source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38497 | ### Show Tags
19 Aug 2015, 01:34
2
KUDOS
1
This post was
BOOKMARKED
Let's assume that the total no. of people is n and the initial average is x.
So we can assume that the total sum of ages would be nx initially.
When the guy aged 39 is added to the total, the new sum of ages would be (nx+39). The new average now wo... | [
"2 years",
"4 years",
"8 years",
"16 years"
] | D | Explanation :
Age decreased = (8 x 2) years
16 years
So, required difference =16 years.
Answer : D |
AQUA-RAT | AQUA-RAT-38498 | the probability of getting exactly two (3 Marks) heads. (i) If two coins are tossed simultaneously, there are three possible outcomes, two heads, two tails or one of each. A fair coin is flipped three times in row. X is the number of trials and P(x) is the probability of success. Show that, if the coin is thrown Il-tim... | [
"2^8",
"2^10",
"3 * 2^8",
"3 * 2^9"
] | A | Fix the first coin as H. The remaining8 coins have 2^8 outcomes.
Ans:A |
AQUA-RAT | AQUA-RAT-38499 | # 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... | [
" 736",
" 768",
" 792",
" 840"
] | D | three letters can be arranged in 3! ways.
only one combination EIU is required.
7 letters can be arranged in 7! ways.
thus W=7!/ 3! * 1 = 840.
D |
AQUA-RAT | AQUA-RAT-38500 | 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... | [
"4 min",
"2 min",
"8 min",
"3 min"
] | D | S = 600/30 = 20 mps
S = 3600/20 = 180 sec = 4 min
Answer: D |
AQUA-RAT | AQUA-RAT-38501 | # 2008 AMC 12A Problems/Problem 17
## Problem
Let $a_1,a_2,\ldots$ be a sequence determined by the rule $a_n=a_{n-1}/2$ if $a_{n-1}$ is even and $a_n=3a_{n-1}+1$ if $a_{n-1}$ is odd. For how many positive integers $a_1 \le 2008$ is it true that $a_1$ is less than each of $a_2$, $a_3$, and $a_4$?
$\mathrm{(A)}\ 250\q... | [
"85",
"87",
"89",
"93"
] | A | a1=1
a2=1
a3=1*4+1=5
a4=5*4+1=21
a5=21*4+1=84+1=85
85 |
AQUA-RAT | AQUA-RAT-38502 | (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 ... | [
"$29,660",
"$29,680",
"$29,700",
"$29,720"
] | C | The car was sold for (0.9)(1.1)($30,000)=$29,700.
The answer is C. |
AQUA-RAT | AQUA-RAT-38503 | # an exam has 50 multiple choice questions with 5 options
An exam has 50 multiple choice questions. Each question has five answer options and each question has 2 grades A-. Assuming that "a student" has no prior knowledge and randomly guess on all questions exam,
1. Compute the expected mean for the student score
2. ... | [
"12",
"25",
"28",
"245"
] | B | 39x = 5 + 12 + 15 + 19 + (x – 4)44
x = 25
Answer: B |
AQUA-RAT | AQUA-RAT-38504 | Assuming the girls have sat down, they leave 3 gaps between them. 1 for each boy. Thus the first boy can pick between 3 chairs, the second boy 2 chairs, and the third doesn't get to pick. So there are $3\cdot 2=3!=6$ ways the boys can sit. Now the girls are a little bit more tricky. Notice that it isn't specified how t... | [
"600",
"720",
"1440",
"4320"
] | A | A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly... |
AQUA-RAT | AQUA-RAT-38505 | ## (i)AB, BC and AC are tangents to the circle at E, D and F.$$BD = 30 cm,DC = 7 cm,\angle BAC = 90$$From the theorem stated,$$BE = BD = 30 cm$$Also $$FC = DC = 7 cm$$Let $$AE = AF = x$$ …. (1)Then $$AB = BE + AE = (30 + x)$$$$AC = AF + FC = (7 + x)$$$$BC = BD + DC = 30 + 7 = 37 cm$$Consider right trianlge ABC, by Pyth... | [
"18",
"19",
"20",
"21"
] | C | AC = 11 and AB = 5, so BC = 6.
BC = 3CD so CD = 2.
The length of AE is AB+BC+CD+DE = 5+6+2+7 = 20
The answer is C. |
AQUA-RAT | AQUA-RAT-38506 | algorithms, optimization
but I still want all items to have 25% share.
Assuming amount can be decimal, how do I find the optimal way of rebalancing this portfolio back to 25% shares? How to determine how many of each item to sell so we won't have to buy it back again (sell everything and spend 25% on each item is not ... | [
"42.88$",
"43%",
"45%",
"45.5%"
] | A | (100%+52%)*(100%-6%) = 152*0.94 = 142.88% an increase of 42.88%
Your gold holdings have increased in value by 42.88%.
The Answer is A |
AQUA-RAT | AQUA-RAT-38507 | # another probability: number of ways for 4 girls and 4 boys to seat in a row
4 posts / 0 new
Ej-lp ACayabyab
another probability: number of ways for 4 girls and 4 boys to seat in a row
In how many ways can 4 girls and 4 boys be seated in a row containing 8 seats if boys and girls must sit in alternate seats?
The ans... | [
"720",
"1720",
"2880",
"6"
] | D | Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6.
Answer: D. |
AQUA-RAT | AQUA-RAT-38508 | 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... | [
"Rs.195",
"Rs.180",
"Rs. 98",
"Rs. 120"
] | D | Let each one’s share is A,B and C respectively, then
B =125A/100 = 120C/100
A =100B/125 =4/5B, C = 100B/120 = 5/6B
4/5B +B +5/6B =395, 79B/30 =395, B =395*30/79 =150
A = 4*150/5 = 120
ANSWER:D |
AQUA-RAT | AQUA-RAT-38509 | # Another probability question from my textbook
Suppose that we have a tennis tournament with 32 players. Players are matched in a completely random fashion, and we assume that each player always has probability 1/2 to win a match. What is the probability that two given players meet each other during the tournament.
... | [
"99 matches.",
"88 matches.",
"49 matches.",
"66 matches."
] | C | Solution:
49 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 49 matches were played.
Answer C |
AQUA-RAT | AQUA-RAT-38510 | 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... | [
"70 kmph",
"120 kmph",
"60 kmph",
"Data Inadequate"
] | A | Let, speed of car from A towards B = x km/hr
Let, speed of car from B towards A = y km/hr
Two cars start at same time which 120km apart = x + y = 120-----(i)
Travel in same direction, A meets B after 6hr = 6x-6y = 120-----(ii)
By Solving equation (i) and (ii), we get
12x = 840
x = 840/12
x = 70km/hr
Substituting x valu... |
AQUA-RAT | AQUA-RAT-38511 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"Rs. 40",
"Rs. 50",
"Rs. 49",
"Rs. 59"
] | B | S.P 1- C.P = C.P – S.P 2
57 - C.P = C.P - 43
2 C.P = 57 + 43;
C.P = 100/2 = 50
ANSWER:B |
AQUA-RAT | AQUA-RAT-38512 | # 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 9/13%",
"7 9/13%",
"3 9/13%",
"4 9/13%"
] | B | 925 --- 75
75 --- ? =>
=75/925 *100= 7 9/13%
Answer: B |
AQUA-RAT | AQUA-RAT-38513 | => 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... | [
"3:9",
"3:10",
"3:21",
"3:12"
] | B | Let the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.
Let the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.
Savings of Bhuvan every month = 1/4(5x)
= (His income) - (His expenditure) = 5x - 2y.
=> 5x = 20x - 8y => y = 15x/8.
Ratio of savings of Amar and Bhuvan
= 6x - 3y : 1/4(5x) = 6... |
AQUA-RAT | AQUA-RAT-38514 | ### 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... | [
"5N",
"7N",
"10N",
"15N"
] | D | In 1992, the company's assets were N.
In 1993, the company's assets were N + 4N = 5N.
In 1994, the company's assets were 5N + 10N = 15N.
The answer is D. |
AQUA-RAT | AQUA-RAT-38515 | (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 ... | [
"Rs. 220",
"Rs. 235",
"Rs. 240",
"Rs. 276"
] | D | The payment should be in ratio of 200:120:230 or 20:12:23
First person should pay 20*660/55 = 240 Rs.
ANSWER:D |
AQUA-RAT | AQUA-RAT-38516 | # 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... | [
"5760",
"14400",
"480",
"5670"
] | D | Let us take opposite of the constraint.
2 girls sitting together: :
1 case is GGBGBBBB.
Total number of ways=3!*5!*5 with just shifting the rightmost girl.
Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 positio... |
AQUA-RAT | AQUA-RAT-38517 | ## Extra 01
How many arrangements can be made using the letters from the word COURAGE? What if the arrangements must contain a vowel in the beginning?
• $$4 \times 6!$$
## Extra Problem 02
How many arrangements are possible using the words
• EYE
• CARAVAN?
## 3(a)
There are (p+q) items, of which p items are homo... | [
"739",
"73",
"360",
"840"
] | C | The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =6!/(1!)(2!)(1!)(1!)(1!)= 360.
Answer:C |
AQUA-RAT | AQUA-RAT-38518 | # Physics kinematics SIN question
1. Dec 30, 2011
### ShearonR
1. The problem statement, all variables and given/known data
A car, travelling at a constant speed of 30m/s along a straight road, passes a police car parked at the side of the road. At the instant the speeding car passes the police car, the police car ... | [
"100 m",
"150 m",
"190 m",
"200 m"
] | A | Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes = (1/60 × 6) km = 1/10 km = 100 m
∴ Distance between the thief and policeman = (200 – 100) m = 100 m.
Answer: A |
AQUA-RAT | AQUA-RAT-38519 | Since the number of ways in which $$5$$ books can be arranged is $$5!=120,$$ we have $$120$$ ways.
• thanks for explanation. Can you point out what is wrong in my analysis Sep 17, 2020 at 11:24
• As mentioned in the comments, you calculated the $C$ books to be next to each other, but they do not need to be next to eac... | [
"9 books",
"8 books",
"1 book",
"4 books"
] | C | The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 21520.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 21520 = 10 and 9 is divisible by ... |
AQUA-RAT | AQUA-RAT-38520 | 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 sec",
"23 sec",
"24 sec",
"25 sec"
] | A | D = 120 + 150 = 270
S = 36 * 5/18 = 10 mps
T = 270/10 = 27 sec
A |
AQUA-RAT | AQUA-RAT-38521 | 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... | [
"167",
"240",
"881",
"278"
] | B | Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B |
AQUA-RAT | AQUA-RAT-38522 | +\frac1{271} +\frac1{273} +\frac1{275} -\frac1{66} +\frac1{277} +\frac1{279} +\frac1{281} +\frac1{283} -\frac1{68} +\frac1{285} +\frac1{287} +\frac1{289} +\frac1{291} -\frac1{70} +\frac1{293} +\frac1{295} +\frac1{297} +\frac1{299} +\frac1{301} -\frac1{72} +\frac1{303} +\frac1{305} +\frac1{307} +\frac1{309} -\frac1{74} ... | [
"466",
"646",
"666",
"324"
] | D | Given Exp. = a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324
Correct Option is D |
AQUA-RAT | AQUA-RAT-38523 | int <- .1/100 # annual interest rate of 0.1%
inf <- 2/100 # annual inflation rate 2%
n <- 10 # number of years
The following is multiple choice question (with options) to answer.
If Re.100 amounts to Rs.300 over a period of 10 years. What is the rate of simple interest? | [
"20%",
"30%",
"15%",
"10%"
] | A | 200 = (100*10*R)/100
R = 20%
Answer:A |
AQUA-RAT | AQUA-RAT-38524 | For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.
Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.
We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, ... | [
"(a) 4",
"(b) 7",
"(c) 11",
"(d) 13"
] | C | N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder G when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C |
AQUA-RAT | AQUA-RAT-38525 | => 18x/4=154
x=308/9
TOTAL WAGES PAID WILL BE
(12/11 + 18/7)*309/9
PLEASE TELL ME WHERE I AM WRONG
Lets try -
SW4 wrote:
Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the differe... | [
"1.1",
"2.1",
"2.2",
"2.3"
] | A | Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 12x+xn and we are told that it equals to 11xn:
11x+xn=11xn --> reduce by x: 11+n=11n -->10n=11
n = 11/10 = 1.1
Answer: A |
AQUA-RAT | AQUA-RAT-38526 | java, xml, swing
<lastWeekSolution>I'm Going to get this</lastWeekSolution>
</week>
<week>
<date>2012/03/12 00:00:00</date>
<riddle>ipso lorem 7</riddle>
<lastWeekSolution>I'm Going to get this</lastWeekSolution>
</week>
<week>
<date>2012/03/19 00:00:00</date>
... | [
"Sunday",
"Tuesday",
"Friday",
"Tuesday"
] | C | Given that 8th Dec 2007 was Saturday
Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day
Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday
Correct answer is Friday |
AQUA-RAT | AQUA-RAT-38527 | 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.
. .... | [
"25",
"26",
"27",
"28"
] | C | Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 115
5x - 20 = 115
5x = 135
x = 27
The answer is C. |
AQUA-RAT | AQUA-RAT-38528 | ### 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 ... | [
"44",
"58",
"74",
"12"
] | A | Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:A |
AQUA-RAT | AQUA-RAT-38529 | 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... | [
"1:2",
"1:3",
"3:1",
"1:5"
] | C | Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/2 + 7/2 = 6 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 6 : 2 = 3:1.
Answer:C |
AQUA-RAT | AQUA-RAT-38530 | 10000000x= 1532216.22162216....
Again, that each block in that infinitely repeating decimal has been replaced by the next one. The decimal parts of 1532216.22162216... and 153.22162216... are exactly the same.
Subracting 1000x= 153.22162216... from 10000000x= 1532216.22162216..., the decimal parts cancel and we have
(1... | [
"37",
"41",
"3.5e-05",
"35"
] | B | 99*0.35=34.65 approx. 35
Answer : B |
AQUA-RAT | AQUA-RAT-38531 | Then we come to the 3-1-1 and 2-2-1 combinations.
For the 3-1-1 combination, in pocket one we can have any three of the five distinct marbles. The order inside one pocket doesn't matter. Therefore, we will use 5C3. For the 2nd pocket, we have two marbles left and we can only pick one because we must leave one for the ... | [
"7",
"13",
"20",
"22"
] | C | Since at most 6 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1... |
AQUA-RAT | AQUA-RAT-38532 | homework-and-exercises, kinematics, velocity, vectors, relative-motion
I've drawn the man swimming at some arbitrary angle $\theta$ at a speed $v$. The river is flowing at a speed $V$, and the time the man takes to cross is $t$. The distance swum by the man is $d_m$ and the distance the water moves is $d_r$.
The key p... | [
"1",
"2",
"3",
"7"
] | A | DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph Answer:A |
AQUA-RAT | AQUA-RAT-38533 | 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... | [
"-14",
"-60",
"0",
"4"
] | B | if a = -1, then putting values in equation
= -[ (2)^2 + (2)^3 + (2^4) + (2^5) ]
= -[ 4 + 8 + 16 + 32 ]
= -60
Answer = B = -60 |
AQUA-RAT | AQUA-RAT-38534 | and number of copies; this app basically calc. a 7) or one from a certain suit (e. Aesther Diviner. Blackjack is a card comparison game between a player and a dealer with a deck of standard playing cards. Using the combinations formula 52 choose 5 shown here, we get:. Let us denote that as P(c1)=1/3. Probability first ... | [
"55/119",
"55/221",
"55/223",
"55/227"
] | B | We have n(s) = \inline {\color{Black}52C_{2}} = = 1326.
Let A = event of getting both black cards
B = event of getting both queens
A∩B = event of getting queen of black cards
n(A) = \inline {\color{Black}26C_{2}} = = 325, n(B)= \inline {\color{Black}4C_{2}} = = 6 and n(A∩B) = \inline {\color{Black}2C_{2}} = 1
P(A) = n(... |
AQUA-RAT | AQUA-RAT-38535 | Notice carefully, the sign of the net increase is negative, clearly indicating the after the successive decrease the value of the original number, decreased instead of increasing. And what was the magnitude??? Right 28%. The net decrease is 28%.
So, before we use this approach to give you an official answer for the ab... | [
"44% increase",
"44% decrease",
"53% increase",
"66% increase"
] | C | if n items are sold for $p each, revenue is $np. If we reduce the price by 15%, the new price is 0.85p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.85p)(1.8n) = 1.53np, which is 1.53 times the old revenue, so is 53% greater.
ANSWER:C |
AQUA-RAT | AQUA-RAT-38536 | # What is the next number in this sequence: $1, 2, 6, 24, 120$? [closed]
I was playing through No Man's Sky when I ran into a series of numbers and was asked what the next number would be.
$$1, 2, 6, 24, 120$$
This is for a terminal assess code in the game no mans sky. The 3 choices they give are; 720, 620, 180
• W... | [
"52",
"55",
"60",
"120"
] | A | A
52
sum of consecutive prime numbers
(2+3 , 5+7 , 11+13 , 17+19 , 23+29) |
AQUA-RAT | AQUA-RAT-38537 | # How many ways can you put 8 red, 6 green and 7 blue balls in 4 indistinguishable bins?
1. Assume all balls with the same color are indistinguishable.
2. The order in which balls are put in a bin does not matter.
3. No bins are allowed to have the same distribution of balls!
For example, this configuration
{RRGGGB}... | [
"11",
"33",
"44",
"23"
] | B | Answer:B |
AQUA-RAT | AQUA-RAT-38538 | # 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... | [
"25200",
"210",
"120",
"1000"
] | A | Required selection = select 3 consonants from 7 and 2 vowels frm 4
= 7C3 * 4C2
= 210
As we have to form 5 letter word the above combination of consonants and vowels can be done in 5! = 120 different ways
Required no. of ways = 210 * 120
= 25200
Ans - A |
AQUA-RAT | AQUA-RAT-38539 | Now we calculate $B$. 5 is prime, so $XYZ$ is divisible by 5 if and only if one of $X$, $Y$, or $Z$ is divisible by 5. We can use inclusion-exclusion: $B$ is the sum of the cases where (at least) $X$, $Y$, or $Z$ is divisible by 5, minus the cases where (at least) two are divisible by 5, plus the cases where all three ... | [
"4",
"6",
"8",
"9"
] | C | PRIME # is the # that has only 2 factors: One is 1 and another is the # itself.
infer that
FOR any given # 1 and the # itself are the definite factors.
Knowing above concepts:
product of X,Y, and Z = XYZ
divisible by 1, xyz, x, y, z, xy,yz,xz ==> total 8
ANSWER "C" |
AQUA-RAT | AQUA-RAT-38540 | It takes 6 days for 3 women and 2 men working together to complete a work --> sum the rates: $$\frac{3}{w}+\frac{2}{m}=\frac{1}{6}$$.
3 men would do the same work 5 days sooner than 9 women --> $$\frac{m}{3}+5=\frac{w}{9}$$.
Solving: $$m=15$$ and $$w=90$$. $$\frac{w}{m}=6$$.
bunuel, pls help
if i equate time i am n... | [
"10.2 Days",
"15.2 Days",
"16.2 Days",
"18 Days"
] | B | Let us assume that the work is laying 40 bricks.
Jane = 4 bricks per day
Ashley = 1 brick per day
Together = 5 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 16
Remaining bricks = 40 - 24= 16
So together, they would take 16/5 = 3.2
Total no. of d... |
AQUA-RAT | AQUA-RAT-38541 | Just to check each case: \begin{align*} f(S_T)=\begin{cases} 3 + \min(30 - S_T,0) + \max(S_T - 35,0) = 3 + 0 + 0 = 3 & \text{if }S_T\leq 30, \\ 3 + \min(30 - S_T,0) + \max(S_T - 35,0) = 3 + (30 - S_T) + 0 = 33- S_T & \text{if }30
I know @KeSchn already answered but hope this helps since this is how I usually do these.... | [
"400",
"500",
"505",
"None of these"
] | B | Explanation:
35/.07 = 3500/7 = 500
Option B |
AQUA-RAT | AQUA-RAT-38542 | (ones digit is $$0$$, because it is the difference of two numbers whose ones digit is $$1$$).
Now if $$3n$$ is divisible by $$10$$, for an integer $$n$$, then $$n$$ is divisible by $$10$$. QED.
The following is multiple choice question (with options) to answer.
The number N is 7,6H4, where H represents the ten's digi... | [
"1",
"3",
"5",
"7"
] | A | Integer is divisible by 9 - Sum of digits is divisible by 9
Answer: A |
AQUA-RAT | AQUA-RAT-38543 | 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... | [
"260",
"150",
"817",
"716"
] | A | A+B+C = 585
4A = 6B = 3C = x
A:B:C = 1/4:1/6:1/3
= 3:2:4
4/9 * 585
= Rs.260
Answer: A |
AQUA-RAT | AQUA-RAT-38544 | Our goal is to find possible values for $x$, then use the equation above to find $n$. The difference between the factors is $(2m + x) - (2m - x) = 2m + x - 2m + x = 2x.$ We have three pairs of factors, $847\cdot1, 121\cdot 7,$ and $77\cdot 11$. The differences between these factors are $846$, $114$, and $66$ - those ar... | [
"None",
"One",
"Two",
"Three"
] | B | This is a tricky worded question and I think the answer is should be D not C...
Here is my reason :
The stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . The stem wants to say that X is a PRIME NUMBER . because any prime
Number has no factor grater than 1 and Itself .... |
AQUA-RAT | AQUA-RAT-38545 | 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... | [
"240 meters",
"360 meters",
"280 meters",
"600 meters"
] | C | Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 16 * 20 = 320 = Length of train
Length of platform = 600 - 320 = 280
Answer: C |
AQUA-RAT | AQUA-RAT-38546 | # Runner's High (Speed)
I find the following mind-boggling.
Suppose that runner $$R_1$$ runs distance $$[0,d_1]$$ with average speed $$v_1$$. Runner $$R_2$$ runs $$[0,d_2]$$ with $$d_2>d_1$$ and with average speed $$v_2 > v_1$$. I would have thought that by some application of the intermediate value theorem we can fi... | [
"25 km/hr",
"27 km/hr",
"60.60 km/hr",
"32 km/hr"
] | C | Explanation :
(400/1000)/(24/3600)=60.60 km/hr
Answer : C |
AQUA-RAT | AQUA-RAT-38547 | The base case is
$$n=1:\;\;\;\;\;1^3+3^3=28\stackrel ?=(1+1)^2(2+4+1)=28\ldots\ldots good$$
Assume for $\,n\,$ and show for $\,n+1\,$:
$$1^3+3^3+\ldots+(2n+1)^3+(2n+3)^3\stackrel{\text{Ind. hypothesis}}=(n+1)^2(2n^2+4n+1)+(2n+3)^3=\ldots$$
-
The following is multiple choice question (with options) to answer.
If 2^... | [
"3",
"6",
"12",
"27"
] | D | 2^2n + 2^2n + 2^2n + 2^2n = 4^28
=> 4 x 2^2n = 4^28 = 2^56
=> 2^2 x 2^2n = 2^56
=> 2^(2n+2) = 2^56
=> 2n+2 = 56=> n =27
So. Answer will be D. |
AQUA-RAT | AQUA-RAT-38548 | The only possible answer is E i.e 12 hrs.
Yes, your approach is very good. The only thing I have an issue with is the approximation used.
Their combined time is 4.8 hrs and hence we know that Jack will take more than 9.6 hrs. 10 hrs is a possible candidate for the correct option in that case. Though I would say that i... | [
"70",
"120",
"140",
"160"
] | A | Cole is twice as fast as Jim and Mitch is 4 times as fast as Jim (it takes Mitch N/2 minutes to prepare 2 omelets, thus N/4 minutes to prepare one omelet).
Say the rate of Jim is x omelet/minute, the rate of Cole 2x omelet/minute, and the rate of Mitch 4x omelet/minute.
Then, from (time)(rate) = (job done):
(40 minutes... |
AQUA-RAT | AQUA-RAT-38549 | You actually want it the other way around: if $a^2+b^2=c^2$ then $a+b+c|abc$. That you can prove very quickly from the general form of primitive Pythagorean triples $(a,b,c)=(m^2-n^2,2mn,m^2+n^2)$.
• \begin{align}a+b+c&=(m^2-n^2)+(2mn)+(m^2+n^2)\\ &=(m^2+m^2)+2mn+(n^2-n^2) \\ &=2m^2+2mn \\ &=2m(m+n).\end{align} And no... | [
"a)82",
"b)84",
"c)85",
"d)87"
] | B | a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: B)
84=8^2+4^2+2^2
A... |
AQUA-RAT | AQUA-RAT-38550 | # 3 balls are drawn from a bag contains 6 white balls and 4 red balls, what is the probability that 2 balls are white and 1 ball is red?
A bag contains 6 white balls and 4 red balls. If 3 balls are drawn one by one with replacement, then what is the probability that 2 balls are white and 1 ball is red?
$$\frac{18}{12... | [
"4/7",
"2/3",
"5/8",
"1/4"
] | A | Total number of balls = 8+6 = 14
number of white balls = 8
Probability = 8/14 = 4/7
Answer is A |
AQUA-RAT | AQUA-RAT-38551 | • #### 1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
1. \begin{aligned} 120m^2 \end{aligned}
2. \begin{aligned} 130m^2 \end{aligned}
3. \begin{aligned} 140m^2 \end{aligned}
4. \begin{aligned} 150m^2 \end{aligned}
Explanation:
\begin{aligned}
\text... | [
"1420",
"1430",
"1450",
"1440"
] | D | First of all we will find the new daily productivity of the farmer in hectares per day: 25% of 120 hectares is 25100⋅120=30 hectares, therefore 120+30=150 hectares is the new daily productivity. Lets x be the planned number of days allotted for the job. Then the farm is 120⋅x hectares. On the other hand, we get the sam... |
AQUA-RAT | AQUA-RAT-38552 | temperature, agriculture
Title: Minimum temperature in Growing Degree Day (GDD) - from daytime or from the whole day? I want to calculate growing degree days.
I have hourly data of temperature between the hours of 00:00 and 23:59.
I want to calculate the growing degree days and I saw that I need the minimum,maximum an... | [
"28",
"27",
"22",
"34"
] | D | M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34
Answer:D |
AQUA-RAT | AQUA-RAT-38553 | 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.
. .... | [
"215",
"310",
"343",
"243"
] | C | Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 7*7*7=7^3=343.
Answer: C. |
AQUA-RAT | AQUA-RAT-38554 | (A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres
let total qty be x liters
so milk 9x/100
9 liters is withdrawn so left with 9x/100- (9/100) * 9 which becomes equal to 6x/100
we have
9/100 * ( x-9) = 6x/100
3x-27 = 2x
x= 27 litres
OPTION B
Director
Joined: 25 Jul 2018
Posts: 731
A vessel is full o... | [
"8",
"15",
"16",
"18"
] | D | Capacity of the tank = (12 x 13.5) liters = 162 liters.
Capacity of each bucket = 9 liters.
Numbers of buckets needed = (162/9) = 18
ANSWER:D |
AQUA-RAT | AQUA-RAT-38555 | $⌊100/2⌋+⌊100/4⌋+⌊100/8⌋+⌊100/16⌋+⌊100/32⌋+⌊100/64⌋=50+25+12+6+3+1=97 .$
Hence, 2 divides $S$ to an odd power. So we need to divide $S$ by $k!$ which 2 divides to an odd power to get a perfect square quotient. This reduces the possibilities for $k$ to 50 or 51. Since
$S={2}^{99}·{3}^{98}·{4}^{97}\dots {99}^{2}·100=\l... | [
"5",
"6",
"7",
"9"
] | C | x^n - 1 will be divisible by x+1 only when n is even.
36^9 - 1 = (6^2)^9 - 1 = 6^18 - 1 which is divisible by 6+1 i.e. 7
Answer is C |
AQUA-RAT | AQUA-RAT-38556 | Can you solve it from here?
-Dan
Is it:
x - 3/2 = + square root 1 / 4 and x - 3/2 = - square root 1/4
then
x = 3/2 + square root 1 /4 and x = 3/2 - square root 1/4
so x = 1.75 or x = 1.25
4. Originally Posted by princess_anna57
Is it:
x - 3/2 = + square root 1 / 4 and x - 3/2 = - square root 1/4
then
x = 3/2 ... | [
"1/3",
"1/9",
"1/81",
"1"
] | C | 1/3 of sqrt(x) = 3x, which means that sqrt(x) = 9x
or x = 81x^2 -> divide by x
1=81x
x=1/81
C. |
AQUA-RAT | AQUA-RAT-38557 | c++, beginner, object-oriented, quiz
__ __ ____ ____
\ \/ /___ __ __ / __ \____ ______________ ____/ / /
\ / __ \/ / / / / /_/ / __ `/ ___/ ___/ _ \/ __ / /
/ / /_/ / /_/ / / ____/ /_/ (__ |__ ) __/ /_/ /_/
/_/\____/\__,_/ /_/ \__,_/____/____/\___/\__,_(_) ... | [
"1/4",
"1/3",
"1/2",
"2/3"
] | A | Assume 100 persons in a company
person knows c++=4/10=100*4/100=20 persons
person knows java=2/4=100*2/4=50 persons
neither=2/8=100*2/8=25 persons
according to our assumption 100 person=20+50+25=95 person covered(5 remaining)
so,total possibility=20 person(c++)+5(remaining)=25 persons
which is 25/100=1/4
ANSWER:A |
AQUA-RAT | AQUA-RAT-38558 | # 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... | [
"$1260",
"$1440",
"$1500",
"$1680"
] | B | Let C.P. be Rs. x.
Then, (1380 - x) x 100 =(x - 1020) x 100
1380 - x = x - 1020
2x = 2400
x = 1200
Required S.P. = 120% of 1200 = 1.20 x 1200 = $1440
Answer : B |
AQUA-RAT | AQUA-RAT-38559 | 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... | [
"12",
"24",
"48",
"96"
] | A | So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=3, y=3. now quickly 2^2(3^1)=12. Than answer should be number 1.
A |
AQUA-RAT | AQUA-RAT-38560 | # Math Help - word problem.
1. ## word problem.
hi ! im having a difficult time answering this word problem.
"Alvin set out from a certain point and travelled at the rate of 6 kph. After Alvin had gone for two hours, Ben set on to overtake him and went 4km the first hour, 5 km the second hour, 6 km the third hour an... | [
"2 1/5 Km",
"3 1/5 Km",
"3 2/5 Km",
"3 3/5 Km"
] | B | Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
B |
AQUA-RAT | AQUA-RAT-38561 | # 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... | [
"900",
"1000",
"1100",
"1200"
] | A | A = B+300.
A=4(B-600).
4(B-600)=B+300.
3B=2700.
B=900.
The answer is A. |
AQUA-RAT | AQUA-RAT-38562 | 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... | [
"39.55$",
"40.63$",
"41.63$",
"42.15$"
] | B | Let x be the amount the most their food can cost.
x + 0.07x + 0. 15x = 50
Solving for x, x = 40.98$, this is the maximum amount that can be used for food.
Hence 40.63$ is the maximum value less than 40.98$
Hence Option B |
AQUA-RAT | AQUA-RAT-38563 | Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?
Total number of pencils Ramesh had = 20
Number o... | [
"32years",
"42years",
"45years",
"35years"
] | B | Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 102
x = 8
Ramesh present age = 4*8+10 = 42 years
Answer is B |
AQUA-RAT | AQUA-RAT-38564 | (b) Here, since the digits must strictly increase from left to right, consider two sub-cases:
(b1) If 0 is not included - Then, there are 9 digits, and for every choice of 4 digits from them, we have exactly one way to arrange them in strictly increasing order. So, there are 9C4 such numbers.
(b2) If 0 is included - ... | [
"5",
"6",
"9",
"7"
] | A | Product of 98 and .08216 is 8.05168.
Therefore number of digits to right of decimal point is 5
Answer is A. |
AQUA-RAT | AQUA-RAT-38565 | 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... | [
" 4",
" 5",
" 24",
" 20"
] | C | IMO C
Given that one chair is taken, i think the remaining 4 dignitaries can be arranged 4!=24. |
AQUA-RAT | AQUA-RAT-38566 | => 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... | [
"$525",
"$550.50",
"$1080.02",
"$522.3"
] | D | The dollars earned will be in the same ratio as amount of work done
1 day work of Z is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
Z's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2350 = $522.3
hence:D |
AQUA-RAT | AQUA-RAT-38567 | # Seating couples around 2 tables
Here's my question and possible answer.
How many possible ways can you arrange 8 married couples between 2 circular tables of 8 identical chairs each such that:
1) each couple must sit at the same table, and,
2) at each table, men and women must sit in adjacent chairs (NOTE: a coup... | [
"15C5 * 9! *4!",
"15C3 * 8! *3!",
"15C4 * 9! *3!",
"16C4 * 9! *5!"
] | D | 10 people can be selected from 16 people in 16C10 ways.
Remaining 6 people can be selected from 6 people in 6C6 ways.
Now, arranging 10 people on a round table = (10-1) ! = 9!
Arranging 6 people on a round table = (6-1) ! = 5!
Hence, total number of ways = 16C10 * 9! * 6C6 * 5!
= 16C4 * 9! * 5!
D |
AQUA-RAT | AQUA-RAT-38568 | # For any two sets, $A - B = B - A$ implies $A = B$
Is the following statement True or False:
For any two sets $A$ and $B$: If $A - B = B - A$ then $A = B$.
If it is true, prove it, otherwise provide a counterexample.
I am unable to come up with a counter example. I think the statement is true but how do I prove it... | [
"only Ⅰ",
"only Ⅱ",
"only Ⅲ",
"only Ⅰ& Ⅲ"
] | D | If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, Ⅰ& Ⅲ are the answers. Therefore, D is the answer. |
AQUA-RAT | AQUA-RAT-38569 | # Homework Help: Probability of choosing stale donuts out of 24
Tags:
1. Sep 2, 2016
### TheSodesa
1. The problem statement, all variables and given/known data
There are 6 stale donuts in a set of 24. What is the probability of:
a) there being no stale donuts in a sample of 10?
b) there being 3 stale donuts in a sam... | [
"45",
"49",
"53",
"57"
] | B | $25 = 4 * $6 + $1
The number of doughnuts is 4*12 + 1 = 49
The answer is B. |
AQUA-RAT | AQUA-RAT-38570 | # Two points of a square $K$ determine a diagonal of another square that is contained in $K$
Let $$K:=[0,1]^2$$ be a square on $$\mathbb{R}^{2}$$. We select 2 random points $$A$$, $$B$$ $$\in [0,1]^{2}$$ in this square. What is the probability that the square whose diagonal is the line segment $$AB$$, is contained in ... | [
"0.25",
"0.5",
"0.75",
"0.1"
] | C | I guess it's mean that square B is placed within square Aentirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 65-16=48 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=48/64 = 0.75.
Answe... |
AQUA-RAT | AQUA-RAT-38571 | # Is it possible to solve for $a, b \in \mathbb{N}$?
I need to solve the following equation so that both $a$ and $b$ are natural numbers.
$$ab - 2a = 2b$$
I must also prove that the solutions found are the only ones possible.
Is it possible to do so, and if yes how can I do it? Can this be solved as some type of di... | [
"2",
"3",
"4",
"5"
] | C | Let us understand the meaning of |a| > 2
Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance... |
AQUA-RAT | AQUA-RAT-38572 | ### 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... | [
"4",
"5",
"34",
"7"
] | D | 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D |
AQUA-RAT | AQUA-RAT-38573 | Going back to $9- x^2= (3- x)(3+ x)= -(x- 3)(x+ 3)\ge 0$, another and perhaps simpler way to see that is this: $a- b> 0$ if and only if $a> b$ and $a- b< 0$ if and only if a< b. If x< -3 then it is also less than 3 so both of x- 3 and x+ 3= x-(3) are negative. Their product (the product of two negative numbers) is posi... | [
"5",
"9",
"10",
"18"
] | D | What is the greatest positive integer x such that 3^x is a factor of 9^9?
9^9 = (3^2)^9 = 3^18
D. 18 |
AQUA-RAT | AQUA-RAT-38574 | ### 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... | [
"70",
"80",
"90",
"100"
] | B | The investors can be categorized into three groups:
(1) Those who have investments in equities only.
(2) Those who have investments in securities only.
(3) Those who have investments in both equities and securities.
Let xx, yy, and zz denote the number of people in the respective categories. Since the total number of i... |
AQUA-RAT | AQUA-RAT-38575 | solubility, alloy, teaching-lab
What other such situations are there is chemistry; when would one actually need to do such simultaneous calculations? You may also give the weight of a sample made of an alloy $\ce{Zn-Mg}$. Then you dip it into some diluted $\ce{HCl}$. Both metals will react simultaneously according to ... | [
"15kg",
"20kg",
"8kg",
"24kg"
] | D | Let the required quantity of copper be x kg
5:3::40:x
5x = 40*3
x = 24kg
Answer is D |
AQUA-RAT | AQUA-RAT-38576 | 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.... | [
"5.1",
"5.4",
"5",
"5.2"
] | B | 1/9+1/18+1/54=10/54=1/5.4. so 5.4 hrs
ANSWER:B |
AQUA-RAT | AQUA-RAT-38577 | ### 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}$$
Director
Joined: 13 Mar 2017
Posts: 703
Location: India
Conc... | [
"87",
"37",
"80",
"36"
] | C | Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer: C |
AQUA-RAT | AQUA-RAT-38578 | Let one woman complete the job in $$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... | [
"5",
"2",
"8",
"4"
] | C | 1. We need to find out the time taken by 3 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 12*3 = 36 days
4. But on day 1 twelve workers had already worked finishing 1/3 of the job. So 3 workers have to finish only 2/3 of the job.
5. Total time taken by... |
AQUA-RAT | AQUA-RAT-38579 | 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... | [
"175.5",
"170",
"169.5",
"180"
] | A | Since first and second varieties are mixed in equal proportions.
average price = 126+135/2 = 130.50
o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x - 153 = 22.50
x = 175.50
ANSWER A |
AQUA-RAT | AQUA-RAT-38580 | #### David Harper CFA FRM
##### David Harper CFA FRM
Staff member
Subscriber
That's interesting, Steve (to me, because I write so many questions).
With regard to "An asset is quoted at 12% annually with continuous rate. Interest is paid quarterly." Note three timeframes are invoked:
1. Interest paid quarterly (4 per ... | [
"165",
"170",
"175",
"150"
] | D | Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.12, money invested = 100×12/8 = Rs.150
ie, market value of the stock = Rs.150
Answer is D. |
AQUA-RAT | AQUA-RAT-38581 | Try to solve it as a diophantine equation
${19x + 96y = D\\ \gcd ( 19, 96 ) = 1}$
${ \text {One possible solution of }\\ 19x + 96y = 1\\ \text{is} \ (\bar x, \bar y) = (-5, 1)\\ \text{thus all the solution of}\\ 19x + 96y = D\\ \text{are } (x,y) = (-5D - 96k, D + 19k) \text{ where } k \in \mathbb{Z}}$
${ \text{in ou... | [
"10",
"18",
"11",
"20"
] | D | Add these two equations
4x + 5y = 20
Divide by 2 ( to Get 4x + 5y)
Answer will be D. 20 |
AQUA-RAT | AQUA-RAT-38582 | a circle and the coordinates of its center? This definition can be used to find an equation of a circle in the coordinate plane. Re: Finding a point on a circle, given only anothe point, the radius, and the arc len The co-ordinates of your blue point cannot be determined with the data given. Then graph the circle. But ... | [
"(0,0)",
"(1,1)",
"(1.5,1.5)",
"(1,-2)"
] | D | I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-1)
But the the center of the circle will lie on (1.5,1.5)
D |
AQUA-RAT | AQUA-RAT-38583 | Case 1 : A pair of socks are present, hence exactly 2 draws for the socks to match. Case 2 : 2 pair of socks are present in the drawer. How?
To start with, instead of looking for a matching pair, let's find the probability that both socks are red.
The Sock Drawer: Probability and Statistics Problem A drawer contains ... | [
"7",
"9",
"11",
"16"
] | D | The worst case scenario is choosing 13 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.
The answer is D. |
AQUA-RAT | AQUA-RAT-38584 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"1/9",
"29/180",
"9/80",
"1/5"
] | C | 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 8*2 = 16 hours;
In 1 hour 15 journeymen can finish 1/16 of the job.
Th... |
AQUA-RAT | AQUA-RAT-38585 | Question
# In a school, there are $$1000$$ student, out of which $$430$$ are girls. It is known that out of $$430, 10$$% of the girls study in class $$XII$$. What is the probability that a student chosen randomly studies in class $$XII$$ given that the chosen student is a girl?.
Solution
## Total number of students ... | [
"210",
"225",
"200",
"250"
] | C | Number of students who speak French are 40 + 10 = 50
Of total students, the percentage of students who do not speak French was 75% --> percentage of who do is 25%
50-------25%
x ------- 100%
x = 50*100/25 = 200 = number of all students
Answer is C |
AQUA-RAT | AQUA-RAT-38586 | 3. Originally Posted by Nath
"I have 2 children. One is female. What is the probability the other is also female?"
This puzzle appeared in New Scientist magazine, and a similar one in Scientific American several months back. The consensus among mathematicians (according to the articles in the magazines), including a f... | [
"54",
"58",
"62",
"60"
] | D | Number of people =100
Females = 40
men = 100-40=60
Half of the men are smoker60/2=30, that means the remaining men 60-30=30 are non smokers.
1/4 females are smoker. i.e 1/4*40 = 10.
40-10=30 females are non smokers
So, total number of non smokers in the town are 30+30 =60
Answer : D |
AQUA-RAT | AQUA-RAT-38587 | Overcounting cricketer combinations
Following this, Navneet had a new problem:
I am stuck on another problem:
A team of 11 is to be selected out of 10 batsmen, 5 bowlers, and 2 keepers such that in the team at least 4 bowlers should be included. Find the number of possible ways of selection.
I tried to solve this q... | [
"64",
"72",
"111",
"721"
] | C | Average = Total Runs / Total wickets
Total runs after last match = 21.5w + 52
Total wickets after last match = w + 5
(21.5w + 52) / (w + 5) = 21.5 - 0.5 = 21
w = 106
so total wickets aftr last match = w+5 = 111
ANSWER:C |
AQUA-RAT | AQUA-RAT-38588 | in a cantilever beam the deflection is $$\delta_{max} = \frac {PL^3}{3EI}$$
In this case assuming free sliding between the planks the load P is going to be supported equally between the 3 planks.
So the deflection will be $$\delta_{max} = \frac {(P/3)L^3}{3EI_{\text{single board}}}$$
Because $I$ is proportional to t... | [
"9 m",
"4 m",
"4 m",
"6 m"
] | A | Answer
Greatest possible length of each plank = H.C.F of 54, 63, 81 = 9 m
Correct Option: A |
AQUA-RAT | AQUA-RAT-38589 | 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... | [
"4 mins",
"6 mins",
"5 mins",
"3 mins"
] | C | Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by A = 3 liters.
Capacity of tank filled in 1 minute by B = 15 liters.
Therefore, capacity of the tank filled by both A and B in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.
ANSWER:C |
AQUA-RAT | AQUA-RAT-38590 | # 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... | [
"191",
"213",
"221",
"223"
] | D | For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 10% of the cost:
Sell Price = Cost + $60
Sell Price = $600 + $60
Thus, the Sell Price is $660 for each item. Selling all 100 items gives the retailer...
100($60) = $2,000 ... |
AQUA-RAT | AQUA-RAT-38591 | greatest common divisor
cehsu
104 views
Greatest Common Divisor
In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For example, the gcd of 8 and 12 is 4.
The greatest common divisor is also known as th... | [
"1",
"S=Cannot be determined",
"S=2",
"5"
] | B | My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B |
AQUA-RAT | AQUA-RAT-38592 | time
Title: Is there a difference between 0.18 and 0.180 seconds? Q. Is there a difference between 0.18 and 0.180 seconds ?
In our databases we are collecting timestamps and there are 2 time instants which are the same for the hour, minute and seconds but the milliseconds field is being returned as:
0.18
0.177 When ... | [
"0.01073",
"0.02073",
"0.03076",
"0.04078"
] | A | My age = 0.0023*0.13/0.236 = 0.000299/0.236 = 0.001266949
My wife age = 0.022*0.12/0.220 = 0.00264/0.220 = 0.012
difference b/w ages = 0.012 - 0.001266949 = 0.01073
ANSWER:A |
AQUA-RAT | AQUA-RAT-38593 | ### 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... | [
"Rs.5000, Rs.500",
"Rs.600, Rs.400",
"Rs.700, Rs.300",
"Rs.300, Rs.700"
] | B | (600÷100)×3×2=34
(400÷100)×8×2=64
Total=100
ANSWER:B |
AQUA-RAT | AQUA-RAT-38594 | # Math Help - Permutation Help!
1. ## Permutation Help!
Problem:
---------
There are 120 five-digit numbers that can be formed by permuting the digits 1,2,3,4 and 5 (for example, 12345, 13254, 52431). What is the sum of all of these numbers?
--------
399 960
I can't get this question...I don't know what to do...
Al... | [
"113323",
"113322",
"114322",
"113321"
] | B | Actually there is the direct formula for this kind of problems.
1. Sum of all the numbers which can be formed by using the n digits without repetition is: (n-1)!*(sum of the digits)*(111…..n times).
2. Sum of all the numbers which can be formed by using the n digits (repetition being allowed) is: n^{n-1}*(sum of the di... |
AQUA-RAT | AQUA-RAT-38595 | 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 7/8",
"27 7/6",
"27 7/4",
"27 7/9"
] | D | Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: D |
AQUA-RAT | AQUA-RAT-38596 | P(30 \leq X \leq 40) = P(29.5 \leq X \leq 40.5)
using the general conversion formula
Z=\frac{X-\mu_{X}}{\sigma_{X}}
where \sigma_{x_i}= \sqrt(350/12) we can write
P \left( \frac{29.5-35}{\sqrt(\frac{350}{12})} \leq \frac{X-35}{\sqrt(\frac{350}{12})} \leq \frac{40.5-35}{\sqrt(\frac{350}{12})} \right)
P \left( -1.018... | [
"188",
"216",
"156",
"680"
] | D | 25% of x = x/4 ; 20% of 1000 = 20/100 * 1000 = 200
Given that, x/4 = 200 - 30 => x/4 = 170 => x = 680.
Answer: D |
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