAT | AQUA-RAT-38765 | # 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?... | [
"5%",
"10%",
"15%",
"35%"
] | D | The formula is
n(AUBUC) = n(A)+n(B)+n(C)-B+A-N
where B is both (it will sum of (AB), (BC), (CA)).
and A is All
and N is neither
so plugging in we get
100 = 60+50+45+10-B-0
B = 65.
exactly two = 65 - 3(10) = 35
subtracting 10% three times as this value is including in all the (AB), (BC), (CA).
Answer D |
AQUA-RAT | AQUA-RAT-38766 | # 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 $$13^2 + 3(13) + 4 = 212$... | [
"1",
"2",
"8",
"11"
] | A | Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
Answer :A |
AQUA-RAT | AQUA-RAT-38767 | Suppose the slower car stands still for one hour. How often will the faster car pass it? Then stop the faster car and start the slower car for another hour. How often will the slow car pass the stopped car? Add.
Consider alternative case when cars complete exactly $4$ and $8$ rounds. It's easily seen that the number o... | [
"65",
"38",
"20",
"28"
] | C | Answer: C) 20 km |
AQUA-RAT | AQUA-RAT-38768 | Then, in any case $(a-b)^2=8$
• -1.This is a low grade method. – N.S.JOHN Apr 17 '16 at 10:42
$$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... | [
"3/80",
"3/5",
"12",
"5/3"
] | C | 25/100 = 1/4
N = 2 ^ 1/4
N^b = 2^3
(2^1/4)^b = 2^3
b =12
Answer: C |
AQUA-RAT | AQUA-RAT-38769 | 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... | [
"574.65",
"514.23",
"508.35",
"536.87"
] | C | Using CI Formula:
A=P(1+r/n)^n*t
A=400(1+3/2)^2*8
A=508.35.
Option: C |
AQUA-RAT | AQUA-RAT-38770 | mechanical-engineering, torque
Title: How to calculate if a motor is capable for a load? I am trying to figure out if a motor I have is capable of spinning a wheel. Here is all of the information I have:
MOTOR: 190 g.cm min.
WHEEL: 26 cm diameter, weighs about 59 grams
I imagine that I would have to calculate the line... | [
"30.68 km/hr",
"31.68 km/hr",
"32.68 km/hr",
"33.68 km/hr"
] | B | Explanation:
In this type of question, we will first calculate the distance covered in given time.
Distance covered will be, Number of revolutions * Circumference
So we will be having distance and time, from which we can calculate the speed. So let solve.
Radius of wheel = 70/2 = 35 cm
Distance covered in 40 revolution... |
AQUA-RAT | AQUA-RAT-38771 | Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A certain stock exchange designates each stock with a one-, [#permalink] 11 Aug 2015, 23:27
Similar topics Replies Last p... | [
"484",
"726",
"1,100",
"1,320"
] | D | Lets consider the below -
The number of stocks that closed at a higher price = H
The number of stocks that closed at a lower price = L
We understand from first statement -> H+L = 2420 ----(1)
We understand from second statement -> H = (120/100)L => H = 1.2L ----(2)
Solve eq (1) & (2) to get H = 1320.
D is answer. |
AQUA-RAT | AQUA-RAT-38772 | Substitute $$1/(b,d)=[b,d]/bd$$ and $$1/(a,c)=[a,c]/ac$$: $$=\left(a,d(a,c)\frac{[b,d]}{bd}\right)\left(c(b,d)\frac{[a,c]}{ac},b\right)$$ Cancel $$d$$'s from first term and $$c$$'s from second term and rewrite: $$=\left(a,\frac{(a,c)[b,d]}{b}\right)\left(\frac{(b,d)[a,c]}{a},b\right)$$ Treat the whole first term like $... | [
"3/10",
"6/17",
"9/25",
"10/33"
] | C | 6a/100 = 10
a = 500/3
b/10 = 6
b = 60
c = b/a = 60*3/ 500 = 9/25
The answer is C. |
AQUA-RAT | AQUA-RAT-38773 | ## Wednesday, August 12, 2015
### The angle between the hour and minute hands of a clock.
Q. The time shown in the clock is 7:35 what is the angle between the hour and minute hands of a clock?
A. Consider the simpler problem if the time is 7:00. As there are 12 hours in a complete revolution of the hour hand, one ho... | [
"(5 + 5/11 )min past 5",
"(5 + 5/11 )min past 7",
"(5 + 5/11 )min past -0",
"(5 + 7/11 )min past 7"
] | B | Explanation:
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min spaces are gained in min = min
so, Required time = min past ... |
AQUA-RAT | AQUA-RAT-38774 | equinox
Title: Understanding date of astronomical events I have a masters in chemistry but pretty much, a layman in astronomy.
So, can you please explain to a novice like me, about this paragraph taken from the Wikipedia article on Makar Sankranti:
There are two different systems to calculate the Makara Sankranti dat... | [
"monday",
"tuesday",
"sunday",
"wednesday"
] | A | feb 14 2005 - tuesday
feb 14 2006 - wednesday
feb 14 2007 - thursday
feb 14 2008 - friday
feb 14 2009 - sunday[since 2008 is leap year , 2 days ll go forward]
feb 14 2010 - monday
ANSWER:A |
AQUA-RAT | AQUA-RAT-38775 | ### Remark 2
68% of all observations fall within 1 standard deviation from the mean.
### Example 5
Find the probability $$P(|Z| > 1)$$.
Key: We wish to find the area of the unshaded region in Figure 5. We may rewrite this probability as
$P( |Z| > 1) = 1 - P(|Z| < 1 )= 1 - .682 = .318$
### Exercise 1
Compute the ... | [
"18%",
"19%",
"20%",
"21%"
] | D | Average = 9.2
SD = 3.5
9.2 - 3.5 < 84% of distribution < 9.2 + 3.5
5.7 < 84% of distribution < 12.7
42% is outside this range.
Given: Distribution is symmetric. So 21% of distribution is less than 5.7 and the other 21% of distribution is greater than 5.7.
Answer: D |
AQUA-RAT | AQUA-RAT-38776 | 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... | [
"49",
"39",
"29",
"19"
] | A | Let the required length be x meters
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)= x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer is A. |
AQUA-RAT | AQUA-RAT-38777 | The answer here is the combination 8C2 (8 teams Choose 2) which mean \frac{8!}{6!x2!} --> \frac{8x7}{2}
To understand that we just have to think that each of the 8 team plays against 7 other (8x7) but they play each team exactly once so we divide the total by 2.
We divide by 2 because "TEAM A VS TEAM B" is the same a... | [
"n(k-1)",
"k(n-1)",
"n(k-2)",
"k(n-2)"
] | A | Explanation :
Let T1 - T6 be the number of teams, and let 1,2,3,4,5,6….be the players in the teams.
Total players if there are no repetition is 6*4 here. Generally, it is n * k. (n = number of teams, k = player/team). However, we see that, in each team, 1 player is repeated. i.e.
T1 & T2 have 4 in common (So 1 can be s... |
AQUA-RAT | AQUA-RAT-38778 | ### 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... | [
"3.0",
"3.36",
"24.78",
"25.0"
] | C | Cost price * 1.13 = Selling price --> Cost price * 1.13 = $28 --> Cost price = $24.78.
Answer: C. |
AQUA-RAT | AQUA-RAT-38779 | 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... | [
"10%",
"15%",
"20%",
"36%"
] | D | Say a recliner is actually worth $100
If she sells 100 recliners then she earns $10000
After the discount of 20%, she will earn $80 per recliner and she sells 70% more ie.,170 recliners
Hence her sales tields 170*80=$13600
Increase in sales=13600-10000=$3600
So% increase = 3600*100/10000 =36%
D is the answer |
AQUA-RAT | AQUA-RAT-38780 | Just need to verify if this one needs to be subtracted or no.
jaytheseer
New member
Mr. Gates owns 3/8 of Macrohard. After selling 1/3 of his share, how much more of Macrohard does Mr. Gates still own?
MarkFL
Staff member
Yes, I would view the subtraction in the form:
If Mr. Gates sold 1/3 of his share, how much o... | [
"3456",
"4056",
"4156",
"4567"
] | B | Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B |
AQUA-RAT | AQUA-RAT-38781 | # 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... | [
"4:1",
"4:2",
"4:5",
"4:3"
] | B | Ratio of their speeds = Speed of first train : Speed of second train
= √16−−√4
= 4:2
Answer is B. |
AQUA-RAT | AQUA-RAT-38782 | 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... | [
"45 minutes",
"50 minutes",
"40 minutes",
"55 minutes"
] | C | As they arrived 40 minutes earlier than usual, they saved 40 minutes on round trip from home to station (home-station-home) --> 20 minutes in each direction (home-station) --> wife meets husband 20 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent w... |
AQUA-RAT | AQUA-RAT-38783 | # Difference between revisions of "2019 AMC 10A Problems/Problem 23"
## Problem
Travis has to babysit the terrible Thompson triplets. Knowing that they love big numbers, Travis devises a counting game for them. First Tadd will say the number $1$, then Todd must say the next two numbers ($2$ and $3$), then Tucker must... | [
"Andy",
"Bob",
"Cary",
"Dora"
] | C | a= 5e
b =3 +e
c = 5b = 15+ 5e (highest of all)
d = b + e = 3+ e +e = 3 + 2e
Ans. C |
AQUA-RAT | AQUA-RAT-38784 | 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... | [
"5 kmph",
"2 kmph",
"7 kmph",
"8 kmph"
] | A | DS = 18
US = 8
S = ?
S = (18 - 8)/2 = 5 kmph
Answer:A |
AQUA-RAT | AQUA-RAT-38785 | # Number of ways in which they can be seated if the $2$ girls are together and the other two are also together but separate from the first two
$5$ boys and $4$ girls sit in a straight line. Find the number of ways in which they can be seated if $2$ girls are together and the other two are also together but separate fr... | [
"(5!)^2",
"(6!)^2",
"3!4!",
"11!"
] | C | first fix one boy and place other 3 in alt seats so total ways is 3!
now place each girl between a pair of boys... total ways of seating arrangement of girls 4!
total is 4!*3!
ANS C |
AQUA-RAT | AQUA-RAT-38786 | Difference between revisions of "2014 AMC 10A Problems/Problem 17"
Problem
Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die?
$\textbf{(A)}\ \dfrac16\qquad\textbf{(B)}\ \dfrac{13}{72}\qquad\textbf{(C)}\ \dfrac7{36}\qquad... | [
"60",
"61",
"64",
"84"
] | B | As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but ... |
AQUA-RAT | AQUA-RAT-38787 | # Math Help - Calculus Help Please
Initially a population contains 1000 individuals. After t minutes the number N of individuals in the populataion is such that dN/dt = -0.25N.
a) write down the expression for N in terms of t
b) Find the rate at which the population is decreasing when it is half its orginal size.
Thi... | [
"80",
"100",
"160",
"240"
] | C | Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 40 minutes the population increases by 40 x 4 = 160 people.
Answer. C. |
AQUA-RAT | AQUA-RAT-38788 | a company has borrowed$85,000 at a 6.5% interest rate. Find the accrued interest for an investment amount of 500 $holding for 15 days at an interest rate of 3 %. Calculating accrued interest payable First, take your interest rate and convert it into a decimal. The interest rate is 5%. Accrued Interest is the Interest a... | [
"5 years",
"6 years",
"7 years",
"9 years"
] | A | (4000*T*5)/100 = (5000*5*4)/100
T = 5 years
ANSWER:A |
AQUA-RAT | AQUA-RAT-38789 | +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... | [
"12",
"13",
"15",
"16"
] | A | A
list of consecutive numbers that does not contain a 'i' in the spelling |
AQUA-RAT | AQUA-RAT-38790 | 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. ... | [
"455",
"570",
"480",
"520"
] | A | Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 182 => 4x/10 = 182
=> 4x = 1820 => x = 455.
ANSWER:A |
AQUA-RAT | AQUA-RAT-38791 | ### 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... | [
"28",
"20",
"27",
"29"
] | B | Average price per book
= (1000+ 800) / (50 + 40)
= 1800 / 90
= Rs.20
Answer:B |
AQUA-RAT | AQUA-RAT-38792 | 29. kc_kennylau
bye
30. anonymous
@aum I thought so. I see how to get the 4 but not the -1 could you help me solve this?
31. aum
My method is what @myininaya suggested. (2x - 3) / (x + 1) < 1 (2x - 3) / (x + 1) - 1 < 0 (2x-3 - x - 1) / (x + 1) < 0 (x - 4) / (x + 1) < 0 The x values that are of interest to us here ... | [
" 3",
" 10",
" 13",
" 16"
] | C | You are asked what the closest lesser integer value to [x] is.
[-11.6] = -12.0
[13.4] = 13.0
[12.7] = 12.0
Therefore , answer is: -12.0 + 13.0 + 12.0 = 13.0
Option A. |
AQUA-RAT | AQUA-RAT-38793 | 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... | [
"28",
"21",
"29",
"27"
] | B | 20 15 5
25 20 8
500 + 300 + 40 = 840/40 = 21
Answer:B |
AQUA-RAT | AQUA-RAT-38794 | Let's compare your method with the correct solution.
Solution: As you noted, either three questions are selected from one section with one each from the other two sections or two questions each are selected from two sections and one is selected from the remaining section.
Three questions from one section and one ques... | [
"50",
"100",
"152",
"150"
] | A | There 3 questions in part A out of which 4 question can be chosen as = 5C3.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 5C4.
Hence, total number of ways,
=5C3*5C4
=[5!/(2!3!)]*[5!/(4!*1)]
= {10}*{5*4!/(4!)}
= 10*5=50.
A |
AQUA-RAT | AQUA-RAT-38795 | Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have
48(35) = 22(38) + 26x
1680 = 836 + 26x
26x = 844
x = 844/26
x = 32 12/26 ≈ 32.5
_________________
Scott Woodbury-Stewart
Founder and CEO
GMAT Quant Self-Study Course
50... | [
"15.5",
"15.4",
"15.25",
"10.4"
] | D | Total age of 20 men = 15.6 x 20 = 312
Now, total age of 25 men = 364.
Total age of five men added later = 364 - 312 = 52.
Hence, the total average of five men = 52/5 = 10.4
ANSWER:D |
AQUA-RAT | AQUA-RAT-38796 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"1:3",
"1:2",
"1:1",
"2:1"
] | B | Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.865
0.9 – 0.1x = 0.865
x = 0.35
Thus ratio of both flours is 1:2
B |
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