source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38597 | in n yrs and A 2 in (n+1) yrs, then Rate of compound interest =(A 2 - A 1)/A 1 *100% Sum = A 1 (A 1 /A 2) n. 596 APPENDIXC:COMPOUNDINTERESTTABLES 1/2% CompoundInterestFactors 1/2% SinglePayment UniformPaymentSeries ArithmeticGradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund ... | [
"198",
"279",
"267",
"200"
] | D | P(11/10)4 - P(6/5)2
= 482
P = 200
Answer: D |
AQUA-RAT | AQUA-RAT-38598 | => 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... | [
"5872",
"5839",
"5832",
"5838"
] | C | ratio of their investments Rs.12000:20000=3:5
12% of the profit for managing the business =12/100*9000=1080
remaining profit=9000-1080=7920
share profit in ratio of investment 7920/5 =1584
Moses's ratio share=3*1584=4752
total money Moses collects=4752+1080=5832
Answer: C |
AQUA-RAT | AQUA-RAT-38599 | +0
# SOS!!!
0
230
7
+223
I cannot get the right answer for this problem for the life of me. If somebody would solve it I'd give them 5 stars.
THE PROBLEM:
(20+(1/4))x +(5+(1/2)) = (7+(1/16))
(solve for x)
#1
+10
(20+(1/4))x + (5+(1/2)) = (7+(1/16))
(20(1/4))x = (7+(1/16)) - (5+(1/2))
x = ( (7+(1/16)) - (5+(1... | [
"2",
"4",
"6",
"8"
] | B | 1. Divide both sides by 7:
2. Simplify both sides:
x - 1 = 3
3. Add 1 to both sides:
x - 1 + 1 = 3 + 1
4. Simplify both sides:
x = 4
B |
AQUA-RAT | AQUA-RAT-38600 | 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... | [
"11",
"7",
"76",
"37"
] | D | 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D |
AQUA-RAT | AQUA-RAT-38601 | # Three Times Larger: Idiom or Error?
Having just written about issues of wording with regard to percentages, we should look at another wording issue that touches on percentages and several other matters of wording. What does “three times larger” mean? How about “300% more”? We’ll focus on one discussion that involved... | [
"16 1⁄6%",
"25%",
"33 1⁄3%",
"50%"
] | D | This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction E is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denomi... |
AQUA-RAT | AQUA-RAT-38602 | 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... | [
"28 sec",
"30 sec",
"17 sec",
"23 sec"
] | B | Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (13 + 23)5/18 = 300* 18 / 36 * 5 = 30 seconds.
Answer : B |
AQUA-RAT | AQUA-RAT-38603 | comes up heads. The student will count the coins and write their answer to the right of each problem. The probability of all three tosses is heads: P ( three heads) = 1 × 1 + 99 × 1 8 100. ' 'The coin is just as likely to land heads as tails. Probability measures and quantifies "how likely" an event, related to these t... | [
"1/4",
"1/3",
"1/2",
"2/3"
] | C | the three coins are HH LL HT
total possiblity are 6
1st head probablity are 2/6,
2 nd head probablity are 0,
third head probablity are 1/6,
The total head probablity is 2/6+0+1/6=1/2,
Then tail probablity is 1-1/2=1/2
ANSWER:C |
AQUA-RAT | AQUA-RAT-38604 | # Math Help - Distance (Word Problem)
1. ## Distance (Word Problem)
Hello I currently am stumped on a word problem that appeared on my homework, it is as follows...
"Driving from Dallas towards Memphis, JoJo averages 50mph. She figured that if she had averaged 60mph the driving time would have decreased by 3 hours. ... | [
"19",
"20",
"22",
"21"
] | B | Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked (t + 1) miles. These distances must sum to 31 miles, so 2t + (t + 1) = 31, which may be solved for t as follows
2t + (t + 1) = 31
2t + t + 1 = 31
3t = 30
T = 10 (hours)
Therefore, Bo... |
AQUA-RAT | AQUA-RAT-38605 | combinatorics, sets, matching
Put your students in a row: $a!$ possibilities. The first $b$ students form the first group, the next $b$ students the second group, etc. The order in the line-up between each group of students does not matter, so we have to divide by th1s number of possibilities which is $(c!)^b$. Again ... | [
"144",
"119",
"113",
"117"
] | D | Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 236 = 27
Greatest - Smallest is 144-27 = 117
So answer must be D. 117 |
AQUA-RAT | AQUA-RAT-38606 | comes up heads. The student will count the coins and write their answer to the right of each problem. The probability of all three tosses is heads: P ( three heads) = 1 × 1 + 99 × 1 8 100. ' 'The coin is just as likely to land heads as tails. Probability measures and quantifies "how likely" an event, related to these t... | [
"1/6",
"2/6",
"3/6",
"4/6"
] | A | 1/2 * 2/6 = 1/6
ANSWER:A |
AQUA-RAT | AQUA-RAT-38607 | Author Message
TAGS:
### Hide Tags
Manager
Joined: 26 Apr 2010
Posts: 122
Concentration: Strategy, Entrepreneurship
Schools: Fuqua '14 (M)
Followers: 2
Kudos [?]: 129 [0], given: 54
$686,000 in bonus money is to be divided among 6 employees. No employe [#permalink] ### Show Tags 26 Nov 2010, 13:52 3 This post was B... | [
"5%",
"12%",
"25%",
"75%"
] | D | Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 4X.
Increase = 4X-X =3X
The increase is what percent of the employees’ new bonus
= (3X/4X)*100
= 75%
Hence D. |
AQUA-RAT | AQUA-RAT-38608 | 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... | [
"10 hours",
"12 hours",
"16 hours",
"18 hours"
] | B | Explanation:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)–(1/2) = 1/12
=> B alone can complete the work in 12 hour
Option B |
AQUA-RAT | AQUA-RAT-38609 | 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... | [
"100",
"625",
"600",
"7500"
] | A | Max No. of crates=6.
Max Weight=100Kg
Max. weight carried = 6*100=100Kg=A. |
AQUA-RAT | AQUA-RAT-38610 | ### 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... | [
"20",
"24",
"18",
"15"
] | C | S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
ANSWER C |
AQUA-RAT | AQUA-RAT-38611 | 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.
Which of the following numbers is the biggest => [-6/7 , -7/8 , -9/10 , -12/13 , -34/35] | [
"-6/7",
"-7/8",
"-9/10",
"-12/13"
] | A | Another way to solve this question :
[-6/7 , -7/8 , -9/10 , -12/13 , -34/35] can be written as
-1+1/7, -1+1/8, -1 + 1/10, -1+1/13, -1+1/35
Now, in order to make the number larger, we need to add something larger to -1.
In first option, we can see 1/7 is the largest of all the other given
Hence, A |
AQUA-RAT | AQUA-RAT-38612 | • In the problem stated above, there are two towers of different heights. The distance of the tower with height $h_1$ to the horizon is $d_1=\sqrt{2rh_1}$. The distance of the tower with height $h_2$ to the horizon is $d_2=\sqrt{2rh_2}$. Thus, the distance between the towers is $d_1+d_2=\sqrt{2rh_1}+\sqrt{2rh_2}$. If $... | [
"(x+z)/2 + 37",
"2x−(37+z)",
"(x−37)/2 + z",
"(x - 37 )/2"
] | D | I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h12= h21+ 37 =>
h1 + h1+ 37 = x => 2h1 = x-37 =? h1 = (x-37)/2
, CORRECT ANSWER D |
AQUA-RAT | AQUA-RAT-38613 | # 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... | [
"28.5",
"27.675",
"30",
"50"
] | D | Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100×(100+42.5)/(100−5)=150
Hence, required % Profit = 150 – 100 = 50%
Answer D |
AQUA-RAT | AQUA-RAT-38614 | # Math Help - Prob. Question
1. ## Prob. Question
Question
5 boys (call them A,B,C,D,E) place their books in a bag. The 5 books are are drawn out in random order and given back to the 5 boys. What is the probability that exactly 3 boys will receive their original book?
Help wanted please. The only way I could think ... | [
"31/90",
"3/10",
"1/3",
"38/45"
] | D | Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
Favourable Outcomes
Case-1: One book is English (out of 5 English books) and one book is Spanish (out of 4 Spanish books) i.e. 5C1*4C1
Case-2: One book is Spanish (out of 4 Spanish books) and one book is Portuguese (out of 2 Po... |
AQUA-RAT | AQUA-RAT-38615 | Back
## A Test Question
Today, Pearl’s $9$ grandchildren are coming to visit! She loves to spoil them, so she opens her purse and finds $13$ dollar bills.
In how many different ways can Pearl distribute those dollars amongst her grandchildren? Keep reading to find out, or skip to today’s challenge for a similar prob... | [
"15",
"17",
"0",
"67"
] | A | If 3 people give you 5 dollars you will have 15
3x5=15 A |
AQUA-RAT | AQUA-RAT-38616 | We are given: .a
5 = 120 .and .a6 = 720
Then: .r .= .a
6/a5 .= .720/120 .= .6
. . The "rule" is multiply-by-six.
Therefore, the preceding term is: .a
4 = 20.
See? .We could have eyeballed the problem . . .
5. Originally Posted by Soroban
. . There is a simpler solution.
I always tell my students that I have a ten... | [
"125",
"280",
"384",
"400"
] | C | Explanation:
Let the number be x.
5*x/6 = 5*x/16 + 200
25*x/48 = 200
x = 384
ANSWER: C |
AQUA-RAT | AQUA-RAT-38617 | 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.
. .... | [
"2/8",
"3/4",
"7/16",
"5/24"
] | D | We will pretend that the Red Hotel has a total of 8 rooms. This means that the Blue Hotel would have 24 rooms. From this, we can deduce that there is 2 bookings at the Red Hotel and 3 bookings at the Blue Hotel. If the two bookings from the Red Hotel moved to the blue hotel that would mean a total of 5 bookings at the ... |
AQUA-RAT | AQUA-RAT-38618 | comes up heads. The student will count the coins and write their answer to the right of each problem. The probability of all three tosses is heads: P ( three heads) = 1 × 1 + 99 × 1 8 100. ' 'The coin is just as likely to land heads as tails. Probability measures and quantifies "how likely" an event, related to these t... | [
"(0.4)^5 + 5(0.4)^4(0.6) + 10(0.4)^3(0.6)^2",
"(0.6)^5 + 4(0.6)^4(0.4) + 6(0.6)^3(0.4)^2",
"(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2",
"(0.6)^5 + 2(0.6)^4(0.4) + (0.6)^3(0.4)^2"
] | A | Probability of Head, P(H) = 0.4
Probability of Tail, P(T) = 0.6
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.4)^3*(0.6)^2
1 Tail and 4 Heads, Probability = 5C1*(0.4)^4*(0.6)^2
0 Tail and 5 Heads, Probability = (0.4)^5
Required Probability = Sum of all Favourable ca... |
AQUA-RAT | AQUA-RAT-38619 | # When will train B catch up with train A?
Printable View
• January 27th 2010, 08:19 PM
bball20
When will train B catch up with train A?
Trains A & B are traveling in the same direction on a parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 5:15 PM. If tra... | [
"5am",
"6am",
"7am",
"8am"
] | B | 1 train 12.00 = 60km ; 2 train 1.30 = 80km;
1 train travel till 1.30 = 90 km.
1 2
150 80 -2.30
210 160 3.30
270 240 4.30
330 320 5.30
360 360 6.00
so they meat at 6am
ANSWER:B |
AQUA-RAT | AQUA-RAT-38620 | # Find the smallest integer $n\geq1$ such that $35n$ is a perfect square and $n/7$ is a pefect cube.
Find the smallest integer $n\geq1$ such that $35n$ is a perfect square and $n/7$ is a pefect cube. What I have so far: we express the prime factorizations of $35$ and $7$ as $5\cdot7$ and $7$, respectively. Then $n$ mu... | [
"5",
"7",
"47",
"9"
] | D | Given 738-x is a perfect cube
so we will take 729 = 9*9*9
738-x = 729
x =738-729 = 9
correct option is D |
AQUA-RAT | AQUA-RAT-38621 | $$3c-3\ge 2c+4$$
which comes out as $$c\ge 7$$. What follows is that then $$b\ge 8$$ and $$a\ge 9$$, so $$a+b\ge 17$$ and therefore $$c+d+e\ge 18$$, and so finally $$a+b+c+d+e\ge 17+18=35$$. So we have at least $$35$$ sweets altogether.
To prove that $$35$$ is the actual minimum, verify that all the conditions are sa... | [
"144",
"189",
"234",
"279"
] | D | Given that Red is to yellow is 2:5, Red is to green is 3:8 and Yellow is to blue is 9:2.
Therefore, the total number of red, yellow, blue and green balls will be 18x, 45x, 10x and 48x respectively, where x is a constant.
If the combined number of red and blue balls is fewer than 85, i.e. max 84 balls, then the maximum ... |
AQUA-RAT | AQUA-RAT-38622 | 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... | [
"98 days",
"21 days",
"48 days",
"18 days"
] | C | WC = 1:2
2x + x = 1/32 => x = 1/96
2x = 1/96 => 48 days
Answer:C |
AQUA-RAT | AQUA-RAT-38623 | 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... | [
"22",
"28",
"25",
"77"
] | C | D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer: C |
AQUA-RAT | AQUA-RAT-38624 | 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... | [
"40",
"20",
"25",
"30"
] | A | 250 Employees:
90 Male, 160 Female
40 Managers, 210 Associates
160 Male Associates implies 50 Female Associates which means the remaining 40 females must be Managers
A. 40 |
AQUA-RAT | AQUA-RAT-38625 | # 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",
"$250",
"$200",
"$150"
] | B | Let C.P. be $x
then, (110% of x)-(90% of x) = 50 or 20% of x=100
x/5 = 50
x=250
C.P. = $250
correct option is B |
AQUA-RAT | AQUA-RAT-38626 | 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... | [
"39, 30",
"41, 32",
"42, 33",
"43, 34"
] | C | Let their marks be (x + 9) and x.
Then, x + 9 = 56 /100(x + 9 + x)
=25(x + 9) = 14(2x + 9)
= 3x = 99
=x = 33
So, their marks are 42 and 33.
ANSWER IS C |
AQUA-RAT | AQUA-RAT-38627 | # 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... | [
" 21",
" 42",
" 120",
" 504"
] | A | Larry, Michael, and Peter have five donuts to share.to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A |
AQUA-RAT | AQUA-RAT-38628 | 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... | [
"6 only",
"12 only",
"6 and 12 both",
"by 18 only"
] | C | (6n^2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
Answer C) 6 and 12 both. |
AQUA-RAT | AQUA-RAT-38629 | Show Tags
14 Aug 2010, 09:44
As already discussed, the method is [(Last-First)/Increment ]+1
If you are refering to mgmat by any chance, this is discussed in Chap4 of Number properties
Intern
Joined: 30 Jun 2017
Posts: 16
Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)... | [
"90",
"95",
"100",
"105"
] | D | The multiples of ten from 10 to 190 inclusive would be an evenly spaced set with 19 terms - 10, 20, 30,.......190
So average = (First term + Last Term)/2 = (10 + 200)/2 = 210/2 = 105
Hence, the correct answer is D. |
AQUA-RAT | AQUA-RAT-38630 | We can argue that the are 21/7= 3 times as many men now so they will require three times as much water, 3(13)= 39 quarts just for the same two weeks. And they need the water for 4/2= 2 times as many weeks so need 2(39)= 78 quarts of water.
The following is multiple choice question (with options) to answer.
Jill has 28... | [
"3",
"6",
"48",
"12"
] | C | Let the number of each size of jar = wthen 1/4w + 1/2w + w = 28 1 3/4w = 28w=16The total number of jars = 3w =48Answer: C |
AQUA-RAT | AQUA-RAT-38631 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"55%",
"64%",
"57%",
"58%"
] | B | Total number of votes polled = (1136 + 7636 + 15628) = 24400
So, Required percentage = 15628/24400 * 100 = 64%
ANSWER : B |
AQUA-RAT | AQUA-RAT-38632 | 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... | [
"33",
"87",
"30",
"88"
] | C | Explanation:
Distance = 500 m
Speed of the train relative to man= ( 63 - 3 ) km/hr = 60 km/hr
= m/s = m/s
Time taken to pass the man = distance/speed = sec = 30 sec
Answer: C) 30 |
AQUA-RAT | AQUA-RAT-38633 | $$\frac{\left(\begin{array}{c}12\\7\end{array}\right)}{7^{5}}$$
If I got it right it will be $$\approx$$ 4.7123 %. Simulating $$10^7$$ weeks in Octave give me 4.7031% of the time.
• Just saw this because I'm doing the same problem, but this answer is actually incorrect. The correct probability is $\approx$ 22.85 %. –... | [
"1/10",
"1/50",
"1/75",
"1/25"
] | A | Explanation:
10*1/100 = 1/10
Option A |
AQUA-RAT | AQUA-RAT-38634 | Thus, the difference is 27-18 = 9 hours, which is answer choice A.
Originally posted by bbear on 17 Jun 2016, 14:31.
Last edited by bbear on 17 Jun 2016, 16:04, edited 1 time in total.
##### General Discussion
VP
Joined: 07 Dec 2014
Posts: 1157
Re: Six machines at a certain factory operate at the same constant rate. ... | [
"2.25.",
"3.125.",
"4.5.",
"5.225."
] | A | Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 3024/( 28*24*2) = 2.25
Answer A |
AQUA-RAT | AQUA-RAT-38635 | in the comments section. At what speed does the second train B travel if the first train travels at 120 km/h. You can approach this as if you were solving for an unknown in math class or you can use the speed triangle. Time, Speed and Distance: Key Learnings. ) Since the distances are the same, I set the distance expre... | [
"80 kmph",
"69 kmph",
"70 kmph",
"90 kmph"
] | B | As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 290 + 400 = 690 km
Thus, Total Speed = 10 hrs
or,Average Speed = 690/10
or, 69 kmph.
ANSWER:B |
AQUA-RAT | AQUA-RAT-38636 | 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... | [
"12/9 days",
"6 days",
"82/8 days",
"22/76 days"
] | B | 6M = 6W ---- 20 days
12M + 8W -----?
12W + 8 W = 20W ---?
6W ---- 20 20 -----?
6 * 20 = 20 * x => x = 6 days
Answer:B |
AQUA-RAT | AQUA-RAT-38637 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"25%",
"28%",
"32%",
"38%"
] | D | given voters in ratio 2:1
let X has 200 votersY has 100 voters
for X 62% voted means 62*200=124 votes
combined for XY has 300 voters and voted 54% so total votes =162
balance votes=162-124=38
As Y has 100 voters so 38 votes means 38% of votes required
Ans D |
AQUA-RAT | AQUA-RAT-38638 | 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... | [
"22",
"30",
"15",
"18"
] | B | 30 workers working already
Let x be the total men required to finish the task in next 100 days
2 km done hence remaining is 8 km
Also, work has to be completed in next 100 days (150 - 50 = 100)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X... |
AQUA-RAT | AQUA-RAT-38639 | 1. ## Last two digits...
I have to find the last two digits of 222227^2010.
So I know that this gets reduced to 27^2010 mod 100
But I don't know how to solve 27^x = 1(mod 100) to get this process going. Or am I going about it wrong?
I have to find the last two digits of 222227^2010.
So I know that this gets reduce... | [
"920",
"930",
"940",
"950"
] | B | Solution:
930
Explanation:
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer
Answer B |
AQUA-RAT | AQUA-RAT-38640 | Leave the $99$ in the exponent of $2$, and calculate which of the twelve angles ($0,\frac\pi6,\dots,\frac{11\pi}6$) the $\frac{99\pi}6$ falls modulo $2\pi$.
The following is multiple choice question (with options) to answer.
When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.? | [
"4.5",
"5",
"4.8",
"5.6"
] | A | if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A |
AQUA-RAT | AQUA-RAT-38641 | 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... | [
"3 days",
"11 days",
"21 days",
"22 days"
] | A | If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 4 × 12/ 16 = 3 days.
Option 'A' |
AQUA-RAT | AQUA-RAT-38642 | The remainder is $\,2 \,P_6(x^2)\,$, which follows for $\,n=6\,$ from the general identity:
\begin{align} P_{2n}(x^2) = \frac{x^{4n}-1}{x^2-1} &= \frac{x^{2n}-1}{x-1} \, \frac{x^{2n}+1}{x+1} \\[5px] &= \, \frac{x^{2n}-1}{x-1} \, \frac{x^{2n}-1+2}{x+1} \\[5px] &= - \, \frac{x^{2n}-1}{x-1} \, \frac{(-x)^{2n}-1}{(-x)-1} ... | [
"145",
"148",
"150",
"153"
] | D | D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158 |
AQUA-RAT | AQUA-RAT-38643 | 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... | [
"170 m",
"100 m",
"270 m",
"320 m"
] | D | Explanation:
Relative speed = (72 - 36) x 5/18 = 2 x 5 = 10 mps.
Distance covered in 32 sec = 32 x 10 = 320 m.
The length of the faster train = 320 m.
ANSWER IS D |
AQUA-RAT | AQUA-RAT-38644 | Fact: there is an equal probability of the last passenger sitting in Seat 1 and Seat 100.
By the time the last passenger boards, the outcome of the lost boarding pass problem is already determined, as there is only one seat for them to choose. We must therefore look at the decisions faced by Passengers 1–99.
For Pass... | [
"33.3%",
"40%",
"50%",
"60%"
] | B | 0.20P = RT + C
0.5(RT) = no C
=> 0.50(RT) had C
0.20P = 0.50(RT)
RT/P = 40%
Answer - B |
AQUA-RAT | AQUA-RAT-38645 | ### 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 ... | [
"60%",
"55%",
"65%",
"77%"
] | D | 7/8 of 2 quarts = 14/8 quarts of water
7/10 of 3 quarts = 21/10 quarts of water
14/8 = 1.75
21/10 = 2.10
Total water = 1.75 + 2.10= 3.85
Total quarts = 5
3.85/5 = 77%
Answer : D |
AQUA-RAT | AQUA-RAT-38646 | # String probability (with conditional prob and combinations)
I'm having trouble with the questions below, all relating to string probability. I'll write the problem and then provide my work for my (incorrect) answer. Please help me figure out what I did wrong.
SET1: Assume a string, allowing repetition, is randomly ... | [
"2/7",
"3/7",
"3/14",
"5/14"
] | D | The number of ways to choose two letters is 8C2 = 28
The number of ways to choose two consonants is 5C2 = 10.
P(no vowels) = 10/28 = 5/14
The answer is D. |
AQUA-RAT | AQUA-RAT-38647 | If your teacher insists on using Inclusion Exclusion, then let $$A_i$$ be the set of arrangements s.t. person $$i$$ gets his/her own gift. Then I-E gives:
$$answer = n^n - \sum_i |A_i| + \sum_{i
Now, $$|A_i| = n^{n-1}$$ since the other $$n-1$$ gifts are unconstrained and each can go to any of $$n$$ recipients. Simila... | [
" y/R",
" y/(R-x)",
" xy/(R-x)",
" ey/(R(R-e))"
] | D | y/(R-e)- y/R
if we simplify this we get choice D, which is the correct answer. |
AQUA-RAT | AQUA-RAT-38648 | # 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... | [
"500",
"277",
"466.7",
"297"
] | C | Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/120 = Rs. 466.7
Answer:C |
AQUA-RAT | AQUA-RAT-38649 | 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... | [
"34%",
"24%",
"22%",
"18%"
] | A | EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of oats in 2nd sol)=34%=A |
AQUA-RAT | AQUA-RAT-38650 | velocity, dimensional-analysis
Title: Why is meters/second the same as meters per second? In quantities such as speed where the derived (SI) unit is m/s, why do we pronounce it and interpret it as meters per second? My guess is that 1 m is associated with 1 second. Similarly, 5 m/s is pronounced and interpreted as 5 m... | [
"5 mps",
"10 mps",
"6 mps",
"7 mps"
] | A | 18 * 5/18
= 5 mps
Answer:A |
AQUA-RAT | AQUA-RAT-38651 | 5. Originally Posted by ANDS!
You have 5 reds. Each of the 5 reds can be paired with 5 greens lets say. So you have 25 Red-Green combos. Each of the 25 Red-Green combos can be paired with one of the 5 yellows. So you have 125 Red-Green-Blue combos. But lets get even more general than that. You have 125 Color1-Color2-Co... | [
"11/10",
"3/95",
"31/10",
"3/55"
] | B | P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x4/20x3/19
= 3/95
Answer: B |
AQUA-RAT | AQUA-RAT-38652 | So total sales for the year, 30000, cash sales 6000. Thus the yearly proportion of cash sales is $\dfrac{6000}{30000}=20\%$. This is the correct percentage.
Now let's compute the monthly averages. For January through October, they are $50\%$. For each of November and December, they are $5\%$.
To find the average of t... | [
"14%",
"21%.",
"31%.",
"37%."
] | B | The average sales for all the other months (11 months) of the year is x.
So, the total sales of those 11 months will be= 11x
Now, this month's sales, which is 400% more than the average of other months' sales, is 5x, (x+400% of x).
Thus, this month's' sales are (5x/16x)*100=31.25% of the total yearly sales. [Total sale... |
AQUA-RAT | AQUA-RAT-38653 | • +1 though irritated that you just scooped me! Apr 20, 2016 at 17:16
• Thanks for the answer. I have made an appropriate system of equations and solved it but my results differ from those from the answers in my textbook. I got $3x^3-2x^2+3x+1$ (confirmed by WolframAlpha: m.wolframalpha.com/input/?i=%28x^2-x-3%29%28ax%... | [
"m/3",
"9m",
"3m^2",
"m^2/3"
] | C | m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
3m^2 = 3 ^ (4x-3)
Answer C |
AQUA-RAT | AQUA-RAT-38654 | 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... | [
"15 5/8 days",
"10 5/8 days",
"12 5/8 days",
"19 5/8 days"
] | B | B
(x – 5)/12 + x/20 = 1
x = 10 5/8 days |
AQUA-RAT | AQUA-RAT-38655 | 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 ... | [
"21",
"31",
"41",
"51"
] | B | He start out with 31eggs.
In the end, he have 3eggs left.
So,
3*2 +1= 7
7*2 +1= 15
15*2 +1= 31
31eggs he had initially.
ANSWER:B |
AQUA-RAT | AQUA-RAT-38656 | homework-and-exercises
I understand that F is directly proportional to m and F is also directly proportional to a as well. Therefore as m and a increases F also increases, but the formula could also be F=m+a, in this case also F increases as m and a increases.
Like if we redefine every formulas in terms of addition in... | [
"1",
"2",
"3",
"4"
] | B | We have,
M = 4c^2/d
If c is doubled and d is increased by a factor of 2, the formula changes to:
M = 4*{(2c)^2}/(2d)
M = 4*{4c^2}/(2d)
M = 4*[2c^2/d]
At first, M = 4c^2/d
After changing c and d, M = 2*4c^2/d
Hence, M changes by a factor of 2.
Answer = B = 2 |
AQUA-RAT | AQUA-RAT-38657 | Player $C$ makes free throw shots with probability $P(A_j|C) = 0.7$, independently, so we have
\begin{align} P(A_1|C) &= P(A_2|C) = 0.7 \\ P(A_1 \cap A_2|C) &= P(A_1|C) P(A_2|C) = 0.49 \\ P(A_1 \cup A_2|C) &= P(A_1|C) + P(A_2|C) - P(A_1 \cap A_2|C) \\ &= 2 \times 0.7 - 0.49 \\ &= 0.91 \end{align}
And so we have our c... | [
"288",
"581",
"168",
"127"
] | B | Explanation:
7 * 84 = 588 - 7 = 581
Answer:B |
AQUA-RAT | AQUA-RAT-38658 | # 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... | [
"21 meter/sec",
"7 meter/sec",
"14 meter/sec",
"18 meter/sec"
] | A | P's speed = 24 m/s
P's distance = 1000m (as it is a km race)
t = 1000/24 = 41.7 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/41.7 = 21 m/s
Hence A is the answer. |
AQUA-RAT | AQUA-RAT-38659 | (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 - ... | [
"3,024",
"4,536",
"5,040",
"9,000"
] | B | No. of ways select first digit (other than 0) * No of wasy select second digit (exclude first digit selected) * no of ways select 3rd digit (exclude first 2) * no of ways to select 4 th digit (excllude first 3 digits)
= 9*9*8*6= 4536
ANSWER:B |
AQUA-RAT | AQUA-RAT-38660 | $(120,34)\simeq S_{5}$
$(120,36)\simeq S_{3}\times(\mathbb{Z}_{5}\rtimes\mathbb{Z}_{4})$
$(144,182)\simeq((\mathbb{Z}_{3}\times\mathbb{Z}_{3})\rtimes\mathbb{Z}_{8})\rtimes\mathbb{Z}_{2}$
$(144,183)\simeq S_{3}\times S_{4}$
$(156,7)\simeq(\mathbb{Z}_{13}\rtimes\mathbb{Z}_{4})\rtimes\mathbb{Z}_{3}$
$(168,43)\simeq((... | [
"100",
"85",
"75",
"66"
] | C | 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
25*4=100
3*25=75 ans is 75
ANSWER:C |
AQUA-RAT | AQUA-RAT-38661 | # Math Help - Prob. Question
1. ## Prob. Question
Question
5 boys (call them A,B,C,D,E) place their books in a bag. The 5 books are are drawn out in random order and given back to the 5 boys. What is the probability that exactly 3 boys will receive their original book?
Help wanted please. The only way I could think ... | [
"186",
"225",
"294",
"302"
] | C | The worst case scenario is to remove all the books on botany, zoology, and geology.
Also we can remove 79 books each from physics and chemistry.
The total is 40 + 45 + 50 + 79 + 79 = 293.
The next book removed must either be physics or chemistry, ensuring 80 books in that subject.
The answer is C. |
AQUA-RAT | AQUA-RAT-38662 | A question on the same concept
The number of television sets sold by Store R last month was approximately what percent less than the number of television sets sold by Store T last month? ( The number of television sets sold by Store R was 20 and number of television sets sold by Store T was 45 as per the attached figu... | [
"30.05%",
"13.15%",
"40%",
"27.15%"
] | D | The total CP = Rs. 16000 + Rs. 8500 = Rs. 24500 and SP = Rs. 31150
Profit(%) = (31150 - 24500 )/24500* 100 = 27.15%
ANSWER:D |
AQUA-RAT | AQUA-RAT-38663 | Thus,
200 x 0.3 = 60 received student loans
200 x 0.4 = 80 received scholarships
We are trying to determine what percent of those surveyed said that they had received neither student loans nor scholarships.
Let’s fill all this information into a table. Note that each row sums to create a row total, and each column ... | [
"4%",
"8%",
"4.2%",
"4.8%"
] | D | Let's say there is a TOTAL of100students at this college.
60 percent of the total number of students are freshmen.
# of freshmen = 60% of 100 =60
40 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 40% of 60 =24
...and, of these, 20 percent are psychology majors..... |
AQUA-RAT | AQUA-RAT-38664 | # 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 ... | [
"7/12",
"5/12",
"3/8",
"1/3"
] | C | Now, rectangle R has an area of 3*4=12. All point that has y-coordinate greater than x-coordinate lie above the line y=xy=x, so in yellow triangle, which has an area of 1/2*3*3=4.5. So, the probability equals to favorable outcomes/total=yellow triangle/rectangle R=4.5/12=3/8.
Answer: C. |
AQUA-RAT | AQUA-RAT-38665 | kinematics, geometry
Title: Path of wheels of a bicycle Why are the wheels of a bicycle moving in concentric circles with the center O?
I know that the velocity of the back wheel is parallel to the frame of the bicycle and the velocity of the front wheel is parallel to the direction in which the wheel points.
FIXED D... | [
"b=2,t=3",
"b=5,t=3",
"b=6,t=3",
"b=2,t=5"
] | C | Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=9............(1)
2b+3t=21............(2)
Rearrange equation (1) and substitute into equation (2)
2b+27-3b=21
-b=-6
b=6
Calculate the number of tricycles t
t=9−b
=9−6
=3
There are 3 tricycles and 6 bicycles.
Answer is C. |
AQUA-RAT | AQUA-RAT-38666 | +0
# the amount of the price
0
284
4
if the price of a pencil is 36% lower than the price of a pen,then the price of a pen is ?
1.)36%higher than a pencil
2.)43.75 higher than a pencil
3.)56.25 % higher than a pencil
4.)64% higher than a pencil
Guest Feb 17, 2015
#1
+84384
+10
If the price of a pencil is 36% ... | [
"2.15",
"4.2",
"5.18",
"3.75"
] | D | 40% --- 15
160% --- ?
40/160 * 15 = 3.75
Answer: D |
AQUA-RAT | AQUA-RAT-38667 | (Now... what can we say about $A$ and the set $\{\{1, 2, 3, 4, 5\}, 1, 2, 3, 4, 5\}?)$
The following is multiple choice question (with options) to answer.
A set of numbers has the property that for any number t in the set,t+3 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 2
II. ... | [
"II only",
"I only",
"I,II only",
"II,III only"
] | C | question is asking for must be there elements.
According to the question if t is there t+3 must be there.
if -1 is the starting element the sequence is as follows.
S ={-1,2,5,8,11....}
if -1 is not the starting element the sequence is as follows
S = {...-4,-1,2,5,8,11...}
By observing the above two sequences we can say... |
AQUA-RAT | AQUA-RAT-38668 | ## A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners
##### This topic has expert replies
Legendary Member
Posts: 2898
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:5 members
### A number of people shared a meal, intending to divide the cost evenl... | [
"Rs.117",
"Rs.100",
"Rs.110",
"Rs.107"
] | A | Let the average expenditure of all nine be Rs.x
Then 12*8+(x+8)=9x or 8x=104 or x=13.
Total money spent = 9x=Rs.(9*13)=Rs.117.
Answer is A. |
AQUA-RAT | AQUA-RAT-38669 | homework-and-exercises, kinematics
Title: Train problem question in kinematics engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last
compartment with velocity v. The middle point of the train passes past the same pole with a velocity of.
My thinking:
Q1 Will the values... | [
"7",
"9",
"5",
"10"
] | B | Sol.
Speed = [ 80x5/18] m/sec =22.2 m / sec.
Time taken = (200/22.2)sec = 9 sec.
Answer B |
AQUA-RAT | AQUA-RAT-38670 | Finally $L_3$ is: $$L_3 = c_0 + 2^{-1}c_{-1} + 2^{-2}c_{-2} + 2^{-3}c_{-3} = 4 + 0.125 = 4.125$$
This approach guarantees that $L_3 < L < L_3 + 2^{-3}$ giving an absolute error of $2^{-4} = 0.0625$ and a percent error of $1.47\,\%$ (in the worst case).
Our best guess $L^\star$ is $$L_3 + 2^{-4} = 4.15625$$ while the ... | [
"34%",
"44%",
"54%",
"64%"
] | D | Let the number be x.
Then, error =(5/3)x - (3/5) x =(16/15)x.
Error% =((16/15)x) x (3/5x)x 100% = 64%.
Answer:D |
AQUA-RAT | AQUA-RAT-38671 | 3. How many numbers that are not divisible by 6 divide evenly into 264,600?
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
4.A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60,... | [
"19",
"19.7",
"19.9",
"20.1"
] | B | Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B) |
AQUA-RAT | AQUA-RAT-38672 | Aren't there 2 possible answers for #1?
x=5, y=2
x=25, y=1
Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 52344
### Show Tags
31 Mar 2014, 00:26
1
karimtajdin wrote:
walker wrote:
jimjohn wrote:
1. z is prime and is 3. So, x=5 SUFF.
Aren't there 2 possible answers for #1?
x=5, y=2
x=25, y=1
Thanks!
Notice that we... | [
" None",
" I only",
" II only",
" III only"
] | A | Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements no... |
AQUA-RAT | AQUA-RAT-38673 | 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... | [
"5/6",
"5/9",
"5/1",
"5/3"
] | A | Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (87.5 - 7.50) / (7.50 - 6) =5/6
Answer: A |
AQUA-RAT | AQUA-RAT-38674 | $4m^2n^2 + (m^4-2m^2n^2+n^4) = (m^2+n^2)^2$
$m^4+2m^2n^2+n^4=(m^2+n^2)^2$
$(m^2+n^2)^2 = (m^2 + n^2)^2$
-
HINT $\$ By difference of squares $\rm \ (m^2+n^2)^2 - (m^2-n^2)^2 =\ (2\:m^2)\ (2\:n^2)\: =\: (2\:m\:n)^2$
The following is multiple choice question (with options) to answer.
If m > 1 and n = 2^(m−2), then 4^m... | [
"16n^2",
"4n^2",
"n^2",
"n^2/4"
] | A | n = 2^(m-2) = 2^m/4
2^m = 4n
4^m = (2^m)^2 = (4n)^2 = 16n^2
The answer is A. |
AQUA-RAT | AQUA-RAT-38675 | special-relativity, time-dilation
#2 already had a head start of 1.4434 s, at t = 5 in frame S, clock #2 will read 1.4434 + 4.3301 = 5.7735 s, and that's the moment at which the firecracker goes off next to it.
The following is multiple choice question (with options) to answer.
If a light flashes every 6 seconds, how... | [
"301 times",
"351 times",
"401 times",
"451 times"
] | A | In 1/2 of an hour there are 30*60 = 1800 seconds
The number of 6-second intervals = 1800/6 = 300
After the first flash, there will be 300 more flashes for a total of 301.
The answer is A. |
AQUA-RAT | AQUA-RAT-38676 | Statement 2: $$a>20$$. Nothing mentioned about $$b$$. Insufficient
Combining 1 & 2: $$a>20 =>2a>40$$. Add $$35$$ to both sides
$$2a+35>40+35 => a+b>75$$. Sufficient
Option C
Is the average (arithmetic mean) of a and b greater than 30? [#permalink] 04 Jan 2018, 11:07
Display posts from previous: Sort by
# Events &... | [
"40",
"50",
"90",
"140"
] | A | -(a + b = 100)
b + c=140
c-a=40
A.40 |
AQUA-RAT | AQUA-RAT-38677 | Let $y_2$ be any common divisor of $(a \cdot b)$ and $(a+b)$. Let $p_y$ be any odd prime factor of $y_2$. Then $p_y$, being prime, divides at least one of $a,b$. WLOG let us assume $p_y|a$. Then $a + b \equiv 0 + b \equiv b$ $($mod $p_y)$. Recall that $p_y|(a+b)$, therefore $0 \equiv a + b \equiv b$ $($mod $p_y)$. But ... | [
"4",
"6",
"8",
"9"
] | B | Just to add some more to Bunuel's explanation, if a number is a multiple of 3, it will be in a form:
n = 3*k, where k is an integer
And if a number is a multiple of 6, it will be in a form :
m = 6*l, where l is an integer
so m = 2 * 3 * l = (2*l) * 3 = 3 * p, where p is an integer.
In other words, the prime factorizati... |
AQUA-RAT | AQUA-RAT-38678 | The statement
"(the integer referred to by the decimal symbol 1) + (the integer referred to by the decimal symbol 1) = (the integer referred to by the decimal symbol 2)"
is indeed always true. Whether or not this is expressed in symbols as
"1 + 1 = 2"
depends on how you choose to represent integers.
The following ... | [
"12/a",
"3/a",
"6/a",
"9/a"
] | B | 1/a + 1/a + 1/a
=3/a
Answer B |
AQUA-RAT | AQUA-RAT-38679 | # Formulation and computation of “the” unique median of an even-sized list
Consider an even-sized set of numbers $X = \{x_k\}$, such as $X = \{1, 2, 7, 10\}$.
The median $m$ is defined as:
$$m = \mathrm{arg \min_x} \sum_k \lvert x_k - x\rvert^1$$
Any $m \in [2, 7]$ is a minimizer of this function, and is therefore "... | [
"5",
"7",
"8",
"W=9"
] | D | mode of list ii =3
median W of list ii =4+6/2 =5
sum of mode + mean = 3+ 5=8
now to make 8 as the median we need to find a value of y such that if the no. of terms in list 1 are odd then y=8 else if even then 7+y /2=8
here its even so
7+y/2=8 from this y= 9 (D) |
AQUA-RAT | AQUA-RAT-38680 | Hint: You may suppose, w.l.o.g. that $$|x-2|<\frac12$$, in which case $$|x-1|>\frac12$$, so that $$\left|\frac{x-2}{x - 1}\right| <2|x-2|.$$
$$\delta<\min(1,\varepsilon)/2$$ should do the job.
The following is multiple choice question (with options) to answer.
If y exceeds x by 26%, then x is less than y by? | [
"16 2/8%",
"20 8/3%",
"20 40/63%",
"76 2/3%"
] | C | X=100 y=126
126------26
100-------? => 20 40/63%
Answer:C |
AQUA-RAT | AQUA-RAT-38681 | Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.
Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.
Back to the problem:
From F.S 1, ... | [
"11.4",
"11.3",
"11.8",
"12.1"
] | D | 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.5 = 69
63 + 69 = 132 – 119.9 = 12.1
6th number = 12.1
Answer: D |
AQUA-RAT | AQUA-RAT-38682 | (A) 9
(B) 12
(C) 18
(D) 24
(E) 27
Weight of 2nd piece = 4 pound
Since the weight is directly proportional to the square of its length., we may write
$$\frac{16}{36^2}$$ = $$\frac{4}{x^2}$$
Solving above, we get x = 18
_________________
If you like the post, show appreciation by pressing Kudos button
Director
Joined... | [
"35",
"20",
"28",
"36"
] | C | 1: 2/3 = 3: 2
2/5 * 70 =28
Answer:C |
AQUA-RAT | AQUA-RAT-38683 | Note: To show that the area of the polygon converges to the area of the circle, note that the area between the polygon and the circle is bounded by $n r \sin \frac{\theta_n}{2} r ( 1 - \cos \frac{\theta_n}{2})$. A calculation along the above lines shows that this converges to $0$.
-
This is very nice – Alyosha Jun 8 ... | [
"20%",
"16%",
"36%",
"64%"
] | B | If area of a circle decreased by x % then the radius of a circle decreases by
(100−10√100−x)%=(100−10√100−30)%
= (100−10√70)%
= 100 - 84 = 16%
Answer B |
AQUA-RAT | AQUA-RAT-38684 | # How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?
How would I go about solving this math problem?
if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$?
I got $a/c = 2/5$ but that is not a corr... | [
"50",
"22",
"56",
"27"
] | A | Explanation:
Let the numbers be 2x and 5x. Then, their H.C.F. = x. So, x = 5.
So, the numbers 10 and 25.
L.C.M. of 10 and 25 = 50.
Option A |
AQUA-RAT | AQUA-RAT-38685 | +0
# SOS!!!
0
230
7
+223
I cannot get the right answer for this problem for the life of me. If somebody would solve it I'd give them 5 stars.
THE PROBLEM:
(20+(1/4))x +(5+(1/2)) = (7+(1/16))
(solve for x)
#1
+10
(20+(1/4))x + (5+(1/2)) = (7+(1/16))
(20(1/4))x = (7+(1/16)) - (5+(1/2))
x = ( (7+(1/16)) - (5+(1... | [
"150",
"120",
"266",
"288"
] | B | (50/100) * X – 50 = 10
5X = 600
X = 120
Answer:B |
AQUA-RAT | AQUA-RAT-38686 | 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... | [
"2000",
"2777",
"2688",
"1000"
] | A | (x*5*1)/100 + [(2500 - x)*6*1]/100 = 130
X = 2000
Answer: A |
AQUA-RAT | AQUA-RAT-38687 | Kudos [?]: 53125 [5] , given: 8043
Re: problem solving question on ratios [#permalink] 16 Dec 2010, 13:47
5
KUDOS
Expert's post
2
This post was
BOOKMARKED
spyguy wrote:
can someone explain in further detail the relationship between the teaching assistants to the number of students in any course must always be greater... | [
"2 : 3 : 4",
"6 : 7 : 8",
"6 : 8 : 9",
"6 : 8 : 7"
] | A | let 100% seats are there in all then mathematics increased by 40% then
5*140/100=7
physics is increased by 50% then
7*150/100=21/2
biology increased by 75% then
8*175/100=14
then ratios of increasing seats are 7:21/2:14
14:21:28
2:3:4
ANSWER:A |
AQUA-RAT | AQUA-RAT-38688 | = 0 \\ a^7+ b^7 + c^7 = -7mk^2$$ Then your identity reads $$\left( -\frac{3m}{3} \right) \left( -\frac{7mk^2}{7} \right) = \left( -\frac{5mk}{5} \right)^2 \\ \left( -m \right) \left( -mk^2 \right) = (mk)^2$$
The following is multiple choice question (with options) to answer.
7M-20=2M,THEN M+7 IS EQUAL TO? | [
"9",
"10",
"11",
"12"
] | C | 7m-20=2m
so, 5m=20
so, m+7=11
ANSWER:C |
AQUA-RAT | AQUA-RAT-38689 | eq2= a1*b - a*a4 - a*a3 + a2*b + a7*b - a8*c;
eq3=a1*d - a3*c - a6*c - a2*c + a4*d + a5*d;
eq4=a^2*a3 + a^2*a4 + a1*b^2 + a2*b^2 + a7*b^2 + a8*c^2;
eq5=a*a3*c - a2*b*c - a*a4*d + a1*b*d-1;
eq6=a2*c^2 + a3*c^2 + a6*c^2 + a1*d^2 + a4*d^2 + a5*d^2;
eq7=a1*b^3 - a^3*a4 - a^3*a3 + a2*b^3 + a7*b^3 - a8*c^3;
eq8=a1*d^3 ... | [
"{A}",
"{G}",
"{L}",
"{B}"
] | B | A = {a, b, c, d, e, f}
B = {b, d, f, g}
correct answer :B - A = {g)
B |
AQUA-RAT | AQUA-RAT-38690 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest be... | [
" $10,200",
" $10,092",
" $10,105",
" $9,405"
] | B | Approach #1:
12 percent annual interest compounded semi-annually --> 6% in 6 moths.
For the first 6 moths interest was 6% of $9,000, so $540;
For the next 6 moths interest was 6% of $9,000,plus6% earned on previous interest of $540, so $540+$12=$552;
Total interest for one year was $540+$552=$1092, hence balance after ... |
AQUA-RAT | AQUA-RAT-38691 | In a bag there are 10 Black balls, 8 White balls and 5 Red balls.
Three balls are chosen at random and one is found to be Black.
Find the probability that remaining two are white.
. $(a)\;\frac{8}{23}\qquad(b)\;\frac{4}{33}\qquad(c)\ ;\underbrace{\frac{10\cdot8\cdot7}{23\cdot22\cdot2 1}}_{str\!ange!} \qquad(d)\;\frac{... | [
"0.9",
"0.75",
"0.6",
"0.8"
] | D | According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 20 + 10)/100 = 80/100 = 0.8.
Answer is D |
AQUA-RAT | AQUA-RAT-38692 | # 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... | [
"28.5",
"46",
"30",
"Data inadequate"
] | B | Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100×(100+38.7)/(100−5) =146
Hence, required % Profit = 146 – 100 = 46%
Answer B |
AQUA-RAT | AQUA-RAT-38693 | 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... | [
"6 (1/4) days",
"9 days",
"7 (3/4) days",
"8 days"
] | B | Work done by P alone in one day = 1/12th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/12 of the total) = 1/36 of the total.
Work done by P and Q, working together in one day = 1/12 + 1/36 = 4/36=1/9 of the total
They would take 9 days to complete the work working together.
AN... |
AQUA-RAT | AQUA-RAT-38694 | ## A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners
##### This topic has expert replies
Legendary Member
Posts: 2898
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:5 members
### A number of people shared a meal, intending to divide the cost evenl... | [
"$24 and $20",
"$25 and $23",
"$38 and $40",
"$37 and $39"
] | A | The total amount for the meal was between 18.5*1.3=24.05 and 18.5*1.1=~20.35. Only option which covers all possible values of the meal is A.
Answer: A. |
AQUA-RAT | AQUA-RAT-38695 | Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION
Algebraic Solution: If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x ... | [
"Rs.1000",
"Rs.1140",
"Rs.860",
"Rs.760"
] | A | Explanation:
90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
ANSWER IS A |
AQUA-RAT | AQUA-RAT-38696 | in the comments section. At what speed does the second train B travel if the first train travels at 120 km/h. You can approach this as if you were solving for an unknown in math class or you can use the speed triangle. Time, Speed and Distance: Key Learnings. ) Since the distances are the same, I set the distance expre... | [
"35.3km/hr",
"42.5km/hr",
"48.9km/hr",
"52.6km/hr"
] | B | Total distance traveled = 250+200+300+100 = 850km
Total time taken = 250/50 + 200/20 + 300/100 + 100/50 = 20 hrs
Average speed =850/20 = 42.5km/hr approximately ;
Answer is B |
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