source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-39497 | harpazo
#### harpazo
##### Pure Mathematics
Sure you do...you know that the number $$54$$ has a value of $$5\cdot10+4$$, right?
Yes but???
#### MarkFL
##### La Villa Strangiato
Staff member
Moderator
Math Helper
Yes but???
But what? If a number has the two digits from left to right as x and y, then the value of the... | [
"68",
"77",
"95",
"86"
] | A | Explanation :
Let the no. be 10x + y.
No. formed by the interchange of digits = 10y + x
We have y - x = 2 .....(i)
y + x = 14 .....(ii)
Solving (i) and (ii), we get x = 6, and y = 8
∴ the no. is 68.
Answer : Option A |
AQUA-RAT | AQUA-RAT-39498 | 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 ... | [
"14 mph",
"20/3 mph",
"70/3 mph",
"80/3 mph"
] | B | Average speed for first two hours, S1 = 40 mph
Distance travelled in these two hours, D1 = 80 miles
Average speed for the entire 5 hour ride, S = 20 mph
Total Distance traveller in the entire 5 hour ride, D = 20 x 5 = 100 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 100 - 80 = 20
Average ... |
AQUA-RAT | AQUA-RAT-39499 | # If $n$ is a positive integer, does $n^3-1$ always have a prime factor that's 1 more than a multiple of 3?
It appears to be true for all $n$ from 1 to 100. Can anyone help me find a proof or a counterexample?
If it's true, my guess is that it follows from known classical results, but I'm having trouble seeing it.
I... | [
"1",
"2",
"3",
"4"
] | C | We're told that N = 4P and that P is a prime number greater than 1. Let's TEST P = 2; so N = 8
The question now asks how many DIFFERENT positive EVEN divisors does 8 have, including 8?
8:
1,8
4,2
How many of these divisors are EVEN? 2,4,8…..3 even divisors.
ANSWER:C |
AQUA-RAT | AQUA-RAT-39500 | Show Tags
18 Jun 2014, 06:09
Thanks much Bunuel
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The perimeter of square S is 40. Square T is inscribed in square S. [#permalink]
Show Tags
... | [
"20 m",
"24 m",
"28 m",
"40 m"
] | D | Perimeter of square = 4 * Side
Perimeter of first square = 24 m.
Side of first square =
∴ Area of first square =
Perimeter of second square = 32 m.
Side of second square =
∴ Area of second square =
Sum of the areas of two squares = 36 + 64 = 100 m2
∴ Side of square =
∴ Perimeter of square = 4 * 10 = 40 m.
D |
AQUA-RAT | AQUA-RAT-39501 | (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%",
"25%",
"30%",
"35%"
] | B | Price of a gallon of gasoline was $30 on the 15th of March
Price of a gallon of gasoline increased by 20 %so the price on 15th of April = 1.2*30 = $36
Price of a gallon of gasoline was $45 on 15th of May
so there was a increase of $9 from 15th of april to 15 th of may
% increase = 9/36 * 100 = 25 %
Correct answer - B |
AQUA-RAT | AQUA-RAT-39502 | # Thread: Trig. with ratio question
1. ## Trig. with ratio question
Hello,
$\triangle$ABC is an acute triangle and H is the triangle's orthocenter.
Express the ratio of $\triangle$ABH's area to $\triangle$ABC's area through the triangle's angles.
(No sketch is given)
According to the answer key, the answer is suppo... | [
"2:3",
"4:5",
"16:9",
"7:9"
] | C | Sol. Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then,
((1/2) X xX 3h)/(1/2) X y X 4h) =4/3 x/y =(4/3 X 4/3)=16/9
Required ratio = 16 : 9.
Ans: C |
AQUA-RAT | AQUA-RAT-39503 | # How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?
How would I go about solving this math problem?
if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$?
I got $a/c = 2/5$ but that is not a corr... | [
"5/4",
"25/16",
"4/5",
"16/25"
] | D | The area of rectangle A is ab.
c=5a/4 and d=5b/4.
The area of rectangle B is cd=25ab/16.
The ratio of rectangle A's area to rectangle B's area is ab / (25ab/16) = 16/25.
The answer is D. |
AQUA-RAT | AQUA-RAT-39504 | We are given: .a
5 = 120 .and .a6 = 720
Then: .r .= .a
6/a5 .= .720/120 .= .6
. . The "rule" is multiply-by-six.
Therefore, the preceding term is: .a
4 = 20.
See? .We could have eyeballed the problem . . .
5. Originally Posted by Soroban
. . There is a simpler solution.
I always tell my students that I have a ten... | [
"30",
"66",
"77",
"88"
] | A | Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 18
3x = 18 => x = 6
=> Smaller number = 5x = 30.
Answer: A |
AQUA-RAT | AQUA-RAT-39505 | ### Show Tags
23 Dec 2016, 09:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios [#permalink]
### Show Tags
09 Nov ... | [
"27.5 litres",
"26.67 litres",
"27.67 litres",
"28.57 litres"
] | D | Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
49%(1-X/100)^2 = 25% * 100%
(1-x/100)^2=25/49------>(1-x/100)^2=(5/7)^2
100-X=500/7
x=28.57...
Ans D |
AQUA-RAT | AQUA-RAT-39506 | Thanks for any help. I am totally confused.
1. 👍 0
2. 👎 0
## Similar Questions
1. ### Probability
jeff has 8 red marbles, 6 blue marbles, and 4 green marbles that are the same size and shape. he puts the marbles into a bag, mixes the marbles, and randomly picks one marble. what is the probability that the marble ... | [
"5/19",
"9/20",
"1/57",
"15/57"
] | C | It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 6/20
Probability of choosing 2nd card of the same type: 5/19
Probability of choosing 3rd card of the same type: 4/18
Multiply and you get 1/57
Answer C. |
AQUA-RAT | AQUA-RAT-39507 | speed-of-light, measurements, si-units, metrology, length
Title: How is the Length of a Meter Physically Measured? I have two parts to this question.
First, I understand that the meter is defined as the distance light travels in 1/299,792,458 seconds. But how is this distance actually measured? The second is obviously... | [
"45cm",
"5cm",
"4cm",
"15cm"
] | B | Explanation:
Convert first all terms into cm.
i.e. 1265 cm, 1525cm, 1065cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 5.
Option B |
AQUA-RAT | AQUA-RAT-39508 | We're asked for the price at which the TOTAL PROFIT from the sale of these units = $42,000. Since there are 600 units, then each unit has to bring in$42,000/600 = $70 in profit. The COST of each unit is$90, so to hit that total profit, we just need to increase that $90 by$70 on each unit.
$90 +$70 = $160 Final Answer:... | [
"1000",
"3000",
"2000",
"4000"
] | C | C
2000
Let C.P. of each cow be $x and C.P. of each cow be $y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each cow = $2000. |
AQUA-RAT | AQUA-RAT-39509 | In solving many kinematic problems for gears, there is a key rule to key in mind: When two gears are meshing, the tangential velocities of both gears at the point of meshing are equal.
(Also, as said in EMiller's answer, gear C seems to be the smaller orange gear, and gear D the larger yellow gear, contrary to the dia... | [
"49",
"4",
"12",
"6"
] | D | Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 4 :: 21 : x 14 * x = 4 x 21
x = (4 x 21)/14
x = 6.
Answer is D. |
AQUA-RAT | AQUA-RAT-39510 | # 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... | [
"10",
"99",
"87",
"66"
] | A | P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A |
AQUA-RAT | AQUA-RAT-39511 | shortest-path
Description:
Tentative distances to B and D determined. C not yet visible.
Shortest distance from previous step taken. No new information on shortest path to B. Tentative distance to C now known. No new information on D.
We choose to backtrack to A, and then move to D because the distance to D (2) is sm... | [
"15!*8!*7!",
"15!*8*7",
"23!/(8!*7!)",
"15!/(8!*7!)"
] | D | If they need to walk 8 blocks north and 7 blocks east, we can express this route as NNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 15 things is 15!
We then divide by the repetitions of N's and E's, which are 8! and 7! respectively.
The number of walk... |
AQUA-RAT | AQUA-RAT-39512 | fact to find the root. 16 is 4 be multiplied ( or ) divided so that the sum the. Is difficult to find the square root of a number is a number ensure you the. Table below 112−7=105 105−9=96 96−11=85 85−13=72 72−15=57 57−17=40 40−19=21 21−21=0 we have already learnt the square of is... Contribute @ geeksforgeeks.org to r... | [
"1,600",
"16",
"4",
"440"
] | A | A number squared is a number multiplied by itself
Ex) 4 squared is 16 because 4*4=16
The square root of a number is a number, that if squared, would equal the number you're trying to find the square root of.
Ex) What is the square root of 16? The square root of 16=4, so 4 squared equals 16
So to solve this equation you... |
AQUA-RAT | AQUA-RAT-39513 | # 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... | [
"2160",
"3120",
"3972",
"6240"
] | C | Let P = $ 100. Then, S.I. $. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = $ 12000. T = 3 years and R = 10% p.a.
CI = 3972
ANSWER C |
AQUA-RAT | AQUA-RAT-39514 | 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... | [
"18 days",
"20 days",
"26.67 days",
"16 days"
] | B | Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/40).
(1/20)*(x-10) + (1/40)*(x) = 1
(x/20) + (x/40) - (10/20) = 1
3x/40 = 3/2
x = 20
Therefore, the answer is B: 20. |
AQUA-RAT | AQUA-RAT-39515 | # Given an Alphabet, how many words can you make with these restrictions.
I'm trying to understand from a combinatoric point of view why a particular answer is wrong. I'm given the alphabet $\Sigma = \{ 0,1,2 \}$ and the set of 8 letter words made from that alphabet, $\Sigma_8$ . There are $3^8 =6561$ such 8 letter wo... | [
"5040",
"2548",
"300",
"547"
] | A | LOGARITHMS' contains 10 different letters.
Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
= 10P4
= (10 x 9 x 8 x 7)
= 5040.
ANSWER A |
AQUA-RAT | AQUA-RAT-39516 | MHF Helper
Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.
1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0... | [
"1/5",
"1/2",
"2/3",
"1/4"
] | B | x: 0.5% is 0.15%-points from 0.65%.
y: 0.8% is 0.15%-points from 0.65%.
Therefore the ratio of products checked by y:x is 1:1.
Thus, worker y checked 1/2 of the products.
The answer is B. |
AQUA-RAT | AQUA-RAT-39517 | fluid-dynamics, newtonian-gravity
and so, when we put these values into $d=\frac{m}{\rho_W\,C_D\,A}\,\log\left(1+\frac{h_{eff}\,C_D\,A}{m\,\left(\frac{1}{\rho_B}-\frac{1}{\rho_W}\right)}\right)$ we get:
$$\begin{array}{ll}h=1{\rm m}&d = 1.13073{\rm m}\\h=3{\rm m}&d = 1.33494{\rm m}\\h=5{\rm m}&d = 1.48701{\rm m}\\h=7.... | [
"20 cm",
"25 cm",
"33.3 cm",
"50 cm"
] | C | Explanation:
Total volume of water displaced =(4 x 50) m3 = 200 m3
Rise in water level = 200/30×20= 0.333m = 33.3cm
Answer: C |
AQUA-RAT | AQUA-RAT-39518 | Hence, if we eliminate at most $13$ sets of $2$ numbers, then each difference of the $2$ numbers from the remaining $105-13=92$ is distinct. However, the difference of $2$ numbers is either $1,2,\cdots, 88,89(=99-10)$, which is a contradiction. QED
Added : Byron Schmuland and Ross Millikan independently show eleven 2-... | [
"29",
"70",
"92",
"Cannot be determined"
] | D | Explanation:
Let the ten's digit be x and units digit by y.
Then,
(10x + y) - (10y + x) = 63
9(x - y) = 63
x - y = 7
Thus, none of the numbers can be determined.
ANSWER IS D |
AQUA-RAT | AQUA-RAT-39519 | Back
## A Test Question
Today, Pearl’s $9$ grandchildren are coming to visit! She loves to spoil them, so she opens her purse and finds $13$ dollar bills.
In how many different ways can Pearl distribute those dollars amongst her grandchildren? Keep reading to find out, or skip to today’s challenge for a similar prob... | [
"6-5",
"5-4",
"3-6",
"2-3"
] | A | 26/4 = 2 R 5 Mrs. Napier will give each student 6 stickers and there
will be 5 left over.
correct answer A |
AQUA-RAT | AQUA-RAT-39520 | MHF Helper
Problem : A bike manufacturer has a plant in Minneapolis and another in Philly. The Minneapolis plant produces 70% of the bikes, of which 1% are defective. The Philly plant produces the other 30%, of which 0.5% are defective.
1: What percentage of bikes made by this company are defective? a) 1% b) 0.85% c) 0... | [
"165%",
"90%",
"60%",
"55%"
] | C | Trucks = 30% of 300 = 90
Other Vehicles (Excluding Trucks) = 300-90 = 210
Diesel Vehicle = 15% of 300 = 45 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 45-15 = 30
Trucks that are NOT diesel = 90 - 15 = 75
Other Vehicles that are NOT diesel Vehicles = 210-30 = 180
Required % = (180/300)*100 = 60%
Ans... |
AQUA-RAT | AQUA-RAT-39521 | # 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... | [
"2000",
"2098",
"2028",
"2218"
] | A | Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.Answer: A |
AQUA-RAT | AQUA-RAT-39522 | (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 ... | [
"I only",
"III only",
"II,III only",
"I,III only"
] | C | II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6=$58, whi... |
AQUA-RAT | AQUA-RAT-39523 | Alternate
10% of journey's = 40 km
Then, total journey = 400 kms
\eqalign{ & {\text{And,}}\,{\text{Average speed}} \cr & = \frac{{{\text{Total distance }}}}{{{\text{Total time}}}} \cr & 30\% {\text{ of journey}} \cr & = 400 \times \frac{{30}}{{100}} \cr & = 120{\text{ km}} \cr & \cr & 60\% {\text{ of journey}} \cr & =... | [
"60",
"61",
"62",
"63"
] | D | This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
100= 55 + 43 - 61 + (# in Neither Group)
=63
The prompt gives you all of the numbers you ... |
AQUA-RAT | AQUA-RAT-39524 | 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 ... | [
"15 min 8 sec",
"16 min 15 sec.",
"8 min 15 sec.",
"10 min 17 sec."
] | B | s=d/t
where t=d/s
therefore 4000*25/100=1000sec
convert 1000sec into min
we get 16min 15sec
ANSWER:B |
AQUA-RAT | AQUA-RAT-39525 | 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.... | [
"3 9/87 hrs",
"3 9/27 hrs",
"3 9/17 hrs",
"3 2/17 hrs"
] | C | Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer: C |
AQUA-RAT | AQUA-RAT-39526 | 5%------------------20%
so ratio is 1:4 in final mixture
Earlier type 1 alcohol was 1
Now it is 1/5 ----> so loss of 4/5 = 80%...
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 56303
Re: Mixture problem-Can someone explain this [#permalink]
### Show Tags
02 Sep 2010, 08:52
11
14
zest4mba wrote:
I... | [
"1200",
"1300",
"1500",
"1800"
] | D | soap:alcohol
Initial ratio soap:alcohol: water --> 6:30:90
Initial soap:alcohol = 6/30 =6:30
after doubled soap:alcohol =2* 6/30 = 12/30=12:30
Initial soap:water = 6/90=6:90
after halved soap:water: 1/2 * 6/90 = 3/90 = 3:90= 12:360
After soap: alcohol:water --> 12:30:360
given alcohol 150 cubic centimeter.
ratio is 60:... |
AQUA-RAT | AQUA-RAT-39527 | 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... | [
"337",
"278",
"189",
"271"
] | C | CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer:C |
AQUA-RAT | AQUA-RAT-39528 | Then, if we keep doing this, we are going to approach to a vertical line with zero area. If we keep increasing its width while decreasing its height, we will approach to a horizontal line with zero area. So, both of these extreme endpoints give us an area of $$0$$. Therefore, it makes sense to have a rectangle with equ... | [
"15%",
"20%",
"25%",
"30%"
] | C | Sol. Required change = (20*100)/(100-20)=25%
C |
AQUA-RAT | AQUA-RAT-39529 | 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... | [
"41",
"30",
"35",
"60"
] | D | D
60
There is a meal for 200 children.
100 children have taken the meal.
Remaining meal is to be catered to 100 children.
Now, 200 children 120 men.
100 children = (120/200)x 100 = 60 men. |
AQUA-RAT | AQUA-RAT-39530 | You want to end up with exactly 6 gallons in the unmarked container.
(YES: the unmarked container > 6 gallons!)
Your mission is to do it in exactly 9 moves, and using the MINIMUM number of gallons of water
from the water supply.
A "move" is any pouring, filling or emptying.
For example, filling the 9-gal from the wat... | [
"25",
"40",
"64",
"80"
] | B | 7/8x-3/4x=5 galls
1/8*x=5gallons
x=40 gallons
ANSWER:B |
AQUA-RAT | AQUA-RAT-39531 | 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 ... | [
"4zx",
"4z/x",
"4x/z",
"4/xz"
] | B | Speed of Peter = x/4 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/4) = 4z/x
Option B
The values 100m and 200m have no role to play here and are just given to confuse you. |
AQUA-RAT | AQUA-RAT-39532 | ### 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... | [
"$2000",
"$1200",
"$2500",
"$1800"
] | B | B's share = 3600*3/9 = $1200
Answer is B |
AQUA-RAT | AQUA-RAT-39533 | ### 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... | [
"4 % decrease",
"12.5 % increase",
"16% decrease",
"16% increase"
] | B | Net% change in revenue
= ( x + y + xy/100) %
= [-25 + 50+ ( -25 x 50)/100]% or 12.5%
ANSWER:B |
AQUA-RAT | AQUA-RAT-39534 | ### Show Tags
12 Nov 2013, 20:38
I solved by thinking about how you find the sum of a series of numbers; average of that set multiplied by how many numbers are in the set. Noting that it was only even numbers in the set A-C could be eliminated since their sums would be FAR too small. From there I thought about how man... | [
"12.8",
"24.2",
"54.6",
"72.1"
] | C | arithmetic mean = sum / total numbers
sum = 47.1 * 8 = 376.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 376.8-158.4 = 218.4
Arithmetic mean of the 4 nos = 218.4/4 = 54.6
Hence, C is the answer. |
AQUA-RAT | AQUA-RAT-39535 | # Permutations of the word $\text{TRIANGLE}$ with no vowels together.
First of all, $$\text{TRIANGLE}$$ has $$8$$ distinct letters, $$3$$ of which are vowels($$\text{I, A, E}$$) and rest are consonants($$\text{T, R, N, G, L}$$).
While attempting this, I came up with the idea of putting alternate vowels and consonants... | [
"None of these",
"64",
"120",
"36"
] | D | Explanation :
The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions.
Let's mark the positions as (1) (2) (3) (4) (5) (6).
Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to ar... |
AQUA-RAT | AQUA-RAT-39536 | ## anonymous 5 years ago 100 people are present in a party. If each of them must do a handshake with all the other people, how many handshakes should be done? Please explain how to get the answer, thanks!
1. anonymous
you need 2 people for an hand shake and u have 100 people so i think that its C(100,2) but i am not ... | [
"10",
"15",
"3",
"9"
] | C | the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 3(3-1)/2 = 3*2/2 = 6/2 = 3
=> the answer is C(3) |
AQUA-RAT | AQUA-RAT-39537 | # probability of the 3rd pick is a boy
10 students are in a class,
4 of these students are boys and 6 are girls
the teacher wanted to randomly select 3 students to represent the class in an event
what is the probability that the 3rd student is a boy?
Here is what I have tried
the probability of that 1st student i... | [
"2/165",
"4/165",
"7/165",
"2/33"
] | B | The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 4C3=4.
P(only girls are chosen)=4/165
The answer is B. |
AQUA-RAT | AQUA-RAT-39538 | # 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... | [
"2000",
"2978",
"2682",
"2688"
] | A | (10*10)/100 = 1%loss
100 --- 99
? --- 1980 =>
Rs.2000
Answer:A |
AQUA-RAT | AQUA-RAT-39539 | # If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
Let $f(x)$ be a function such that $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$. Then for what value of $k$ is the relation $f(x + k) = f(x)$ necessarily true for every real $x$?
The answer/solution... | [
"125",
"977",
"289",
"1077"
] | A | Let x =1 and y = 1
f(1 + 1) = f(1) + f(1) + 7 x 1 x 1 + 4 ⇒⇒ f(2) = 19
Let x =2 and y = 2
f(2 + 2) = 19 + 19 + 7 x 2 x 2 + 4 ⇒⇒ f(4) = 70
Let x = 1 and y = 4
f( 1 + 4) = 4 + 70 + 28 + 4 = 106
f(2) + f(5) = 125
Answer:A |
AQUA-RAT | AQUA-RAT-39540 | (A) 1
(B) 2
(C) 4
(D) 6
(E) 8
11. What is the area of the shaded region of the given 8 X 5 rectangle?
The following is multiple choice question (with options) to answer.
The perimeter of a square is 52 m. Find the area of the square. | [
"132 m².",
"169 m².",
"146 m².",
"189 m²."
] | B | Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m² = 169 m².
ANSWER :B |
AQUA-RAT | AQUA-RAT-39541 | => 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... | [
"12.5%",
"20%",
"25%",
"50%"
] | C | Assume
Hours Worked: 10 hours
Hourly Wage: 10 $
Weekly Wage: 100 $
After decrease of 20 % in Hourly Wage would become 8 $
Hours Worked would have to be 12.5 hours in order to maintain Weekly Wage of 100 $
% increase in number of hours worked = (12.5 - 10 ) / 10
= 0.25 * 100
= 25%
Answer is C |
AQUA-RAT | AQUA-RAT-39542 | --------------
Back to your question, after finding the 2 breakpoints, namely 0, and 1. We then, split it into 3 different parts:
1. x < 0:
When x < 0, x is negative, right? So |x| = -x
When x < 0, x - 1 is also negative, right? So |x - 1| = -(x - 1) = -x + 1
So, when x < 0, your function will be (without absolute ... | [
"-x/-y",
"x/y",
"-x/y",
"2xy"
] | C | - / + = -
Answer : C |
AQUA-RAT | AQUA-RAT-39543 | Since the the percentage of tagged fish in the second catch approximates the percentage of tagged fish in the pond, the approximate number of fish in the pond is:
0.04(total fish) = 50
This equation assumes that there are 50 fish tagged in the total population. We do not know that. The only thing we know is that that... | [
"1200",
"1300",
"1400",
"1500"
] | D | Let x be the number of eggs that were laid.
(2/5)(4/5)(1/4)x = 120
(8/100)x = 120
x = 1500
The answer is D. |
AQUA-RAT | AQUA-RAT-39544 | Veritas Prep Reviews
Math Expert
Joined: 02 Sep 2009
Posts: 37109
Followers: 7252
Kudos [?]: 96499 [0], given: 10752
### Show Tags
05 Jun 2013, 23:44
PKPKay wrote:
Sarang wrote:
For 1 hour-
Machine A rate- 2000 envelopes
Machine B+C rate- 2400 envelopes
Since A + C = 3000 envelopes A's rate is 2000 envelopes as ab... | [
"14",
"15",
"16",
"18"
] | C | 40 printing presses can do 1/12 of the job each hour.
30 printing presses can do 3/4*1/12 = 1/16 of the job each hour.
The answer is C. |
AQUA-RAT | AQUA-RAT-39545 | 98% Female, simple interpolation. First premise 90% female, leaves 10%, second premise only leaves 2% of the existing 10%, hence 98% female
-
The following is multiple choice question (with options) to answer.
10 % of 2 is equal to | [
"0.2",
"0.4",
"0.6",
"0.7"
] | A | 10 % of 2 = (10 / 100) * 2 = 0.2
Answer: Option A |
AQUA-RAT | AQUA-RAT-39546 | 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 years",
"2 years",
"3 years",
"4 years"
] | B | Sol.
Total age of 5 members, 3 years ago = (17 x 5)years = 85 years.
Total age of 5 members now = (85 + 3 x 5)years = 100 years.
Total age of 6 members now = (17 x 6)years = 102 years.
∴ Age of the baby = (102 - 100)years = 2 years
Answer B |
AQUA-RAT | AQUA-RAT-39547 | 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... | [
"20 paise",
"65 paise",
"56 paise",
"87 paise"
] | A | Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 50 : x
250 * x = (100 * 50)
x = (100 * 50) / 250
x = 20
ANSWER: A |
AQUA-RAT | AQUA-RAT-39548 | 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.
. .... | [
"30",
"32",
"31",
"33"
] | B | Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2*2=2^5=32.
Answer: B. |
AQUA-RAT | AQUA-RAT-39549 | 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$$ (from the initial 90... | [
"227",
"266",
"230",
"500"
] | D | Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 50/3
3(x + 300) = 2400 è x = 500m.
Answer: D |
AQUA-RAT | AQUA-RAT-39550 | c#, beginner, io
Example run:
Welcome to Buzzway Subs!
May I take your order?
Catering Menu:
Sandwich Platter: $39.99
Cookie Platter: $19.99
Purchase how many of Sandwich Platter for $39.99 each?
1
Purchase how many of Cookie Platter for $19.99 each?
2
Subtotal: 79.97
Tax: 4.80
Total: 84.77
Your total due is $84.77... | [
"$40 and $42",
"$39 and $41",
"$38 and 40",
"$37 and $39"
] | B | let tip=t
meal cost=35.50
range of tip = from 10% of 35.5 to 15% of 35.5 = 3.55 to 5.325
hence range of amount paid= 35.5+T= 39.05 to 40.825
ANSWER:B |
AQUA-RAT | AQUA-RAT-39551 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"16 2/3%",
"30%",
"33 1/3%",
"33 1/6%"
] | C | Explanation:
675 ---- 225
100 ---- ? => 33 1/3%
ANSWER IS C |
AQUA-RAT | AQUA-RAT-39552 | javascript
Title: More efficient version of an ID calculator in JavaScript The following function takes two numbers that are linked with a "user" and calculates an ID number based on that. I have been trying to make this as clean as possible, and would like some advice on how to make this more efficient. an example of... | [
"75142",
"64851",
"5149",
"69993"
] | D | (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
D) |
AQUA-RAT | AQUA-RAT-39553 | or two consecutive tails ($TT$) are observed. What is the probability that three of those selected are women? Two standard dice with 6 sides are thrown and the faces are recorded. $$P(A \cup B\cup C)=a+b+c-ac-bc=\frac{11}{12}.$$ two previous problems. $GG$ from $\frac{1}{3}$ to about $\frac{1}{2}$. Compare your Example... | [
"215/216",
"216",
"1/216",
"none"
] | A | the die has 6 sides and it was rolle 3 times, then 6*6*6=216
the number of ways to get 4 is 1
then 1/216
the probability would be
1-1/216=215/216
Answer A |
AQUA-RAT | AQUA-RAT-39554 | 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... | [
"18",
"19",
"20",
"21"
] | A | A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 1/12 work in 1 day...
They did 2/3 w... |
AQUA-RAT | AQUA-RAT-39555 | # 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... | [
"8499.98",
"8489.98",
"8412.98",
"8732.98"
] | C | Explanation:
Ratio of their shares = 31,000 : 36,800 = 155 : 184.
Mark's share = Rs. (18400 * 155/339) = Rs. 8412.98.
Answer: C) 8412.98 |
AQUA-RAT | AQUA-RAT-39556 | 12:14 AM
@MatheinBoulomenos nice
12:25 AM
quick question... IF we have eight people showing up for free concert tickets and we want to figure out how many ways can exactly 3 of them get tickets, isn't that just 8 choose 3 or $\binom{8}{3}$?
yes
ok so if we wanted to find out how many subsets of size k are there from... | [
"1/8",
"1/3",
"1/2",
"1/4"
] | C | Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)
=... |
AQUA-RAT | AQUA-RAT-39557 | They're compounding this much every day, so if I were to write this as a decimal ... Let me just write that as a decimal. 0.06274%. As a decimal this is the same thing as 0.0006274. These are the same thing, right? 1% is .01, so .06% is .0006 as a decimal. This is how much they're charging every day. If you watch the c... | [
"$1,400",
"$1,800",
"$4,000",
"$21,400"
] | C | Original amount = 50,000
Fine for July = 50,000 * 1% = 500
Fine for August = lesser of the 2 , 500+1000= 1500 or 500*2=1000 . Pick 1000
Fine for September = 1000+1000=2000 or 1000*2 = 2000. Pick 2000
Fine for October = 2000+1000=3000 or 2000*2 = 4000. Pick 4000.
The wording of the question should be have been clearer a... |
AQUA-RAT | AQUA-RAT-39558 | earth
Well, lets look at the values returned compared to days in a non-leap year:
Month N1 Day Diff
1. 30 31 -1
2. 61 59 +2
3. 91 90 +1
4. 122 120 +2
5. 152 151 +1
6. 183 ... | [
"s.2900",
"s.3570",
"s.4500",
"s.4550"
] | A | Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8900
= 35600 ----(2)
(2)-(1) i.e. May - Jan =3600
Salary of May is Rs.6500
Salary of January = Rs.2900
Answer:A |
AQUA-RAT | AQUA-RAT-39559 | # What is the largest integer value of $n$ for which $8^n$ evenly divides $(100!)$?
I know that this may be an unnecessary question, but I am a bit confused. The problem asks for the highest integer $$n$$ such that $$8$$ to the power of $$n$$ is divisible, evenly of course, by $$100$$. Now, I searched the site, and, i... | [
"6",
"12",
"24",
"36"
] | B | Q: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer W that must divide n is:
A 6, B 12, C 24, D 36, E 48
n^2 is divisible by 72, but it must also be greater than 72. If n is an integer, then n^2 must be a perfect square. The factorization of 72 is (8)(9), so if it is multiplied b... |
AQUA-RAT | AQUA-RAT-39560 | ### 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... | [
"560",
"561",
"562",
"571.6"
] | D | Total price of 8 t-shirts= 8*530=4240
Total price of 5 t-shirts=5*505=2525
Total price of 3 t-shirts=4240-2525=1715
Average price of 3 t-shirts=1715/3=571.6
Correct option Answer:D |
AQUA-RAT | AQUA-RAT-39561 | # Linear Algebra Money Question
bleedblue1234
## Homework Statement
I have 32 bills in my wallet in the denominations $1,$5, and $10, worth$100 in total. How many of each denomination do I have?
## Homework Equations
A= # $1 bills B= #$5 bills
C= # $10 bills A+B+C = 32 1A+5B+10C = 100 ## The Attempt at a Solution ... | [
"90",
"94",
"96",
"97"
] | A | Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
A |
AQUA-RAT | AQUA-RAT-39562 | 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... | [
"21:22",
"13:17",
"15:43",
"11:18"
] | D | Let the number of boys and girls be 2x and 3x
their increased number is 110% of 2x and 120% of 3x
2x*110/100 and 3x*120/100
11x/5 and 18x/5
Required ratio = 11x/5 : 18x/5 = 11:18
Answer is D |
AQUA-RAT | AQUA-RAT-39563 | 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}$$ job/day... | [
"56",
"48",
"30",
"40"
] | B | B = 1/16 – 1/24 = 1/48 => 48 days
ANSWER B |
AQUA-RAT | AQUA-RAT-39564 | in n yrs and A 2 in (n+1) yrs, then Rate of compound interest =(A 2 - A 1)/A 1 *100% Sum = A 1 (A 1 /A 2) n. 596 APPENDIXC:COMPOUNDINTERESTTABLES 1/2% CompoundInterestFactors 1/2% SinglePayment UniformPaymentSeries ArithmeticGradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund ... | [
"2999",
"2770",
"2708",
"2000"
] | D | P(11/10)4 - P(6/5)2 = 482
P = 2000
Answer: D |
AQUA-RAT | AQUA-RAT-39565 | Question
# Three natural numbers are taken at random from a set of numbers $$\left \{ 1, 2, .... 50 \right \}$$.The probability that their average value taken as $$30$$ is equals
A
30C289C2
B
89C250C47
C
89C8750C3
D
None of these
Solution
The following is multiple choice question (with options) to answer.
Find the ... | [
"8",
"9",
"10",
"11"
] | C | Average of the first 'n' natural numbers = (n + 1)/2
We get (19 + 1)/2 = 10
ANSWER:C |
AQUA-RAT | AQUA-RAT-39566 | # Minimum tickets required for specified probability of winning lottery
In a lottery, 1/10 of the 50 000 000 tickets give a prize.
What is the minimum amount of tickets one should buy to have at least a 50% chance to win?
Would be very glad if you could explain your methodology when resolving this. Please consider t... | [
"Alice should get $13,000; Bob should get $11,000",
"Alice should get $16,000; Bob should get $8,000",
"Alice should get $17,000; Bob should get $7,000",
"Alice should get $17,500; Bob should get $6,500"
] | B | A = $8
B = $4
A share 8 parts & B share 4 parts
Total 12 parts -----> $24000
----> 1 part -------> $2000
A share = 8 parts -----> $12000
B |
AQUA-RAT | AQUA-RAT-39567 | solution: solution to get the median: the mean compared to sets a mean questions with solutions b Question! To new CBSE exam Pattern, MCQ questions for Class 10to help you are presented 6 ICSE.. A- a ; each being equal to the common difference we will help you sum must 12! Step 3: the given mean of a set of numbers dee... | [
"12",
"14",
"16",
"8"
] | B | set {1, 2, 9}
Mean = (1+2+9)/3 = 4
Meadian = Middle term = 2
Range = Highest - Lowest = 9-1 = 8
Mean+Median+Range = 4+2+8 = 14
Answer: Option B |
AQUA-RAT | AQUA-RAT-39568 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"42",
"27",
"28",
"20"
] | B | Explanation:
Distance covered = 120+120 = 240 m
Time = 16 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/16 = 15 m/s
Speed of each train = v = 15/2 = 7.5 m/s
= 7.5×36/10 km/hr = 27 km/hr
Answer: Option B |
AQUA-RAT | AQUA-RAT-39569 | distance from a given point called centre. You can use the formula for the volume of a cylinder to find that amount! In this tutorial, see how to use that formula and the radius and height of the cylinder to find the volume. As you can imagine, as the discs become thinner, the volume of the sphere gets more accurate. (... | [
"24.",
"28.",
"36.",
"42."
] | A | Diameter of tube= 5 inches
Height of wooden tube= 15 inches
Two tubes can stand in 31 inches height
Two tubes can fit in 11 inches length
Two tubes can fit in 10 inches width
So, one box can hold 8 tubes
Three boxes can hold= 8*3= 24 tubes
A is the answer |
AQUA-RAT | AQUA-RAT-39570 | # Math
How do you divide fractions???
Cross multiply:
For example, 4/5 divided by 6/7 would be 28/30 or 14/15.
3/4 divided by 2/3 would be 9/8 or 1 and 1/8
Actually, the word cross multiply is a misnomer. What is being done is multiplying by the reciprocal
for instance 4/5 divide by 6/7 is the same as 4/5 multipl... | [
"17/36",
"36/17",
"17/6",
"17/1"
] | D | 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/4 - 1/6 = (6-4)/24 = 2/24 = 1/12
So 17/12/1/12 = 17/12 * 12 = 17/1
Answer - D |
AQUA-RAT | AQUA-RAT-39571 | If stock price is $$X = (0,30)$$; we use the 7 puts (A) for profit = 7(40 - X); 9 (B) puts are used giving a loss = 9(30 - X). Total earning = 7(40-X) -9(30-X) + 2$= 2X + 12$ > 0
- 3 years, 2 months ago
Assume that the $40 put is still priced at$10.
What would be the price of the $30 put option, where there will be ... | [
"Rs. 8,751",
"Rs. 8,571",
"Rs. 9,751",
"Rs. 9,571"
] | B | Solution: X : Y : Z = (8,000 * 36) : (12,000 * 36) : (20,000 * 27) = 8 : 12 : 15.
So B's share = Rs. (20000 * 15/35) = Rs. 8,571.
Answer: Option B |
AQUA-RAT | AQUA-RAT-39572 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. .... | [
"11",
"22",
"77",
"33"
] | C | Add the numbers of highlighters.
24 + 28 + 25 =77.
Answer is C. |
AQUA-RAT | AQUA-RAT-39573 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"48",
"9",
"7",
"67"
] | A | :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125
= 48 sec.
Answer: A |
AQUA-RAT | AQUA-RAT-39574 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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... | [
"140",
"135",
"150",
"170"
] | B | Speed=(54x5/18)m/sec = 15 m/sec.
Length of the train = (Speed x Time).
Length of the train = (15 x 9)m = 135 m.
Answer is B. |
AQUA-RAT | AQUA-RAT-39575 | # 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... | [
"Rs.20043.94",
"Rs.20043.99",
"Rs.20043.91",
"Rs.20043.92"
] | A | Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A |
AQUA-RAT | AQUA-RAT-39576 | Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.
Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.
Back to the problem:
From F.S 1, ... | [
"5",
"15",
"20",
"21"
] | A | When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 60
So, the sum of ALL 5 integers = (60)(5) =300
The average of three of the integers is 65
So, the sum of the 3 integers = (65)(3) =19... |
AQUA-RAT | AQUA-RAT-39577 | Or, 1 = $154/4 And Total pay = 154/4*18 =>$ 693
Hence answer will be (E) $693 The wage difference is not with respect to time , correct approach will be with respect to work done.. ( Errorr is highlighted in red ) Further explanation as provide to you via PM Wages/Salary can be of 2 types ( Something You will certainl... | [
"$1.40",
"$2.40",
"$3.40",
"$4.40"
] | C | Manager wages per hour = $8.50
Dishwasher wages per hour = half of manager's wages. = 1/2($8.50) ==> $4.25
Chef wages per hour = 20% greater than Dishwasher wages
--> 20% of $4.25 = (20*($4.25)) /100
--> ($85)/100
--> $0.85
Therefore,
Chef wages per hour = $4.25 + $0.85 ==> $5.10
Difference of wages between manager and... |
AQUA-RAT | AQUA-RAT-39578 | Hint: You may suppose, w.l.o.g. that $$|x-2|<\frac12$$, in which case $$|x-1|>\frac12$$, so that $$\left|\frac{x-2}{x - 1}\right| <2|x-2|.$$
$$\delta<\min(1,\varepsilon)/2$$ should do the job.
The following is multiple choice question (with options) to answer.
If y exceeds x by 25%, then x is less than y by? | [
"21%",
"29%",
"20%",
"80%"
] | C | X=100 y=125
125--------25
100--------? => 20%
Answer:C |
AQUA-RAT | AQUA-RAT-39579 | human-biology, cancer, medicine
Title: Why are only few cigarette smokers prone to cancer? It's tacit that only a few populace of smokers get cancer. What spares the others from it or what specifically cause cancer in those populace? See this Washington Post Article Cigarette smokers are most certainly prone to cancer... | [
"20%",
"80%",
"90%",
"75%"
] | B | Statement: 60% of People Surveyed (PS) Admitted to being Smokers (AS). Of the people who took the survey who were Smokers (S), 25% declined to admit to being smokers (notAS). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
PS = 100%
AS/PS = 60%
notAS/S = 25% => 100% - 25% => A... |
AQUA-RAT | AQUA-RAT-39580 | 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... | [
"65 hrs",
"16 hrs",
"88 hrs",
"55 hrs"
] | B | 1/20 + 1/30 = 1/12
1 + 1/3 = 4/3
1 --- 12
4/3 --- ?
4/3 * 12 = 16 hrs
Answer:B |
AQUA-RAT | AQUA-RAT-39581 | for full-screen mode. TRIG WHEEL 1. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. Interested in seeing how well you grasp a specific area of trigonometry? Take Study. 11 mm into kilometers and divided. They are going to start the chapter on graphing trigonometric functions on ... | [
"5,280(x/y)",
"5,280(y/z)",
"5,280(xy)",
"5,280/(xy)"
] | B | In one hour, at the rate of y miles per hour, Ben covers y miles, so 5,280y feet.
The number of revolutions = distance/circumference = 5,280y/z.
Answer: B. |
AQUA-RAT | AQUA-RAT-39582 | In $2x^3- 3x^2+ a+ 1= 0$, there are either one or two sign changes depending upon whether a+ 1 is positive or negative. If a< 1, so that a+ 1 is negative, the signs are "+, -, -" so there is one sign change and exactly one positive root. If a> 1, so that a+ 1 is positive, the signs are "+, -, +" so there are two sign c... | [
"a/2",
"a",
"3a/2",
"a^2"
] | D | one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = 2a
c= b
a = 1
substituting these values in 1, we have
2^2*a^2 = 4b => b =a^2
Answer is D. |
AQUA-RAT | AQUA-RAT-39583 | # 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... | [
"587",
"679",
"740",
"860"
] | C | CP = SP + 1CP = SP - g
620 + x = 980 - 2x
3x = 360 => x
= 120
CP = 620 + 120
= 740
Answer:C |
AQUA-RAT | AQUA-RAT-39584 | • so $x=12$ or $x=-14$
Let $$\mathbb S$$ be a set of all even integers, i.e:
$$\mathbb S = \{x | x = 2k, k\in \mathbb Z \}$$
Suppose we have two consecutive elements $$x_1$$ and $$x_2$$ in the set $$\mathbb S$$, i.e:
$$x_1 = 2k$$ ...(1)
$$x_2=2k+2$$ ...(2)
...such that their product is 168, i.e:
$$(2k)(2k+2)=168... | [
"23",
"24",
"25",
"26"
] | C | Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 13+12 = 25.
The answer is C. |
AQUA-RAT | AQUA-RAT-39585 | 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... | [
"27 seconds",
"29 seconds",
"40 seconds",
"11 seconds"
] | C | Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C |
AQUA-RAT | AQUA-RAT-39586 | (1) $$a^2+b^2>16$$
Doesn't tell us about the value of a. a could be 2 or 10 or many other values.
(2) a=|b|+5
a is 5 or greater since |b| is at least 0. This tells us that 'a' does not lie between -4 and 4. Hence this statement is sufficient to answer the question.
_________________
Karishma
Veritas Prep | GMAT Inst... | [
"0 and 1",
"1 and 2",
"2 and 3",
"3 and 4"
] | D | for the greatest possible value of B^4, we must minimize the value of B^4 i.e. lets say A^4 = 0
then we need to find a number B such that B^4 < 100. 3^4 = 81 and 4^4 = 256 so we can say that the maximum possible value of B can be a little more than 3 hence answer = between 3 and 4
hence D |
AQUA-RAT | AQUA-RAT-39587 | 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... | [
"2400",
"2550",
"5050",
"6275"
] | A | Set A contains 4 , 6 ... 50
Set B contains 104 , 106 ... 150
Number of terms in each set = 24
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*24 = 2400
Answer A |
AQUA-RAT | AQUA-RAT-39588 | Less rigorous and mathematical, but perhaps more intuitive approach:
(a) note that for each girl,
there is no relationship at all between the number whispered and the number said; they are parts of different cycles.
(b)
in the group of girls we care about, the thought-of numbers averaged to $[1, 3, 5, 7, 9]$.
(c)
... | [
"9",
"8",
"7",
"6"
] | A | 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Answer: A |
AQUA-RAT | AQUA-RAT-39589 | # 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... | [
"5(5/19)",
"5(1/5)",
"5",
"4(1/19)"
] | A | Solution: Sell sugar = 950g instead of 1000g.
Profit in Sugar = 1000 - 950 = 50g.
Now, % profit = (50*100)/950 = 5(5/19)%.
Short-Cut
% profit = (Goods left/Goods sold)*100.
= (50/950)*100 = 5(5/19)%.
Answer: Option A |
AQUA-RAT | AQUA-RAT-39590 | (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 ... | [
"28%",
"32%",
"36%",
"40%"
] | B | Let x be the number of stamps in the original collection.
The percentage of the collection given away is:
0.2x + 0.15(0.8x) = 0.2x + 0.12x = 0.32x = 32%
The answer is B. |
AQUA-RAT | AQUA-RAT-39591 | 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... | [
"33",
"18",
"21",
"12"
] | A | Present age of total members = 6 X 40 = 240
7 yrs back their ages were = 6 x 7 = 42
Ages at the birth of youngest member = 240 - 42 = 198
Therefore, avg age at the birth of youngest member = 198/6 = 33.
ANSWER:A |
AQUA-RAT | AQUA-RAT-39592 | If $\displaystyle H(x)=\frac{2x\sin\alpha}{[x^2-2x\sin\alpha+1][x^2+2x\sin\alpha+1]},$
$$H(-x)=\frac{2(-x)\sin\alpha}{[(-x)^2-2(-x)\sin\alpha+1][(-x)^2+2(-x)\sin\alpha+1]}$$
$$=\frac{-2x\sin\alpha}{[x^2+2x\sin\alpha+1][x^2-2x\sin\alpha+1]}=-H(x)$$
The following is multiple choice question (with options) to answer.
If ... | [
"-2.4",
"0.268",
"1.166 repeating",
"4.555 repeating"
] | D | x is an integer, which of the following is a possible value of H=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.... |
AQUA-RAT | AQUA-RAT-39593 | (A) 9
(B) 12
(C) 18
(D) 24
(E) 27
Weight of 2nd piece = 4 pound
Since the weight is directly proportional to the square of its length., we may write
$$\frac{16}{36^2}$$ = $$\frac{4}{x^2}$$
Solving above, we get x = 18
_________________
If you like the post, show appreciation by pressing Kudos button
Director
Joined... | [
"10",
"20",
"88",
"77"
] | A | 1: 2/5 = 5: 2
2/7 * 35 = 10
Answer: A |
AQUA-RAT | AQUA-RAT-39594 | # Clock losing time puzzle
The question goes as:
A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. The table clock loses 5 minutes in the 1st hour, 10 minutes in the second hour and ... | [
"12:54:40 AM",
"12:56:24 AM",
"01:16:40 PM",
"12:54:24 AM"
] | D | Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 12:54:24 am (A... |
AQUA-RAT | AQUA-RAT-39595 | 0.00698 acre1 acre = 43560 square feet304 sq ft * 1 acre/43560 sq ft = 0.00698 acre
### Number of sq ft per acre?
1 sq mi=5280ft x 5280ft = 27878400 sq ft/sq mi/ 27,878,400 sq ft/sq mi divided by 640acres/sq mi = 43,560 sq ft /acre 1 acre = 43,560 sq ft
### How many square feet are in 1.8 acre?
1 acre = 43,560 sq f... | [
"$5,330",
"$3,360",
"$450",
"$360"
] | C | Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 450(C) |
AQUA-RAT | AQUA-RAT-39596 | 1111121, 1111202, 1111211, 1112002, 1120002, 1120012, 1120102, 1121002, 1121102, 1122002, 1200002, 1200012, 1200102, 1200112, 1200202, 1201002, 1201012, 1202002, 1210002, 1210102, 1210202, 1211002, 1212002, 1220002, 1220102, 2000002, 2000012, 2000022, 2000102, 2000112, 2000122, 2000202, 2000212, 2001002, 2001012, 20010... | [
"1",
"11",
"21",
"31"
] | D | 1+10=11
11+10=21
21+10=31
ANSWER:D |
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