source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38297 | Amir has identified why the book's answer and your's differ, Felix Brauer
An urn contains 3 white balls and 4 black balls. Second urn contains 6 white balls and 4 black balls. From the first urn are draws 2 balls and they dropped in the second urn. Then from the second urn is drawn one ball which is white. What is the... | [
"1/2",
"1/5",
"1/5",
"3/7"
] | D | Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 10/15
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefor... |
AQUA-RAT | AQUA-RAT-38298 | c#, formatting
/// <summary>
/// Calculates and returns the general discount
/// based on the <see cref="AccountStatus"/>
/// </summary>
/// <param name="accountStatus"></param>
/// <returns></returns>
private static decimal GetDiscountPercentage(AccountStatus accountStatus)
{
swi... | [
"31.7",
"31.4",
"31.6",
"31.1"
] | C | 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4
= 31.6
Answer:C |
AQUA-RAT | AQUA-RAT-38299 | => 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... | [
" 64%",
" 120%",
" 96%",
" 80%"
] | A | Juan's income = 100 (assume);
Tim's income = 40 (60 percent less than Juan's income);
Mary's income = 64 (60 percent more than Tim's income).
Thus, Mary's income (64) is 64% of Juan's income (100).
Answer: A. |
AQUA-RAT | AQUA-RAT-38300 | 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... | [
"2",
"3",
"3 1/5",
"4"
] | C | Suppose 1 man can do work in X days..
so 4 men will do in ..
6/X=1/8*1/2 as half job is done
X=96
now 9 more are added then
15/96=1/2*1/d for remaining half job
d=3 1/5 Number of days
C |
AQUA-RAT | AQUA-RAT-38301 | # 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... | [
"k(1.06)^2",
"k(1.06)^8",
"k(1.015)^2",
"k(1.015)^8"
] | D | term (n) = 2
value of k at the end of 2 yrs, if compounded annually=k(1+r)^n=k(1+0.06)^2
quarterly int. rate (r) = 1.5%
term (n) = 2x4 = 8
value of k at the end of 2 yrs, if compounded qtrly =k(1+r)^n=k(1+0.015)^8
ANSWER:D |
AQUA-RAT | AQUA-RAT-38302 | thermodynamics, energy, home-experiment
Note 3: Peak hours tend to be during the day (this may reverse if we get wide-spread solar energy), so keeping the house cool during the day would cost even more. You pretty much have it right. We have two scenarios:
1 - Leave air conditioning on all day. Say that outside temper... | [
"about 14 minutes",
"about 12 minutes",
"about 15 minutes",
"about 16 minutes"
] | B | Take LCM of 20 and 25 = 100
20*5=100/ 25*4=100.
So if both are switched on together , room cooled in 100/(5+4)=100/9=11.11 minutes
11.11 can be round to 12 minutes , so about 12 minutes
ANSWER: B |
AQUA-RAT | AQUA-RAT-38303 | The totient of $210$ - the number of values between $1$ and $210$ that are relatively prime to $210$ - is $(2-1)(3-1)(5-1)(7-1)=48$. Using this, we can say that there are $48\cdot5=240$ numbers not divisible by these four numbers up to $1050$. Some of these of course are out of range of the original question; we'll hav... | [
"61",
"63",
"65",
"67"
] | B | X/210 = 30/100
100X = 210X30
X =(210X30)/100
X =6300/100
= 63
ANSWER = B = 63 |
AQUA-RAT | AQUA-RAT-38304 | $\therefore \sum_{n=1}^{20} (2^n) - 20 = 2097150 - 20 = 2097130$
Which is the same answer as yours, however the answer in the book says $2097170$. They must of added the 20 instead of subtracted it. OK thanks
4. Originally Posted by chancey
Right, but thats not the answer in the back of the book...
I did it this way... | [
"1845",
"1978",
"1945",
"1862"
] | B | Let the numbers be x and 2000-x
L.C.M. = x(200-x) = 21879
x^2 - 2000x + 21879 = 0
(x-1989) (x-11) = 0
x = 1989 and x = 11
Difference = 1989-11 = 1978
Answer is B |
AQUA-RAT | AQUA-RAT-38305 | investment Banking Course, Download Valuation... As are bonds less than 365 days, most developed countries use simple interest is bonds! Is 1-Feb-2020, and investors collect returns when the bond “ days maturity... The market price quarterly, or the coupon Equivalent rate ( CER.. For calculating return on investment an... | [
"277",
"278",
"120",
"276"
] | C | Let the present worth be Rs. x. Then,
S.I. = (132 - x)
(x * 5 * 2) / 100 = (132 - x)
10x = 13200 - 100x
110x = 13200 => x = 120.
Answer:C |
AQUA-RAT | AQUA-RAT-38306 | # 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... | [
"50%",
"100%",
"150%",
"200%"
] | B | we can make two equations from the given info..
let selling price be S and cost price be C..
so profit=P=S-C...
if S is doubled profit is tripled..
so 5P=4S-C..
or S=4P...
therefore C=P..
% of profit=P/P=100%
B |
AQUA-RAT | AQUA-RAT-38307 | Since he did not score 45, he lost an average of 4.5 upon the total number of innings, which includes the latest innings as well.
So 45 runs upon x innings will give an average of 4.5
Hence 45/x = 4.5 i.e. x = 10. (Remember, x includes the latest inning as well)
Problem 6:
The average of 8 scores is 87. Of these, t... | [
"179",
"194",
"269",
"177"
] | B | Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 – 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x – 180
x + (x - 180) = 208
2x = 388
x = 194 runs
ANSWER: B |
AQUA-RAT | AQUA-RAT-38308 | a company has borrowed$85,000 at a 6.5% interest rate. Find the accrued interest for an investment amount of 500 $holding for 15 days at an interest rate of 3 %. Calculating accrued interest payable First, take your interest rate and convert it into a decimal. The interest rate is 5%. Accrued Interest is the Interest a... | [
"867",
"270",
"267",
"278"
] | B | I = (500*9*6)/100
= 270
Answer: B |
AQUA-RAT | AQUA-RAT-38309 | sum(res==0)/B
[1] 0.120614
So the probability is around 12%. Some ideas for an analytical solution (or approximation) would be nice! A similar question (without a complete answer).
The following is multiple choice question (with options) to answer.
50% of a number is added to 120, the result is the same number. Find ... | [
"300",
"277",
"240",
"99"
] | C | :
(50/100) * X + 120 = X
2X = 480
X = 240
Answer: C |
AQUA-RAT | AQUA-RAT-38310 | => 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 days",
"4 days",
"5 days",
"6 days"
] | C | if a labour worked for 25 days he should get 50 Rs.
but in this he is getting 13 Rs less. if he don't go for work for 1 day he will loose 2.5 Rs then
no of days(Absent)=13/2.5=5.2. Means he was absent for 5 days
ANSWER:C |
AQUA-RAT | AQUA-RAT-38311 | The midpoint of $\displaystyle DE$ is: $\displaystyle M(3\tfrac{1}{2},\,2).$
The median to side $\displaystyle DE$ starts at $\displaystyle \,M$, passes through $\displaystyle \,C,$
. . and extends to $\displaystyle \,F$, where: .$\displaystyle FC \,=\,2\!\cdot\!CM.$
Going from $\displaystyle \,M$ to $\displaystyle \... | [
"80",
"93.5",
"92",
"98"
] | B | Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98,108
The median quiz score was 93.5 (Four quiz scores were higher than 93.5 and four were lower.)
B |
AQUA-RAT | AQUA-RAT-38312 | # Difference between revisions of "2017 AMC 10A Problems/Problem 25"
## Problem
How many integers between $100$ and $999$, inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999?$ For example, both $121$ and $211$ have this property.
$\mathrm{\textbf{(A)} \ }226... | [
"900",
"648",
"720",
"252"
] | B | We know that numbers between 100 and 1000 will be 3 digit integers.
Let the arrangement be ABC where A,B,C represent distinct digits.
We have 9 options for A (as 0 can not start a 3 digit number), 9 options again for B and 8 for C, giving a total of 9*9*8 = 648 options.
ANSWER B |
AQUA-RAT | AQUA-RAT-38313 | # Ten-digit number that satisfy divisibilty rules for 2,3,4,5,6,7,8,9,10&11
Question: Arrange the digits 1,2,3,4,5,6,7,8,9,0 to make a ten-digit Number that satisfies all of the divisibility rules for 2,3,4,5,6,8,9,10,&11. BONUS: make the number also divisible by 7
• Should I add no-computer tag? – Omega Krypton Oct ... | [
"13",
"11",
"16",
"17"
] | B | 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42.
11 Numbers.
10/3 = 3 and 43/3 = 14 ==> 14 - 3 = 11. Therefore 11 digits
B) |
AQUA-RAT | AQUA-RAT-38314 | quantum-mechanics, soft-question, popular-science
The situation here is uncertain because of issues far displaced from chaos or quantum. The challenges arise because it is massively difficult to isolate the input factors and determine them.
School performance, for example, could esily be expected to be influenced by m... | [
"Only conclusion I follows",
"Only conclusion II follows",
"Either I or II follows",
"Neither I nor II follows"
] | D | The statement concentrates on the increasing viewership of TV. and does not stress either on increasing the readership of newspapers or making studies regarding the same. So, neither I nor II follows.
D |
AQUA-RAT | AQUA-RAT-38315 | sum(res==0)/B
[1] 0.120614
So the probability is around 12%. Some ideas for an analytical solution (or approximation) would be nice! A similar question (without a complete answer).
The following is multiple choice question (with options) to answer.
If y > 0, (6y)/20 + (3y)/10 is what percent of y? | [
"40%",
"50%",
"60%",
"70%"
] | C | can be reduced to 3y/10+3y/10 =3y/5=60%
C |
AQUA-RAT | AQUA-RAT-38316 | # Difference between revisions of "2017 AMC 10A Problems/Problem 25"
## Problem
How many integers between $100$ and $999$, inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999?$ For example, both $121$ and $211$ have this property.
$\mathrm{\textbf{(A)} \ }226... | [
"90",
"82",
"80",
"45"
] | C | three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-dig... |
AQUA-RAT | AQUA-RAT-38317 | ### 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... | [
"Rs.3601",
"Rs.3618",
"Rs.4200",
"Rs.3619"
] | C | Manager's monthly salary
= Rs. (1950 * 16 - 1800 * 15)
= Rs. 4200 Answer:C |
AQUA-RAT | AQUA-RAT-38318 | 7,7),(1,8,7),(2,9,7),(8,0,8),(7,1,8),(9,1,8),(6,2,8),(5,3,8),(4,4,8),(3,5,8),(2,6,8),(1,7,8),(0,8,8),(1,9,8),(9,0,9),(8,1,9)
The following is multiple choice question (with options) to answer.
0, 3, 8, 15, 24, ? | [
"28",
"35",
"48",
"25"
] | B | The sequence is a series of squares-1
0, 3, 8, 15, 24, 35
Answer : B. |
AQUA-RAT | AQUA-RAT-38319 | # Number of rectangles with odd area.
We have a $10\times 10$ square.
How many rectangles with odd area are on the picture?
I say lets choose a vertex first, there are $11\cdot11=121$ possibilities.
Now, choose odd width and side (left or right) and odd length and side (up or down). There are $5$ possibilities to eac... | [
"5",
"6",
"10",
"11"
] | D | r*c=90 and (11+4)(c-2)=90 --> r=11 and c=8.
Answer:D. |
AQUA-RAT | AQUA-RAT-38320 | # Thread: Help with probability question/
1. ## Help with probability question/
I'm struggling with probability questions, even those that should be easy! We didn't really go over techniques of solving these types of questions, and the textbook doesn't really address these types of problems (it's more of a stats book... | [
"5/11",
"8/15",
"9/20",
"10/21"
] | D | The total possible ways of selecting a 5-member team is 7C5 = 21
The possible ways which include John and Peter is 5C3 = 10
The probability of choosing both John and Peter is 10/21
The answer is D. |
AQUA-RAT | AQUA-RAT-38321 | # Math Help - Annual Compounding Interest
1. ## Annual Compounding Interest
Jane has $6 and Sarah has$8. Over the next few years, Jane invests her money at 11%. Sarah invests her money at 8%. When they have the same amount of money, how much will they have? Assume annual compounding interest, and round to the nearest... | [
" $20000",
" $15000",
" $12000",
" $10000"
] | B | Since investment doubles in 48/r years, then for r=8 it'll double in 48/8=~6 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*3=$15,000 .
Answer: B. |
AQUA-RAT | AQUA-RAT-38322 | There are 3 crates of apples A, B and C. The ratio of the number of apples in crate A to crate B to crate C is 8 : 5 : 3. David removed 42 apples from crate A and placed them into crate C. as such, there are 2 more apples in crate C than crate B. How many apples are there altogether?
2. HINT: 3k + 42 = 5k + 2
4. Orig... | [
"Rs 34",
"Rs 33",
"Rs 8",
"None of the above"
] | A | Explanation :
Let the person buy c chocolates, 2c buiscuits. Therefore, apples is >3c.
In any case, total cost will be
=>cost of chocolates + cost of biscuits + cost of apples.
=> (c*1) + [2c*0.5] + (2*something greater than 3c).
Thus, Total cost=>
=> 2c + (2* something greater than 3c).
Here, the total cost is an even... |
AQUA-RAT | AQUA-RAT-38323 | java, algorithm, knapsack-problem
Title: Stampcalculator - Given a set of stamps, what combinations are there to reach a certain amount? Background
My mother has a hobby of buying and reselling books via online trading sites. After a price is agreed on, the books have to be put into an envelope for mailing. On this en... | [
"(9x-5)/2",
"(7x+4)/2",
"5x+6",
"6x+5"
] | C | we can take
X+2 = 10
X= 8
So 3c envelopes will be 6
and 7c envelopes will be 4
So total cost will be 46
Then that is our target
Plug x =8 in answer choices
Only c works
Correct Answer : C |
AQUA-RAT | AQUA-RAT-38324 | 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 ... | [
"41",
"63",
"72",
"63"
] | C | 44 + 28 + 10 = 82%
100 – 82 = 18%
400 * 18/100 = 72
ANSWER:C |
AQUA-RAT | AQUA-RAT-38325 | # Lottery problem - dependent vs. independent events?
A lottery sells $10,000,000$ tickets with probability of winning at $\large\left(1\over 5000000\right)$
Let $t$ to represent the number of tickets sold. Using the formula $1-\left(4999999\over 5000000\right)\large^t$, the probability of there being a winner is app... | [
"$9 x 10^4",
"$9.90 x 10^6",
"$1.00 x 10^7",
"$1.05 x 10^7"
] | A | The max product of any two balls can be 9 * 10 = 9900 = 9 * 10
If we multiply it by $1000 the max amount will be 9 * 10^4.
A |
AQUA-RAT | AQUA-RAT-38326 | & \text{if b\equiv0\pmod{4}}\\ \\ \binom{n^2/4}{(b-1)/4} & \text{if b\equiv1\pmod{4}}\\ \\ 0 & \text{otherwise.}\end{cases}$$ Specializing to $b=n,$ we get $$C(n,n,C_4)=\begin{cases}\binom{n^2/4}{n/4} & \text{if n\equiv0\pmod{4}}\\ \\ \binom{(n^2-1)/4}{(n-1)/4} & \text{if n\equiv1\pmod{4}}\\ \\ 0 & \text{otherwise.}\en... | [
"20 : 35 : 63",
"20 : 15 : 27",
"30 : 35 : 65",
"25 :34: 68"
] | B | Expl : A : B = 4 : 3
B : C = 5 :9 = 5*3/5 : 9 *3/5 = 3 : 27/5
A : B : C = 4 : 3 : 27/5 = 20 : 15 : 27
Answer: B |
AQUA-RAT | AQUA-RAT-38327 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"140",
"150",
"160",
"170"
] | C | M=mathematics marks
E=english marks
M+E=240-(1eqution)
M=E+E/2-(2 equation)
put 2nd equation in 1st equation
E+E/2+E=240
3E/2=240
3E=240*2
3E=180
E=180/3
E=160
ANSWER:C |
AQUA-RAT | AQUA-RAT-38328 | 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... | [
"346",
"356",
"366",
"376"
] | D | 3x+4x+5x=240
x=20
6x+4x+9x=340
x=17.89
5*20+6*20+8*20=380-4=376
ANSWER:D |
AQUA-RAT | AQUA-RAT-38329 | The square of every integer is of the form either $3k+1$ or $3k$
How can I prove that square of every integer is of the form either $3k+1$ or $3k$, but not $3k+2$?
My approach
I considered first, the integer $n$ to be even and then $n= 2m$; and if $n$ is odd then $n=2m+1$ but this step takes me to nowhere. I get usu... | [
"2",
"5",
"8",
"7"
] | D | Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-1, +/-4 and +/-8, so the difference could be 7,9, or 12. Since only one of them is among the choices, then it must be the correct answer.
Answer: D. |
AQUA-RAT | AQUA-RAT-38330 | 2. ### math
list all the 3 digit numbers that fit these clues. the hundreds digits is less than 3. the tens digit is less than 2. the ones digit is greater than 7
3. ### Math
Think of a five-digit number composed of odd numbers. The thousands digit is two less than the ten thousands digit but two more than the hundr... | [
"300,000",
"349,999",
"350,000",
"399,999"
] | B | E 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B |
AQUA-RAT | AQUA-RAT-38331 | 05 Jan 2010, 14:01
IMO it's (A)
From Statement 1:
n = a * a * a * a * b * b * b
n has 13 factors: 12 different combinations of a & b + 1.
Statement 2 tells nothing: n could have only 2 prime factors but what about non-prime factors?! we should consider them too. f.e. 35, 25, 49 and so on.
Manager
Joined: 22 Jul 200... | [
"45",
"50",
"60",
"72"
] | D | AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 80
y - 80 + (y/4) = 80
5y/4 =160
y = 128
2x/3 = 128 - 80 = 48
x = 144/2 = 72
Answer: D |
AQUA-RAT | AQUA-RAT-38332 | Suppose an urn contains 8 red,5 white and 7 blue marbles.a.If 3 marbles are drawn at random from the urn with replacement,what is the probability that three marbles are red?
8. ### Math
there are 9 blue marbles, 4 black marbles, 5 white marbles and 6 red marbles. If the probability of drawing a blue marble is now 1/3,... | [
"b/(b+g)",
"(b+5)/(g+3)",
"(b+5)/(b+g+7)",
"(b+5)/(b+g+3)"
] | C | no of fav outcomes i.e. blue MArbles = b+5
Total no of outcomes i.e. total Marbles = (b+5)+(g+2)= b+g+7
probability = (b+5) /(b+g+7)
Answer C |
AQUA-RAT | AQUA-RAT-38333 | 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, ... | [
"{6, 12}",
"{6, 15}",
"{21,28}",
"{9, 15}"
] | C | p/q= d=p/q+7
d= .75 q
d= .6(q+7)
we get d = 21 and q = 28. Answer = C. |
AQUA-RAT | AQUA-RAT-38334 | 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... | [
"30",
"31",
"32",
"33"
] | D | # components A and B could manufacture efficiently:
A: 50*70% = 35
B: 50*30% = 15
# components A and B effectively manufacture:
A: 50*36% = 18
B: 50*64% = 32
Max. # components efficiently manufactured:
18 (from A) and 15 (from B) = 33
ANSWER:D |
AQUA-RAT | AQUA-RAT-38335 | 2. Mike says:
of course i meant 5 buckets, one for each student ;).
3. meichenl says:
Let there be $c$ cookies and $n$ students. Denote the number of ways to distribute $c$ cookies between $n$ students by $S_n(c)$. This is claiming that for a given number of students, the number of ways to distribute the cookies is ... | [
"35",
"105",
"60",
"210"
] | C | The question states that there are no more than 5 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4 or 5 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies ... |
AQUA-RAT | AQUA-RAT-38336 | # Expected number of hours that all employees take a break at the same time?
This is derived from a real question my company has, so the wording might sound a bit weird.
There are 4 employees, each working 8 hours a day. Breaks are in 1 hour blocks and employees may only take breaks at the beginning of an hour (so th... | [
"81",
"231",
"336",
"350"
] | A | Looks easy: -- 6C4*5C1 + 6C5 -- 81 (A). |
AQUA-RAT | AQUA-RAT-38337 | Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day... | [
"11",
"13",
"20 3/17",
"14"
] | B | Explanation:
Ratio of times taken by A and B= 100:130 =10:13
suppose B takes x days to work the 10:13::23:x =>x=23 x 13/10 = 299/10
A’s one day work = 1/23 and B’s is 10/299
Then A+B ‘s work = 1/23 + 10/299 = 23/299 =1/13 => 13 days
Answer: Option B |
AQUA-RAT | AQUA-RAT-38338 | 10. A $$2$$-foot brick border is constructed around a square cement slab. If the total area, including the border, is $$121$$ square feet, then what are the dimensions of the slab?
11. The area of a picture frame including a $$2$$-inch wide border is $$99$$ square inches. If the width of the inner area is $$2$$ inches... | [
"4955",
"4899",
"4650",
"7200"
] | A | Explanation:
no. of bricks= volume of the wall/volume of 1 brick = (900 x 500 x 18.5) / (21 x 10 x 8) = 4955
Answer: A |
AQUA-RAT | AQUA-RAT-38339 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"100",
"90",
"92",
"94"
] | A | 88-82=6*4=24 points
2*88=176
176+24=200 points to be scored in the 2 tests.
Avg of 2 tests = 200/2=100
Answer: A
Traditional Method:
Total scored till now 82*4=328
Total score to avg 88 in 6 tests = 88*6=528
Total to be scored on 2 tests = 528-328=200
Avg on 2 tests = 200/2 = 100
Answer A |
AQUA-RAT | AQUA-RAT-38340 | 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 ... | [
"3:4",
"3:5",
"4:3",
"1:3"
] | B | total profit =1000
ratio=300/500
=3:5
ANSWER:B |
AQUA-RAT | AQUA-RAT-38341 | speed of the car in miles per hour? what dimensions should he use? Custom Solutions. Find the fraction. Find the fraction. Given : This year, the chickens laid 30% less eggs than they did last year and they laid 3500 eggs this year. This was$14 less than twice what she spent for a blouse. So, the chickens laid 5000 egg... | [
"32 rolls",
"54 rolls",
"108 rolls",
"120 rolls"
] | D | Explanation:
Number of cuts made to cut a roll into 10 pieces = 9.
Therefore Required number of rolls = (45 x 24)/9 = 120.
Answer: D |
AQUA-RAT | AQUA-RAT-38342 | # 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... | [
"100%",
"175%",
"125%",
"180%"
] | C | If marked price is Rs 100/-
Selling price = Rs 80/-
Profit = 80*0.2= Rs 16
CP= Rs 64
List price = 64*100/80 = Rs 80
so marked price is 100*100/80 = 125%
ANSWER:C |
AQUA-RAT | AQUA-RAT-38343 | time, sun
d represents the day of the year for 2000. For example d=7
would be January 7th, 2000.
If you're willing to lose some precision in exchange for
convenience, you can compute the day of the current year (instead
of counting all the way back to 2000), since the sun's declination
repeats yearly (roughly speaking... | [
"wednesday",
"thursday",
"friday",
"saturday"
] | A | There is difference of 31 days from 3rd Dec 1999 to 3rd Jan 2000..
31/7 left with 3 odd days..
that is wednesday
ANSWER:A |
AQUA-RAT | AQUA-RAT-38344 | We have 8 members and a 3 slots. So total number of ways is 8*7*6, divided by 3! for double counts. 8*7*6/3!=56 .
Now what are the number of ways can we have two teams members on the committee?
We can pick any of the 8 for the first slot. The second slot is reserved for the team member of the first slot, so 1 ways. An... | [
"165",
"187",
"277",
"266"
] | A | Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2)
= 165 ways
Answer: A |
AQUA-RAT | AQUA-RAT-38345 | Hint: if $$8$$ is the largest single digit factor than doesn't it make sense that the largest such three digit number would be in the $$8$$ hundreds.
Now, that was the hard way. Were there any handy mathematical observations you might have used to make this easier? Would knowing that $$24 = 2^3*3$$ is the unique prime... | [
"30",
"120",
"210",
"300"
] | B | 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.
100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.
Then we want to know what is the largest possible GCF of x and 2100.
Well 1200 = 3 * 4 * 10 * 10
We want x to include... |
AQUA-RAT | AQUA-RAT-38346 | # 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... | [
"228",
"350",
"289",
"500"
] | B | P - 238 = (P*4*8)/100
P = 350
Answer: B |
AQUA-RAT | AQUA-RAT-38347 | 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... | [
"108 kmph",
"82 kmph",
"92 kmph",
"72 kmph"
] | D | Let the speed of faster train be f and slower train be y.
Time taken to cross each other traveling in the same direction = 250 +150/ (x-y) = 40………(1)
Time taken to cross each other traveling in the opposite direction = 250+150 /(x+y) = 8 …….(2)
From (1) and (2) f= 30 m/s and s = 20 m/s
Speed of slower train = 20 * 18/5... |
AQUA-RAT | AQUA-RAT-38348 | Hence: 5x/100*(t-1/2) + x = 1100 = 4x/100*(t) + x
Solving, xt will get cancelled and you will get:
11000 = 11x
x is 1000
sum of both investments is 2x = 2000 which is Option D
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1326
Location: Viet Nam
Andrew borrows equal sums of money under simple i... | [
"Rs. 850",
"Rs. 900",
"Rs. 980",
"Rs. 990"
] | A | Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mterest u — 12 : wzo — x
Therefore, by u xglurmula.
_umxx
’ Rx’: (
, _ma>< 1nzn—xv
\4Ve|\a\e,Jc— 5“
:> ~(:51DD—S*(or6x:51UU
or, J: : w 350
. The sum of money burrowed : Rs. 850
A) |
AQUA-RAT | AQUA-RAT-38349 | 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 ... | [
"0.",
"6.",
"8.",
"10."
] | A | Total = 102
failed in math = 102/3=34
failed in literature=108/6=17
the least failed in both can be 0
while max can be 17
Answer A |
AQUA-RAT | AQUA-RAT-38350 | # Math Help - Permutation Help!
1. ## Permutation Help!
Problem:
---------
There are 120 five-digit numbers that can be formed by permuting the digits 1,2,3,4 and 5 (for example, 12345, 13254, 52431). What is the sum of all of these numbers?
--------
399 960
I can't get this question...I don't know what to do...
Al... | [
"150",
"339",
"342",
"359"
] | C | Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer R= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C |
AQUA-RAT | AQUA-RAT-38351 | Since we are not interested on the numerical value of this equation, but that the result of the equation to be an integer, not a fraction, the n outside of the parenthesis is irrelevant.
So the equation could be written as, (3n ± 1)/2, and the result of this equation is always an integer for any odd or even value of n... | [
"2",
"3",
"5",
"7"
] | C | If p divides 3n+4, then p divides 24n+32.
If p divides 8n+9, then p divides 24n+27.
Then p must equal 5.
The answer is C. |
AQUA-RAT | AQUA-RAT-38352 | The average of even number of consecutive integers is nothing but the
average of the middle two numbers - number 3(x) and number 4(y)
The average of odd number of consecutive integers is the middle integer.
Therefore, $$\frac{x+y}{2}= 18.5 => x+y = 37$$ where x = 18 and y = 19
Hence, the third element must be the aver... | [
"21",
"29",
"19",
"14"
] | C | Explanation:
Sum of 10 even numbers = 18 * 19 = 342
Average = 342/18 = 19
Answer: Option C |
AQUA-RAT | AQUA-RAT-38353 | 27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14... | [
"30",
"31",
"32",
"33"
] | B | leave the number 31 in the series,then note that 29,30,31
hence 31 is the result
ANSWER:B |
AQUA-RAT | AQUA-RAT-38354 | 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, ... | [
" I only",
" II only",
" III only",
" I and II only"
] | A | Problem statement was difficult to parse. but some how I managed to understand what we can do.
1) x/y = 15 + 0.15
2) x/y = 18 + 0.18
3) x/y = 17 + 0.17
w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)
therefore :
1) y*0.15=60 -- we can get y an integer.
2) y*0.18=60 -- we can't get y an integer.
3) y*0.17=60 -- we can't ge... |
AQUA-RAT | AQUA-RAT-38355 | For some reason I find it easier to think in terms of letters of a word being rearranged, and your problem is equivalent to asking how many permutations there are of the word YYYYBBBBB.
The formula for counting permutations of words with repeated letters (whose reasoning has been described by Noldorin) gives us the co... | [
"2880",
"7670",
"1192",
"5039"
] | D | Explanation:
Number of words which can be formed = 7! - 1 = 5040- 1 = 5039.
Answer: D |
AQUA-RAT | AQUA-RAT-38356 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"wnp",
"wn/p",
"(w + n)/p",
"wnp/(w + n)"
] | D | let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/w
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/w)+(d/n)
=d(w+n)/wn
d=wmn/(w+n)=D |
AQUA-RAT | AQUA-RAT-38357 | python, python-3.x, programming-challenge
Title: Sum square difference Problem description:
The sum of the squares of the first ten natural numbers is,
1² + 2² + … + 10² = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + … + 10)² = 55² = 3025
Hence the difference between the sum of the squares o... | [
"35 and 46",
"35 and 49",
"35 and 42",
"35 and 41"
] | A | Explanation:
Let the numbers be x and y. Then,
Adding (i) and (ii), we get :
Subtracting (ii) from (i), we get :
So, the numbers are 35 and 46
Answer: A |
AQUA-RAT | AQUA-RAT-38358 | # 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... | [
"$100",
"$115",
"$125",
"$130"
] | C | Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500... |
AQUA-RAT | AQUA-RAT-38359 | # Write 100 as the sum of two positive integers
Write $100$ as the sum of two positive integers, one of them being a multiple of $7$, while the other is a multiple of $11$.
Since $100$ is not a big number, I followed the straightforward reasoning of writing all multiples up to $100$ of either $11$ or $7$, and then fi... | [
"17",
"16",
"15",
"14"
] | B | 7^2+5^2+4^2=49+25+16 = 90
7+5+4 =16
Hence answer is B |
AQUA-RAT | AQUA-RAT-38360 | ### 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 ... | [
"20%",
"15%",
"33.33%",
"18%"
] | B | Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 10 liters of milk.
Therefore, profit percentage = 15 %. Answer: B |
AQUA-RAT | AQUA-RAT-38361 | 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... | [
"Rs.16000",
"Rs.12000",
"Rs.15000",
"Rs.13000"
] | C | Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).
{(x * 15 * 1)/100 } + { [(24000 – x) * 18 * 1]/100 } = 4050
or 15 x + 432000 - 18x = 405000 or x = 9000.
Money borrowed at 15% = Rs 9000 .
Money borrowed at 18% = Rs 15000.
answer :C |
AQUA-RAT | AQUA-RAT-38362 | I made a mistake. After I get 10 planes, I should count the lines, because 3 plane could share the same line.
Let the 5 points be 12345. The 10 plane contain the points are
123 (the plane contain 123)
124
125
134
135
145
234
235
245
345
When two points appear on more than 2 row , it means more than two planes will shar... | [
"03",
"4",
"5",
"1"
] | A | You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines.
AB , AC
BA , BC
CA , CB
There is a problem: line AB is the sa... |
AQUA-RAT | AQUA-RAT-38363 | This seems way too high, and there's probably something I'm missing here. Any thoughts on this calculation, or what it should be?
• Your locker's combination is now the target. You are hoping either the one on your left matches it OR the one to your right matches it. It seems to me is a simple '+' instead of '*'. – Mi... | [
"6",
"8",
"10",
"5"
] | A | as no. 3rd key position get fixed.so we have to calculate total no. of configuration of rest three key.
which is permutation of three item,3P3=3!=6
answer A |
AQUA-RAT | AQUA-RAT-38364 | # Calculating probability of 8 letter String [closed]
Computer generate 8 string password with letters a,b,c,d,e. Each letter is chosen independently and with equal liklihood of being selected.
What is the probability that the string has 8 of the same letter?
What is the probability that there is at least one a and ... | [
"63^4",
"62^5",
"72^4 * 73",
"73(62^4)"
] | C | Total number of passwords = number of 5 character password +number of 6 character password
= 72^4 + 72^5 (Since there is no limitation on repetition , each character can be chosen in 72 ways )
=72^4(1+ 72)
=72^4 * 73
Answer C |
AQUA-RAT | AQUA-RAT-38365 | # Kinematics Problem
1. Feb 24, 2008
### undefinable
1. The problem statement, all variables and given/known data
Alvin races Ophelia to Physics class. Alvin has a headstar of 13m and travels at a constant speed of 7m/s. Phelia is initially travelling at 1.2m/s but then begins to accelerate at 1.5m/s2 until she rea... | [
"228",
"2197",
"666",
"100"
] | D | A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.Answer: D |
AQUA-RAT | AQUA-RAT-38366 | A boy and his sister. When you subtract two from the boy’s real age and add two to his sister’s age, his sister
becomes twice his NEW (subtracted) age. If you subtract three from his real age instead and add three to his sister then she becomes thrice his NEW (subtracted) age. What are their real ages?
A little more de... | [
"20",
"21",
"22",
"23"
] | D | Let the daughter's present age be x years. Then, man's present age = (x + 25) years.
(x + 25) + 2 = 2(x + 2)
x + 27 = 2x + 4
x = 23.
Answer:D |
AQUA-RAT | AQUA-RAT-38367 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"125.5 meters",
"126.5 meters",
"127.5 meters",
"128.5 meters"
] | C | Explanation:
When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.
Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.
So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.
So, in a race of 600 meters, the nu... |
AQUA-RAT | AQUA-RAT-38368 | 4. ### MikeML AAC Fanatic!
Oct 2, 2009
5,450
1,066
Psec/1bolt * 5bolts/1rev * 1rev/78.4in *...
The OP specified that the circumference of the wheel is 78.4in. Why do we need to include the radius in the conversion?
Last edited: Sep 8, 2015
5. ### Wendy Moderator
Mar 24, 2008
20,766
2,536
Because I missed that littl... | [
"724 m",
"704 m",
"287 m",
"278 m"
] | B | In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm
= 704 m
Answer:B |
AQUA-RAT | AQUA-RAT-38369 | homework-and-exercises, special-relativity, inertial-frames, observers
But how much has John aged, according to Mike?
During t1, John was stationary according to Mike and therefore aged t1. During t2 + t2, John was moving at 0.5c, so aged
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"21",
"24",
"27",
"30"
] | D | P = 3Q so Q = P/3
P+11 = 2(Q+11) = 2(P/3+11)
P/3 = 11
P = 33
Three years ago, P was 30.
The answer is D. |
AQUA-RAT | AQUA-RAT-38370 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"2hrs",
"6hrs",
"5hrs",
"4hrs"
] | B | Part filled by A in 1 hour = 1/10
part filled by B in 1 hour = 1/15
Part filled by A+B in 1 hour = 1/10 + 1/15 = 1/6
Both the pipes will together will fill the tank in 6 hours.
Answer is B |
AQUA-RAT | AQUA-RAT-38371 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"26 sec",
"32 sec",
"13 sec",
"48 sec"
] | D | Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 800 * 3/50
= 48 sec.
Answer:D |
AQUA-RAT | AQUA-RAT-38372 | harpazo
#### harpazo
##### Pure Mathematics
Sure you do...you know that the number $$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... | [
"18",
"24",
"42",
"81"
] | B | Let the two digit number is 10x+y
Product of the digits x*y=8
10x+y+18=10y+x
on solving this we get X-y=-2
x+y=6
by solving the above two equations we get x=2 and y=4
therefore the digit is 10*2+4=24
ANSWER:B |
AQUA-RAT | AQUA-RAT-38373 | # 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... | [
"15000",
"15029",
"26882",
"82976"
] | A | Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x
= 18000 - 10/100(18000)
= 18000 - 1800
= Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer:A |
AQUA-RAT | AQUA-RAT-38374 | Advertisement Remove all ads
# Answer the following : The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. - Mathematics and Statistics
Sum
Answer the following :
The mean height of 200 studen... | [
"A)48.55",
"B)49",
"C)51",
"D)61"
] | A | Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55kg
Answer is A |
AQUA-RAT | AQUA-RAT-38375 | The price then decreased by 12% during 2013
A 12% DECREASE is the same a multiplying the price by 0.88
So, the new price = ($100)(1 + p/100)(0.88) The price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012 If the original price was$100, then the price at the end of 2013 was $110 So,... | [
"1.5 years",
"2 years",
"3 years",
"13 years"
] | B | not sure whether you like this:
81 - (81 x 67%)/3 = 81 - (81 x 2) / 3 = 27 = 81 / 31 = 81 / (3x3x3x3) = 81 / 3^4
so the time = 4 x 6 months = 24 months or 2 years. answer is B |
AQUA-RAT | AQUA-RAT-38376 | c#, winforms, fixed-point
Title: Divide decimal by range of fractions, and then convert the fraction that is closest to a whole number to a mixed fraction My program will divide the decimal (\$30.0575\$) by a range of fractions (\$\frac{1}{1}, \frac{1}{2}, \frac{1}{4}, \dots, \frac{1}{48})\$ leaving me with list of im... | [
"8/25",
"16/50",
"17/50",
"19/50"
] | A | Answer
0.32 = 32/100 = 8/25
Correct Option: A |
AQUA-RAT | AQUA-RAT-38377 | If stock price is $$X = (0,30)$$; we use the 7 puts (A) for profit = 7(40 - X); 9 (B) puts are used giving a loss = 9(30 - X). Total earning = 7(40-X) -9(30-X) + 2$= 2X + 12$ > 0
- 3 years, 2 months ago
Assume that the $40 put is still priced at$10.
What would be the price of the $30 put option, where there will be ... | [
"240",
"99",
"278",
"277"
] | A | (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A |
AQUA-RAT | AQUA-RAT-38378 | # Ratio between the width of the intersection of two identical intersecting circles and radius, when the intersection is $\frac{\pi r^2}{2}$
Or more visually, if all sections of the below diagram were equal in area and the circles are identical, what is the ratio of s and r, or what is s in terms of r.
I came up with... | [
"4:25",
"2:9",
"1:9",
"3:7"
] | A | r1: r2 = 2: 5
Î r1^2: Î r2^2
r1^2: r2^2 = 4:25
Answer: A |
AQUA-RAT | AQUA-RAT-38379 | ### Show Tags
04 Aug 2019, 03:54
generis wrote:
Ayush1692 wrote:
If y is a positive integer, and |x| < 5 − y, then what is the least possible value of x ?
A. 4
B. 1
C. 0
D. -1
E. -4
Don't remove brackets and solve. The question asks for the logic behind absolute value.
$$y$$ is a positive integer
$$|x| < 5 − y$$
... | [
"1.2",
"0.2",
"1.8",
"2.2"
] | A | Since y* is defined as the greatest positive even integer less than or equal to y, then 7.2* = 6 (the greatest positive even integer less than or equal to 7.2 is 6).
Hence, 7.2 –7.2* = 7.2 - 6 = 1.2
Answer: A. |
AQUA-RAT | AQUA-RAT-38380 | 0\cr −1 \cr −1\cr 1 \cr 0 } \right ],\kern 1.95872pt \left [\array{ 1\cr 1 \cr 3\cr 0 \cr 3 } \right ]\right \}\right \rangle & & & & \cr ℒ\kern -1.95872pt \left (G\right ) = ℛ\kern -1.95872pt \left (L\right ) & = \left \langle \left \{\left [\array{ 1\cr 0 \cr 0\cr 0 \cr −{1\over 3} } \right ],\kern 1.95872pt \left [\... | [
"9",
"7",
"$",
"5"
] | D | Explanation:
5 is the ninth to the right of the twentieth element from the right end of the above arrangement
ANSWER IS D |
AQUA-RAT | AQUA-RAT-38381 | 2nd largest value = 231+510.222
so largest difference between them = 222
C . $2^{22}$
111111111 can be written as $2^{10}-1$
So Largest No. 1.111111111 x $2^{31}$ equivalent to ($2^{10}-1$) x $2^{-9}$ x $2^{31}$
Second largest No. 1.111111110 x $2^{31}$ equivalent to ($2^{10}-2$) x $2^{-9}$ x $2^{31}$
difference ... | [
"10",
"1000",
"100",
"10000"
] | C | 10^222 ÷ 10^220 = 10^(222 - 220) = 10^2 = 100
Answer is C |
AQUA-RAT | AQUA-RAT-38382 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"15 sec",
"18 sec",
"19 sec",
"28 sec"
] | B | D = 180
S = 36 * 5/18 = 10 mps
T = 180/10 = 18 sec
Answer:B |
AQUA-RAT | AQUA-RAT-38383 | To get the required result in the book you first have to calculate the amount of the equivalent annual payment. The formula for payments at the beginning of every month is
$C_1=12\cdot r+\frac{\color{blue}{13}\cdot r\cdot i}{2}$
In case of payments at the end of every month $\color{blue}{13}$ has to be replaced by $1... | [
"6",
"7",
"9",
"10"
] | B | First payment--$500
Total amount to be repaid--$1093500
First month payment--$500
Second month payment--$500*3=$4500
Third month payment--$4500*3=$13500
Fourth month payment--$13500*3=$40500
Fifth month payment--$40500*3=$121500
Sixth month payment--$121500*3=$364500
Seventh month payment--$364500*3=$1093500
Answer is ... |
AQUA-RAT | AQUA-RAT-38384 | Let one woman complete the job in $$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}$$ job/day... | [
"6 p.m.",
"7 p.m.",
"8 p.m.",
"10 p.m."
] | C | Let the total work be 24 units.
Frances can complete 2 units/hr
Joan can complete 2.67 units/hr
Work done by Frances in 8 hours is 16 units ; work left for Joan is 8 units ( 24 - 16)
Time required by Jones to complete the remaining work will be 8/2.67 => 3 hours
Given Jones starts at 5PM , so she would complete the wor... |
AQUA-RAT | AQUA-RAT-38385 | Problem #2: A box contains 18 tennis balls, 8 new 10 old. 3 balls are picked randomly and played with (so if any of them were new, they become 'old'), and returned to the box. If we pick 3 balls for the second time (after this condition), what is P that they are all new? I broke this down into 4 pieces: P(3 new second ... | [
"11",
"88",
"25",
"88"
] | C | A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.Answer: C |
AQUA-RAT | AQUA-RAT-38386 | homework-and-exercises, special-relativity, inertial-frames, observers
But how much has John aged, according to Mike?
During t1, John was stationary according to Mike and therefore aged t1. During t2 + t2, John was moving at 0.5c, so aged
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"15",
"20",
"18",
"22"
] | A | Let the present age of Arun and Deepak be 4x and 3x
4x+6 = 26
4x = 20
x = 5
Deepak's age = 3x = 15 years
Answer is A |
AQUA-RAT | AQUA-RAT-38387 | 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... | [
"5 seconds",
"4.3 seconds",
"3 seconds",
"2.5 seconds"
] | B | Explanation:
First convert speed into m/sec
Speed = 154*(5/18) = 42 m/sec
Time = Distance/speed
= 180/42 = 4.3 seconds
Option B |
AQUA-RAT | AQUA-RAT-38388 | Finally, if $$D=2$$ (i.e., $$ABCD=1002$$), we can only have $$c+f=3+9$$ or $$c+f=5+7$$. In either case we'll need $$b+e=9$$, which is possible only as $$2+7$$ or $$4+5$$. If $$c+f=3+9$$, either of these is possible, while neither is possible if $$c+f=5+7$$. So again we get just two solutions, namely $$243+759=1002$$ an... | [
"4.",
"8.",
"12.",
"16."
] | A | EQ1: A - B - C + D = 13
EQ2: A + B - C - D = 9
(1) Subtract EQ1 from EQ2
A - B - C + D = 13
- A +B - C - D = 9
------------------------
-2B + 2D = 4
(2) Simplify
-B + D = 2
B - D = -2
(B-D)^2 = (-2)^2 = 4
My answer: A |
AQUA-RAT | AQUA-RAT-38389 | $38k - (2*38 - 7)l = 34$
$38(k-2l) + 7l = 34$. Let $m=k-2l$
$38m + 7l = 34$.
$(3+ 5*7)m + 7l = 34$
$3m + 7(5m + l) = 34$. Let $n = 5m+l$.
$3m + 7n = 34$
$3m + 2*3n + n = 34$
$3(m + 2n) + n = 34$. Let $a = m+2n$.
$3a + n = 34$.
Let $a=11; n = 1$. So $a=m+2n; 11=m + 2; m = 9$. and $n= 5m + l; 1=5*9 +l; l = -44$.... | [
"117",
"126",
"252",
"336"
] | B | Explanation:
L.C.M of 3, 4, 5, 6 = 60
therefore Required Number is of the form 60k+6.
Least value of k for which (60k+6) is divisible by 9 is k = 2
therefore Required Number = (60 x 2+6)=126.
Answer: B |
AQUA-RAT | AQUA-RAT-38390 | # Probability a 9-digit number has the digits 2,4, and 6 next to each other.
The integers $1,2,3,....,9$ are arraned (at random) in a row, resulting in a $9$-digit integer (without replacement). What is the probability that:
The result is even? $\frac49$ or $\frac{4(8!)}{9!}$
The result is divisible by $5$? The numb... | [
"1/9",
"10/243",
"2/45",
"10/271"
] | C | If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 12/(9... |
AQUA-RAT | AQUA-RAT-38391 | homework-and-exercises, special-relativity, inertial-frames, observers
But how much has John aged, according to Mike?
During t1, John was stationary according to Mike and therefore aged t1. During t2 + t2, John was moving at 0.5c, so aged
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"12 years.",
"24 years.",
"17 years.",
"16 years."
] | B | Let the son's present age be x years. Then, (56 - x) = x
2x = 56.
x = 28
Son's age 4 years back (28- 4) = 24 years.
ANSWER :B |
AQUA-RAT | AQUA-RAT-38392 | # computing probability that at least one letter matches with envelope
Four letters to different insurers are prepared along with accompanying envelopes. The letters are put into the envelopes randomly. Calculate the probability that at least one letter ends up in its accompanying envelope.
### Attempt
Since this is... | [
"1/2",
"6/7",
"0",
"1/12"
] | C | Explanation :
Answer is Zero. Question is asking whether there is any chances of one letter getting inserted in an improper envelope, but there can-not be onr case as if one gets improper there is another letter who will be inserted in the improper envelope too...
Hence C is the answer.
Answer : C |
AQUA-RAT | AQUA-RAT-38393 | # 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 ... | [
"16",
"121",
"45",
"456"
] | A | 128 is the total sum of money.
as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils
128-120 = 8
so now we need to get 8 from either 5 dollar bills or 1 dollar bills
8 - 5 (use only 1 5 dollar bill) = 3
so we can get 3 from using 3 $1 bills.
Hence 16 ( ... |
AQUA-RAT | AQUA-RAT-38394 | I'm assuming that the four fingers are given, e.g., the fingers of one hand without the thumb. An arrangement of five distinguishable rings on the four labeled fingers amounts to a linear arrangement of $1$, $2$, $3$, $4$, $5$, and three indistinguishable zeros as separators. There are ${8!\over3!}=6720$ such arrangeme... | [
"a) thumb",
"b) the index finger",
"c) the middle finger",
"d) the ring finger"
] | D | Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1997 has to be the ring finger
Answer is (D) |
AQUA-RAT | AQUA-RAT-38395 | # Difference between revisions of "2017 AMC 10A Problems/Problem 25"
## Problem
How many integers between $100$ and $999$, inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999?$ For example, both $121$ and $211$ have this property.
$\mathrm{\textbf{(A)} \ }226... | [
"12",
"13",
"16",
"15"
] | C | Multiples of 25 = 25,50,75,-----400
Number of multiples of 25 => 25*16= 400
Answer is C |
AQUA-RAT | AQUA-RAT-38396 | # If $28a + 30b + 31c = 365$, then what is the value of $a +b +c$?
Question: For 3 non negative integers $a, b, c$; if $28a + 30b + 31c = 365$ what is the value of $a +b +c$ ?
How I approached it : I started immediately breaking it onto this form on seeing it :
$28(a +b +c) +2b +3c = 365 .......(1)$ $30(a +b +c) -2a... | [
"31.5",
"25.5",
"32.5",
"33.8"
] | A | A/B=7/5,
B/C=3/4,C=30
B=90/4
4A/90=7/5
A=630/20
A=31.5
ANSWER:A |
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