source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-39597 | ### Show Tags
03 Oct 2019, 11:34
OFFICIAL EXPLANATION
Hi All,
We're told that each of 60 cars is parked in one of three empty parking lots. After all of the cars have been parked, the largest lot holds 8 more cars than the middle lot and 16 more cars than the smallest lot. We're asked for the number of cars that are... | [
"18",
"16",
"12",
"24"
] | D | N - Not rented trucks; R - Rented trucks
N + R = 26
N + R/2 = 14
R = 24
D |
AQUA-RAT | AQUA-RAT-39598 | # 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... | [
"25%",
"30%",
"50%",
"20%"
] | C | S.P. = $225
Gain = $75
C.P. = 225-75 = 150
Gain% = 75/150 * 100 = 50%
Answer is C |
AQUA-RAT | AQUA-RAT-39599 | sides of equal length. Q2. Isosceles Right Triangle has one of the angles exactly 90 degrees and two sides which is equal to each other. Correct Answer: D. Step 1: An isosceles right triangle has two sides equal and measure of one of its angles is 90°. The isosceles right triangle has a right angle and two acute angles... | [
"4",
"4√2",
"14",
"8√2"
] | C | ans C ..14..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=4 or yz=7*\sqrt{2}..
therefore hyp=xy=14 |
AQUA-RAT | AQUA-RAT-39600 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"$16.32",
"$18.00",
"$21.60",
"$34"
] | D | The discounted price of one can of soda is (0.85)($0.40), or $0.34. Therefore, the price of 72 cans of soda at the discounted price would be (100)($0.34)= 34
Answer: D. |
AQUA-RAT | AQUA-RAT-39601 | ### 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... | [
"5",
"10",
"15",
"25"
] | A | Total applicants = 40
Political science = 15 and Non political science = 40 - 15 = 25
GPA > 3.0 = 20 and GPA <= 3.0 = 20
10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0
GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) T= 20 - 15 = 5
Answe... |
AQUA-RAT | AQUA-RAT-39602 | autocad
Title: What is the suitable multiplier for all units? I create Auto CAD Drawing using Primary units decimal (mm). I need to add alternative unit as Architectural. What is the suitable multiplier for all units?
After adding new value So
1 Millimeter = 0.0393701 Inches
You can get this from many places, some be... | [
"98.74 inches",
"78.74 inches",
"88.74 inches",
"58.74 inches"
] | B | One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm
x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches
correct answer B |
AQUA-RAT | AQUA-RAT-39603 | Veritas Prep Reviews
Math Expert
Joined: 02 Sep 2009
Posts: 37109
Followers: 7252
Kudos [?]: 96499 [0], given: 10752
### Show Tags
05 Jun 2013, 23:44
PKPKay wrote:
Sarang wrote:
For 1 hour-
Machine A rate- 2000 envelopes
Machine B+C rate- 2400 envelopes
Since A + C = 3000 envelopes A's rate is 2000 envelopes as ab... | [
"1⁄3",
"4⁄3",
"80",
"200"
] | D | 1 item takes 3/5 min so it takes 120 min to produce x
3x/5=120 the x=200
Answer:D |
AQUA-RAT | AQUA-RAT-39604 | # Given an Alphabet, how many words can you make with these restrictions.
I'm trying to understand from a combinatoric point of view why a particular answer is wrong. I'm given the alphabet $\Sigma = \{ 0,1,2 \}$ and the set of 8 letter words made from that alphabet, $\Sigma_8$ . There are $3^8 =6561$ such 8 letter wo... | [
"124",
"150",
"212",
"243"
] | D | 3^5 = 243
The answer is D. |
AQUA-RAT | AQUA-RAT-39605 | 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... | [
"297m",
"276m",
"267m",
"180m"
] | B | Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B |
AQUA-RAT | AQUA-RAT-39606 | 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... | [
"Equal to N",
"25% greater than N",
"20% greater than N",
"25% less than N"
] | B | Correct answer is (B).
This year, the price of an employee is price1=P/N.
If this price decreases by 20% it becomes Price2=P/N*0.8
Then with P dollars, you can hire P/Price2 employees i.e. P/(P/N*0.8) i.e. N/1.1 i.e. 1.25*N
Which is 25% greater than N. |
AQUA-RAT | AQUA-RAT-39607 | # Difference between revisions of "1984 AIME Problems/Problem 4"
## Problem
Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. ... | [
"31",
"24",
"29",
"25"
] | D | The total of 15 numbers = 15X11 = 165
The total of first 7 and last 7 numbers is = 7 X 14+7 X 6 = 140
So, the middle number is (165 - 140 ) = 25
D |
AQUA-RAT | AQUA-RAT-39608 | Let $P(X_1, \ldots, X_n)$ a polynomial. Substitute $X_i\mapsto X_i + a_i$ and get $$P(X_1+ a_1, \ldots, X_n + a_n) = \sum c_{\alpha} X_1^{\alpha_1} \ldots X_n^{\alpha_n}$$ and so
$$P(X_1, \ldots, X_n) = \sum c_{\alpha} (X_1-a_1)^{\alpha_1} \ldots (X_n-a_n)^{\alpha_n}$$
Note that $c_{(0,\ldots, 0)} = P(a_1, \ldots, a_... | [
"n is any natural number",
"n is an even natural number",
"n is an odd natural number",
"n is prime"
] | A | For every natural number n, (X^n - A^n) is always divisible by (X - A)
Answer A. |
AQUA-RAT | AQUA-RAT-39609 | ### 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... | [
"8",
"9",
"10",
"11"
] | B | 15n + 35 = 17(n+1)
2n = 18
n = 9
The answer is B. |
AQUA-RAT | AQUA-RAT-39610 | # Polynomial Challenge III
#### anemone
##### MHB POTW Director
Staff member
Let $f(x)=x^4+px^3+qx^2+rx+s$, where $p,\,q,\,r,\,s$ are real constants. Suppose $f(3)=2481$, $f(2)=1654$, $f(1)=827$.
Determine the value of $\dfrac{f(-5)+f(9)}{4}$.
#### mente oscura
##### Well-known member
Let $f(x)=x^4+px^3+qx^2+rx+s$... | [
"-4",
"0",
"-2",
"-3"
] | A | #p# = ap^3 + bp - 1
#-4# = 2
putting p = -4 in above equation
-64a -(4b +1) = 2 or
#-4# = (64a+4b+1) = -2
therefore 64a+4b = -3 .....(1
now putting p = 4
#4# = 64 a+4b - 1
using equation 1(64a+4b = -3)
#4# = -3-1 = -4
hence A |
AQUA-RAT | AQUA-RAT-39611 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"Rs.3300",
"Rs.3100",
"Rs.3500",
"Rs.4200"
] | A | 6600:4400:11000
3:2:5
3/10 * 11000
= Rs.3300
AnswerA |
AQUA-RAT | AQUA-RAT-39612 | 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. ... | [
"2000 votes",
"2500 votes",
"3000 votes",
"4000 votes"
] | C | Answer: Option 'B'
(100%-20%=80%
48%-32%=16%
16% = 16×30 = 480
100% =100×30 =3000 votes)
C |
AQUA-RAT | AQUA-RAT-39613 | 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... | [
"20 seconds",
"30 seconds",
"40 seconds",
"48 seconds"
] | D | Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 460+140 = 600 meter
Time = Distance/speed
=600∗2/25=48seconds
Option D |
AQUA-RAT | AQUA-RAT-39614 | Our goal is to find possible values for $x$, then use the equation above to find $n$. The difference between the factors is $(2m + x) - (2m - x) = 2m + x - 2m + x = 2x.$ We have three pairs of factors, $847\cdot1, 121\cdot 7,$ and $77\cdot 11$. The differences between these factors are $846$, $114$, and $66$ - those ar... | [
"2",
"2.2",
"1",
"4"
] | C | I solved the second degree equation and found it like this:
x^2 - mx - 42 = 0
(x-7)(x+6) = 0
x=7 or x= -6
Substituting both values for x in the equation we find:
x^2 - mx -42
=> (-6)^2 - m(-6) = 42
=> 36+ 6m= 42
=> 6m = 42-36=6
=> m = 1
And with 7, using a similar process we end up with:
(7)^2 - m(7) =42
-7m = 42-49= -... |
AQUA-RAT | AQUA-RAT-39615 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"3630",
"2890",
"2707",
"2700"
] | A | 6300:4200:10500
3:2:5
3/10 * 12100
= 3630
Answer:A |
AQUA-RAT | AQUA-RAT-39616 | ## 28.
The Correct Answer is (D) — Graphs for answer choices A and B imply that the area of this rectangle can be 800$\small&space;ft^{2}$ or greater. These values are not possible with only 40ft of fencing material. Similarly, the graph for answer choice C says that the area can be as large as 400$\small&space;ft^{2}... | [
"a.10",
"b.16",
"c.17",
"d.24"
] | D | Pretty Simple..the answer is choice (D) 24.
All that one has to do is :
1: Convert 1 1/4 into an improper fraction (5/4) or a decimal (1.25)
2: Divide 30 by 5/4 (or 1.25)
Answer =24 (D) |
AQUA-RAT | AQUA-RAT-39617 | # How many ways to pair 6 chess players over 3 boards, disregarding seating arrangement.
The problem is how many chess pairs can I make from $6$ players, if it doesn't matter who gets white/black pieces, and it doesn't matter on which of the $3$ boards a pair is seated.
I have a possible solution which doesn't seem r... | [
"20",
"1440",
"120",
"2880"
] | D | 4 black chess pieces can be arranged in 4! ways and 5 white pieces can be arranged in 5 ! ways.
W_W_W_W
Number of ways = 4!*5! = 24 * 120 = 2880
Answer D |
AQUA-RAT | AQUA-RAT-39618 | Difficult Probability Solved QuestionAptitude Discussion
Q. If the integers $m$ and $n$ are chosen at random from integers 1 to 100 with replacement, then the probability that a number of the form $7^{m}+7^{n}$ is divisible by 5 equals:
✔ A. $\dfrac{1}{4}$ ✖ B. $\dfrac{1}{7}$ ✖ C. $\dfrac{1}{8}$ ✖ D. $\dfrac{1}{49}... | [
"0.5",
"1",
"0.25",
"0.75"
] | A | because x(x+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
and, thus, a probability of 1/2 that it will be divisible by 4
1*1/2=1/2 =0.5
Answer : A |
AQUA-RAT | AQUA-RAT-39619 | python, beginner, parsing, csv
Full text: On the other hand, we denounce with righteous indignation and dislike men who are so beguiled and demoralized by the charms of pleasure of the moment, so blinded by desire, that they cannot foresee the pain and trouble that are bound to ensue; and equal blame belongs to those ... | [
"2",
"HH",
"28",
"28J"
] | D | Answer:D |
AQUA-RAT | AQUA-RAT-39620 | 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... | [
"85%",
"80%",
"75%",
"70%"
] | B | The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
50% of all employees are women, so non-union women are 50%-18% = 32%
40% of all employees are non-union.
The percent of non-union employees who are women is 32%/40% = 80%
The answer ... |
AQUA-RAT | AQUA-RAT-39621 | in usage again whenever we have to find the angle of elevation or the height of a pole or a mountain. For example, an orientation represented as 225° is equivalent to -135° (360° - 225°). It is also known as a 45-90-45 triangle. It is half of a complete angle. Observe the right triangle angles. This is the only right t... | [
"FG",
"HG",
"HF",
"n/a"
] | A | A) the angle FG is a right angle. HF, and HG are acute. |
AQUA-RAT | AQUA-RAT-39622 | I am also in High School, and it is my understanding that if there is a number squared and then square rooted then it is (by definition) just the original number. Taking your example of -5, plugging it in you would get sqrt (-5)^2 = -5. (-5)^2 is 25 and square rooting it is 5 which is not equal to -5. To avoid this, yo... | [
" 9/4",
" 3/2",
" 4/3",
" 5/3"
] | D | sq rt(5x/3) = x
=> 5x/3 = x^2
=> x = 5/3
Ans - D |
AQUA-RAT | AQUA-RAT-39623 | 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.
. .... | [
"120",
"64",
"96",
"80"
] | A | class 1 have 3x student and class 2 have 5x student.
3x-15/5x-15=1/2,6x-30=5x-15,x=15
45+75=120 student
answer A |
AQUA-RAT | AQUA-RAT-39624 | It helps to try out the strategy with a smaller number of students. With only five students you teacher's method gives $$4^5-\binom{4}{1}\cdot3^5+\binom{4}{2}\cdot2^5-\binom{4}{3}\cdot1^5=1024-972+192-4=240$$ ways. You can check that this is right by observing that some book must be distributed to two students and each... | [
"10",
"4",
"2",
"14"
] | C | number of pens = 848
number of pencils = 630
Required number of students = H.C.F. of 848 and 630 = 2
Answer is C |
AQUA-RAT | AQUA-RAT-39625 | => 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... | [
"233",
"600",
"510",
"771"
] | C | Explanation:
Total salary of 8 workers and supervisor together = 9 × 430 = 3870
Now total salary of 8 workers = 3870 − 870 = 3000
Total salary of 9 workers including the new supervisor = 9 × 390 = 3510
Salary of the new supervisor = 3510 − 3000 = 510
Answer: C |
AQUA-RAT | AQUA-RAT-39626 | • #### 1. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
1. \begin{aligned} 120m^2 \end{aligned}
2. \begin{aligned} 130m^2 \end{aligned}
3. \begin{aligned} 140m^2 \end{aligned}
4. \begin{aligned} 150m^2 \end{aligned}
Explanation:
\begin{aligned}
\text... | [
"22",
"38",
"37",
"56"
] | D | Answer: D) 56 sec |
AQUA-RAT | AQUA-RAT-39627 | What length of string will make 4 complete revolutions in a length of 12 inches around the cylinder of radius $\frac{2}{\pi}$?.
$t_{0}=8{\pi}$, because we have 4 rev.
a=radius of cylinder = $\frac{2}{\pi}$
$c=\frac{12}{8\pi}=\frac{3}{2\pi}$
$\boxed{8{\pi}\sqrt{\left(\frac{2}{\pi}\right)^{2}+ \left(\frac{3}{2\pi}\ri... | [
"2 cm",
"4 cm",
"8 cm",
"10 cm"
] | A | Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
12*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 16 = 1 cm^3
R = 1 cm
D = 2 cm
The answer is A. |
AQUA-RAT | AQUA-RAT-39628 | This is an essential point. A mathematical concept typically can be modeled in a number of different ways. We must not confuse the concept with one model. This is another aspect of the abstractness of mathematics.
I continued:
Now let's look back at your problem.
You are trying to answer this question:
Each time Su... | [
"$9.40",
"$11.30",
"$12.14",
"$17.80"
] | C | Pa = price of A
Pb = price of B
Ta = time for A to complete the job
Tb = time for B to complete the job
Given
Pa = 1.4 Pb
Ta+20 = Tb
Pa*Ta = Pb*Tb=850
1.4Pb * (Tb-20) = Pb*Tb
1.4 Pb Tb - Pb Tb = 1.4 Pb * 20
0.4PbTb = 28Pb
Tb = 28/0.4 = 70
Pb=850/70 ~ 12.14
C |
AQUA-RAT | AQUA-RAT-39629 | # 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... | [
"2789",
"2772",
"1250",
"6725"
] | C | CP = SP * (100/(100 + profit%))
= 1250(100/160) = Rs. 1250.
Answer: C |
AQUA-RAT | AQUA-RAT-39630 | 2. Estimate the probability that in 18 independent measurements of this tower, the average of the measurements is between 199 and 201, inclusive.
Exercise $$\PageIndex{8}$$
For Example $$\PageIndex{9}$$ estimate $$P(S_{30} = 0)$$. That is, estimate the probability that the errors cancel out and the student’s grade po... | [
"330",
"500",
"520",
"540"
] | C | I drew a diagram:
1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620
Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100... |
AQUA-RAT | AQUA-RAT-39631 | PRIME NUMBERS:
1. 1 is not a prime, since it only has one divisor, namely 1.
2. Only positive numbers can be primes.
3. There are infinitely many prime numbers.
4. the only even prime number is 2. Also 2 is the smallest prime.
5. All prime numbers except 2 and 5 end in 1, 3, 7 or 9.
PERFECT SQUARES
1. The number of di... | [
"16.1",
"15.1",
"14.1",
"17.1"
] | C | Explanation:
Sum of first 9 prime no. which are odd = 158
Average = 127/9 = 14.1
Answer:C |
AQUA-RAT | AQUA-RAT-39632 | You've created your diagram like this, calculated the area of the triangle I've labelled, and then multiplied that area by $6$. Notice however, by your divisions, we've split the hexagon into $12$ triangles, so we would need to multiply the area by $12$, not $6$, which explains why your area for Sol $2$ is half the are... | [
"a) 1 only",
"b) 1 and 2 only",
"c) 1 and 3 only",
"d) 2 and 3 only"
] | D | when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.
lets say base = 12 , height =8 (angle = 90)
maximum area = (1/2)*12*8 = 48 ( this is the same maximum area even when base is 8 and height is 12).
if we fix the base and keep lowering the angle, it will result ... |
AQUA-RAT | AQUA-RAT-39633 | Question
# In measuring the length and breadth of a rectangle, errors of 5% and 3% in excess, respectively, are made. The error percent in the calculated area is
A
7.15%
B
6.25%
C
8.15%
D
8.35%
Solution
## The correct option is C 8.15% Let actual length and breadth of the rectangle be 'l' and 'b' respectivel... | [
"4.05%",
"4.02%",
"4%",
"3%"
] | A | Percentage error in calculated area
=(2+2+(2×2)/100)%
=4.04%
ANSWER:A |
AQUA-RAT | AQUA-RAT-39634 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"$280",
"$300",
"$320",
"$340"
] | A | J+K=800 so K=800-J
2J=K+40
2J=(800-J)+40
3J=840
J=280
The answer is A. |
AQUA-RAT | AQUA-RAT-39635 | 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, ... | [
"2",
"4",
"6",
"8"
] | A | n = 3p + 1 = 7q + 5
n+2 = 3p + 3 = 7q + 7
n+2 is a multiple of 3 and 7, so it is a multiple of 21.
The answer is A. |
AQUA-RAT | AQUA-RAT-39636 | 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. ... | [
"2500",
"2600",
"2700",
"2900"
] | C | Total number of votes = 7500
Given that 20% of Percentage votes were invalid
Valid votes = 80%
Total valid votes = 7500x (80/100)
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
Valid votes that 2nd candidate got = total valid votes x 45/100
7500x (80... |
AQUA-RAT | AQUA-RAT-39637 | & = \frac{13^4}{\dfrac{52!}{4!48!}}\\[2mm] & = \frac{13^4}{\dbinom{52}{4}} \end{align*}
The following is multiple choice question (with options) to answer.
Which of the following equivalent to (1/125)^2? | [
"(0.03)^5",
"(0.04)^3",
"(0.05)^6",
"(0.06)^3"
] | B | (1/125)^2 = (1/5^3)^2 = (1/5)^6 = (1/25)^3 = (0.04)^3
Answer: Option B |
AQUA-RAT | AQUA-RAT-39638 | # 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... | [
"1/2",
"7/8",
"32/35",
"11/12"
] | B | answer isB
Total probability=7C3=48
4C3 +4C2*4C1+4C1*4C2=4+24+24=42
therefore the probability that at least one of the fashion magazines will be selected= 42/48=7/8
B |
AQUA-RAT | AQUA-RAT-39639 | ## 1 Answer
Case 2:
3 < x < 6
|x-3|= (x-3)
|x-6|= -(x-6)
(x-3)-(x-6)<5
3<5
3<5 is true, so 3 < x < 6 is also solution for |x − 3| + |x − 6| < 5
Finally we have |x − 3| + |x − 6| < 5 $\Leftrightarrow$ 2 < x < 7
The following is multiple choice question (with options) to answer.
if x/4-x-3/6=1,then find the valu... | [
"6",
"4",
"5",
"1"
] | A | (x /4)-((x-3)/6)=1=> (3x-2(x-3) )/12 = 1 => 3x-2x+6=12 => x=6.
Answer is A |
AQUA-RAT | AQUA-RAT-39640 | Ans.: A
Director
Joined: 12 Nov 2016
Posts: 776
Re: Triathlete Dan runs along a 2-mile stretch of river and then swims bac [#permalink]
### Show Tags
19 Apr 2017, 23:24
dynamo wrote:
Triathlete Dan runs along a 2-mile stretch of river and then swims back along the same route. If Dan runs at a rate of 10 miles per hou... | [
"1/9",
"2/15",
"3/15",
"1/4"
] | A | Dan travels 4 miles round trip.
Running part: (2/8 = 1/4*60 = 15 minutes)
Swimming Part: (2/6 = 1/3*60 = 20 minutes)
4 miles in (15+20) minutes
4/35 = 1/9 mile per minute
Answer: 1/9 mile per minute |
AQUA-RAT | AQUA-RAT-39641 | Puzzle of gold coins in the bag
At the end of Probability class, our professor gave us the following puzzle:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we ca... | [
"28",
"27",
"26",
"25"
] | D | x=20p;y=25p;
x+y=50;
0.20x+0.25y=11.25;
25x+25y=1250;
20x+25y=1125;
=>x=25;
ANSWER:D |
AQUA-RAT | AQUA-RAT-39642 | 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... | [
"8",
"10",
"12",
"15"
] | C | Suppose A,B,C takes x,x/2,x/3 hours to finish the work
Then, 1/x + 2/x + 3/x = 1/2
6/x = 1/2
x = 12
Answer is C |
AQUA-RAT | AQUA-RAT-39643 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"8",
"5",
"7",
"4"
] | C | Let the cost of 1 book = x, let the cost of 1 magazine = y
2x + 2y = 26
x = (26 - 2y)/2
x = 13 - y
Again,
(13 - y) + 3y = 27
13 + 2y = 27
2y = 14
y = 7
Answer: C |
AQUA-RAT | AQUA-RAT-39644 | Just to check each case: \begin{align*} f(S_T)=\begin{cases} 3 + \min(30 - S_T,0) + \max(S_T - 35,0) = 3 + 0 + 0 = 3 & \text{if }S_T\leq 30, \\ 3 + \min(30 - S_T,0) + \max(S_T - 35,0) = 3 + (30 - S_T) + 0 = 33- S_T & \text{if }30
I know @KeSchn already answered but hope this helps since this is how I usually do these.... | [
"-29",
"-19",
"18",
"29"
] | C | 45-[28-{37-(15-*)}]= 57 => 45-[28-{37-15+*}]=57
45-[28-37+15-*]=57 => 45[43-37-*]=57
45-[6-*]=57 => 45-6+*=57
39+*=57 => *=57-39
= 18
ANSWER:C |
AQUA-RAT | AQUA-RAT-39645 | # Placing m books on n shelves such that there is at least one book on each shelf
Given $m \ge n \ge 1$, how many ways are there to place m books on n shelves, such that there is at least one book on each shelf?
Placing the books on the shelves means that:
• we specify for each book the shelf on which this book is pl... | [
"1!",
"2!",
"5!",
"15!"
] | B | Solution
Since books C,D and E are arranged first and second, only books A and B will change order. Therefore it an arrangement problem involving 2 items and the number of different order is given by
2!
Answer B |
AQUA-RAT | AQUA-RAT-39646 | Points where a line intersects the function $(x-1)^{\frac 1 3}$
I'm trying to do the following exercise:
Find the equation of the line tangent to the graph of $f(x)= (x-1)^{1/3}$ at the point $x=2$. Find also if that line intersects the graph of f(x) at any other point. If it does, then find its coordinates.
Well, I... | [
"(40,0)",
"(30,0)",
"(0,40)",
"(40,30)"
] | A | Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above val... |
AQUA-RAT | AQUA-RAT-39647 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"8",
"4",
"5",
"7"
] | D | 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D |
AQUA-RAT | AQUA-RAT-39648 | ## anonymous one year ago Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out a... | [
"27",
"76",
"70",
"21"
] | C | 1/20 - 1/28 = 1/70
70 minutes.Answer: C |
AQUA-RAT | AQUA-RAT-39649 | They will have the same amount of money in about ${\color{blue}10\tfrac{1}{2}}$ years.
At that time, they will have: . $6(1.11^{10.5}) \:=\:8(1.08^{10.5}) \:\approx\:{\color{blue}\17.95}\;\;{\color{red}(d )}$
You are so right, soroban. I actually solved for time instead of amount. I've edited my post to indicate that... | [
"3:5",
"1:4",
"3:1",
"3:2"
] | B | They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
2000 : 8000 => 1:4
Answer:B |
AQUA-RAT | AQUA-RAT-39650 | ## Output
The sum of series till 7 is 1260
This approach is not efficient as it takes time complexity of the order of N.
Another approach is using the mathematical formula for the sum of series. As we have discussed in the problem description, the series can be said the summation of (n)*(n+1)*(n+2).
Using this info... | [
"30,200",
"29,800",
"30,400",
"40,400"
] | A | Spot the above series is a combination of two APs.
The 1st AP is (1 + 6 + 11 + ....) and the 2nd AP is (4 + 5 + 6 + ...)
Since the terms of the two series alternate
S =(1 + 6 + 11 + .... to 100 terms) + (4 + 5 + 6 + .... to 100 terms)
=> 100[2 x 1 + 99 x 5]/2 + 100[2 x 4 + 99 x 1]/2 --->(Using the formula for the sum o... |
AQUA-RAT | AQUA-RAT-39651 | Sort by:
1)If r is an odd prime, let it be of the form 2n+1 where n is a positive integer. If we put this value of r in our equation, we get 2(n+1)q-2np=(2n+1)^2. As L.H.S. is even and R.H.S is odd we won't have any solutions for p,q,r in this case. So r=2. We get 3q-p=4 which means q=(p+4)/3. We can see that q can be... | [
"5z + 7",
"5z − 35",
"5z + 35",
"(z + 7)/5"
] | C | P = 5Q
Q = R+7 = z+7
P = 5(z+7) = 5z + 35
The answer is C. |
AQUA-RAT | AQUA-RAT-39652 | thermodynamics
Say you own a theme park where, every hour, each adult has to pay ${\rm d}\mu_a=\$7$ (money=energy) and each kid has to pay ${\rm d}\mu_k=\$3$.
We assign positive signs to when they put money out of their pockets.
If there are $n_a=10$ adults and $n_k=5$ kids in the park, and if this number of people ... | [
"269",
"184",
"174",
"169"
] | C | Let x be the number of people
x=5m+2
x=6n
x=30p+12
Least = 30+12= 42
Highest = 30*4+12 = 132
Total = 174
ANSWER:C |
AQUA-RAT | AQUA-RAT-39653 | # 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... | [
" $20000",
" $15000",
" $12000",
" $10000"
] | D | Since investment doubles in 54/r years, then for r=6 it'll double in 54/6=~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*2=$10,000 .
Answer: D. |
AQUA-RAT | AQUA-RAT-39654 | ### Show Tags
16 Jun 2018, 09:16
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?
1) The average of the prices of all of the shirts and sweaters that the store sold during the sale wa... | [
"$25",
"$10",
"$29.65",
"$35.95"
] | B | S.P. of each of the article = 50/2 = $25
Let M.P = $x
40% of x = 25
x = 25*.4 =$10
Answer is B |
AQUA-RAT | AQUA-RAT-39655 | • is 107
• is 560
• is 840
• cannot be determined from the given information
### Key Concepts
Integers
Arrangement
Algebra
AIME I, 1990, Question 8
Combinatorics by Brualdi
## Try with Hints
Let the columns be labelled A,B and C such that first three targets are A, A and A the next three being B, B and B and th... | [
"2",
"19",
"35",
"40"
] | D | APPLE = 1+16+16+12+5=50 i.e 5*0=0
FLOWER = 6+12+15+23+5+18=79 i.e 7*9=63
BASKET =2+1+19+11+5+20=58 5*8=40
ANSWER:D |
AQUA-RAT | AQUA-RAT-39656 | 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
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"5",
"8",
"19",
"26"
] | A | J = L+12
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+17
Let's subtract equation (1) from equation (2)
A+9 = 14
A = 5
The answer is A. |
AQUA-RAT | AQUA-RAT-39657 | ## Circular Combination
1. Arrange 8 dancers in circular fashion.
2. Use 8 pearls in a band to make a necklace.
3. Arrange 8 science and 7 arts students circularly so no two arts students are together.
• 7!
• $$\frac{(8-1)!}{2}$$
• $$^8P_7 \times \space 7!$$
# Combination
## Concept
A, B, C
In how many ways can we... | [
"41",
"66",
"36",
"70"
] | B | 8 shirts
9 pants
we can combine 2 shirts with (9-3) pants
2*6=12
we can combine the other shirts (6) with any pants (9)
6*9=54
Thus total :12+54=66 ANS:B |
AQUA-RAT | AQUA-RAT-39658 | $(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((... | [
"149",
"169",
"289",
"209"
] | C | 17^2= 289 because follow sequence of square of the prime numbers
ANSWER:C |
AQUA-RAT | AQUA-RAT-39659 | to solve for the other. Logic To Calculate Percentage Difference Between 2 Numbers. Sale Discount Calculator - Percent Off Mortgage Loan Calculator - Finance Fraction Calculator - Simplify Reduce Engine Motor Horsepower Calculator Earned Value Project Management Present Worth Calculator - Finance Constant Acceleration ... | [
"396",
"36",
"3996",
"40"
] | A | (1/10)*4000 - (1/10)%*4000 =
400 - (1/1000)*4000 =
400 - 4 = 396
The answer is A. |
AQUA-RAT | AQUA-RAT-39660 | homework-and-exercises, fluid-statics, bernoulli-equation
You ignore the area of the hole.
Rate of water going in: $r'= \frac{0,2cm^3}{s}$
Rate of water going out: $r=1mm^2*\sqrt{2gh}$
Set the two rates equal and solve for $h$
$\frac{0,2cm^3}{s} = 1mm^2*\sqrt{2gh}$
$\frac{0,2cm^3}{s*0,01cm^2} = \sqrt{2gh}$
$\fra... | [
"4500",
"2678",
"3600",
"3400"
] | C | (2000 * 3 * 36)/60
= 3600 M3
Answer:C |
AQUA-RAT | AQUA-RAT-39661 | (D)
Manager
Joined: 03 Aug 2017
Posts: 64
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
### Show Tags
05 Oct 2019, 22:16
Bunuel wrote:
If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
A. 63
B... | [
"$860",
"$850",
"$840",
"$830"
] | A | 50 pages typed 1x
35 pages typed 2x (original + one revision)
15 pages typed 3x (original + two revisions)
50(6)+35(6+4)+15(6+4+4)=300+350+210=860
Answer - A |
AQUA-RAT | AQUA-RAT-39662 | 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 2/5",
"10 2/0",
"12 2/3",
"10 2/1"
] | C | 2/20 + 4/15 + x/20 = 1
x = 38/3 = 12 2/3 Answer: C |
AQUA-RAT | AQUA-RAT-39663 | evolution, mathematical-models, theoretical-biology, population-dynamics, population-genetics
Title: Effective population size when the population sizes varies from season to season Let's think of a species which has four generations per year and which population size changes from season to season so that the populati... | [
" 2^3",
" 3^2",
" 2(3^10)",
" 3(2^6)"
] | D | 3*2^n where n is the #of month --> 3*2^6 Answer (D) |
AQUA-RAT | AQUA-RAT-39664 | Puzzle of gold coins in the bag
At the end of Probability class, our professor gave us the following puzzle:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we ca... | [
"16",
"42",
"16",
"84"
] | B | 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B |
AQUA-RAT | AQUA-RAT-39665 | python, programming-challenge, primes, factors
Title: Calculate the first largest factor of 600851475143 ٍProblem description:
The prime factors of 13195 are 5, 7, 13 and 29. Largest prime factor 13195 is 29.
What is the largest prime factor of the number 600851475143 ?
Prime Factor:
any of the prime numbers that can ... | [
"462",
"450",
"480",
"504"
] | D | Explanation:
HCF of the two numbers = 42
HCF will be always a factor of LCM
42 is factor of LCM
other two factors are 11 & 12
Then the numbers are (42 11) and (42 x 12)
= 462 and 504
Answer: Option D |
AQUA-RAT | AQUA-RAT-39666 | Thanks
• Your "40% overlap" would mean taht the surface overlaping is 40% of the surface of which rectangle ? – Evargalo Sep 28 '17 at 16:13
• I want to know if, say, 40% of the other rectangle is contained inside the self rectangle – John Lexus Sep 28 '17 at 16:14
For the equations, I will let the left of the first ... | [
"33%",
"44%",
"55%",
"56%"
] | B | The question is very easy. My logic is the following:
A surface = 6*a^2
After 20% increase A surface = 6* ((1.2a)^2) = 6*1.44*a^2
The increase in the surface area = (6*1.44*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.44-1))/(6*a^2) = 1.44-1=0.44 = 44%
ANSWER:B |
AQUA-RAT | AQUA-RAT-39667 | This leaves ten admissible configurations, and for each there are $(3!)^2=36$ ways of permuting the boys and girls, for a total of 360 ways.
• ok, but where exatcly am i going wrong? – Anvit Dec 10 '17 at 11:21
• @AnvitGarg Note that you have considered the case that boys and girls should sit in alternate positions. B... | [
"10",
"19",
"20",
"9"
] | D | D |
AQUA-RAT | AQUA-RAT-39668 | ### Show Tags
21 Jul 2010, 07:18
4
for venn diagrams in case of 3 cases:
Total = m(a) + m(b) + m(c) + m(a&b) + m(b&c) + m(c&a) - 2*m(a&b&c)
So, 70 = 40 + 30 + 35 - m(a&b) - m(b&c) - m(c&a) - 2*15
=> -35 = - [ m(a&b) + m(b&c) + m(c&a) ] - 30
Therefore, m(a&b) + m(b&c) + m(c&a) = 5
Target Test Prep Representative
Statu... | [
"30",
"10",
"18",
"28"
] | C | Answer
Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.
Then, (A U B) is the set of students who have enrolled at least one of the two subjects. As the students of the class have enrolled for at least one of the two subjects, A U B = 40
We know A U B ... |
AQUA-RAT | AQUA-RAT-39669 | 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... | [
"102",
"116",
"103",
"512"
] | B | The number of triangle can be formed by 10 points = 10C3.
Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3-4C3 = 120-4 = 116.
Ans: B |
AQUA-RAT | AQUA-RAT-39670 | In layman terms, this means if we assume there is a smallest number X where X>0 but there is no number such that X>Y>0, then X is the difference between 1 and 0.999... As all my opponent's formulas rely on the idea that 0.999... is a real number, he fails the idea when applied to hyperreal numbers.
The following is mu... | [
"19,104",
"19,903",
"19,356.732",
"19,502"
] | B | Correct Answer: (B)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 99 * 10. The largest value must be less than 199 * 100. This means that 990 < xy < 19,900. (B) is outside of this range, so it is not a possible product of xy. |
AQUA-RAT | AQUA-RAT-39671 | # Difference between revisions of "1984 AIME Problems/Problem 4"
## Problem
Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. ... | [
"30",
"98",
"27",
"21"
] | A | Explanation:
Let the numbers be 4x, 5x and 6x, Then, (4x + 5x + 6x ) / 3 = 25
=> 5x = 25
=> x = 5.
Largest number 6x = 30.'
Answer: A) 30 |
AQUA-RAT | AQUA-RAT-39672 | # If both integers $x$ and $y$ can be represented as $a^2 + b^2 + 4ab$, prove that $xy$ can also be represented like this …
There is a set $Q$ which contains all integral values that can be represented by $$a^2 + b^2 + 4ab$$, where $a$ and $b$ are also integers. If some integers $x$ and $y$ exist in this set, prove th... | [
"-30",
"-24",
"-5",
"5"
] | B | here x and y are integers .
x^2=2y,xy =256.
substitute (x^2)/2=y in xy => x^3=256*2=>x^3=512.
here x^3 is positive ,
x is also positive.
x=8 then y=32.
x-y=-24
so option B is correct |
AQUA-RAT | AQUA-RAT-39673 | # Math Help - help
1. ## help
mr.lopez needs 3/4 kg of apples to make a pie.how many pies can he make if he uses 20 kg of apples?
name a fraction that is between 1/2 and 1/3....?
which of the following fractions is closest to one?
a)2/3 b)3/4 c)4/5 d)5/6
three pizzas were evenly shared among some friends. if each ... | [
"18 1/4",
"18 1/2",
"18 3/4",
"17"
] | D | 15x+8y=5x+14y
x=3/5y. Answer D |
AQUA-RAT | AQUA-RAT-39674 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"Rs.1520",
"Rs.1570",
"Rs.1500",
"Rs.1550"
] | C | Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs.1500
Answer:C |
AQUA-RAT | AQUA-RAT-39675 | # probability question on a customer
A very frustrated customer is trying to find an electronic receipt on their phone so they can return an item. The trouble is that the customer has three email accounts and can't remember which, one, account it was sent to. The customer assumes that there is an equal probability for... | [
" 0.25",
" 1-0.93^10",
" 1-0.95^10",
" 1-0.05^10"
] | B | Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.93^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.93^10.
Answer: ... |
AQUA-RAT | AQUA-RAT-39676 | # Probability based on a percentage
We have a group of 15 people, 7 men and 8 women.
Randomly selecting 5 people, what's the probability to pick 3 men and 2 women? What's the probability to pick at least 1 man?
I tried solving the first question like this: $${7 \choose 3} = \frac{7!}{(7-3)!3!} = 35$$ and $${8 \choos... | [
"3⁄20",
"31⁄60",
"9⁄40",
"1⁄3"
] | B | Consider a group of 100 women and 200 men, a total of 300 people. 30% of them, which is 90, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 45.
It means that there are 200 - 45 = 155 men who own a car, and this represents 155/300 = 31/60 of the total.
Answe... |
AQUA-RAT | AQUA-RAT-39677 | # 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... | [
"74%",
"44%",
"68%",
"64%"
] | D | r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D |
AQUA-RAT | AQUA-RAT-39678 | A: 9
B: 12
C: 16
D: 18
E: 24
This is a copy of the following OG question: five-machines-at-a-certain-factory-operate-at-the-same-constant-rate-219084.html
_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2231
Location: India
Concentration: General Ma... | [
"648",
"1800",
"2600",
"10800"
] | C | Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines 6 : 10 :: 390 : x
Time (in minutes) 1 : 4
6 x 1 x x = 10 x 4 x 390
x = (10 x 4 x 390)/(6)
x = 2600.
ANSWER:C |
AQUA-RAT | AQUA-RAT-39679 | 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... | [
"16",
"12",
"18",
"22"
] | D | 2*11=22.Answer is D. |
AQUA-RAT | AQUA-RAT-39680 | 2) $$r = 17$$
- Since, point (p, r) lie on all the line, we can plugin the point in above equation
$$r = ap - 5 => 17 = ap - 5$$
$$r = p + 6 => 17 = p + 6$$
$$r = 3p + b => 17 = 3p + b$$
- Again, we do not need to solve for all the variables and just recognize that the above equations will lead to single value of b. He... | [
" y = 3x + 4",
" y = –3x – 6",
" y = (1/3)x – 1",
" y = (–1/3)x + 2"
] | C | I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is... |
AQUA-RAT | AQUA-RAT-39681 | ### 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... | [
"33",
"20",
"88",
"37"
] | B | It is the same as a person with 20 years more age replaces an existing person of the group ( or village)
Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.
Alternatively : ( n x ... |
AQUA-RAT | AQUA-RAT-39682 | 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, ... | [
"20",
"24",
"28",
"36"
] | A | The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 80 is 80/2 = 40
The average of the even numbers from 0 to 40 is 40/2 = 20
The answer is A. |
AQUA-RAT | AQUA-RAT-39683 | 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... | [
"270 metres",
"245 metres",
"235 metres",
"220 metres"
] | B | Explanation:
Solution 1Speed =45 km/hr=45×518 m/s=12.5 m/s=45 km/hr=45×518 m/s=12.5 m/s
Time =30 s=30 s
Distance travelled =12.5×30=375 m=12.5×30=375 m
Length of the bridge =375−130=245 m
ANSWER IS B |
AQUA-RAT | AQUA-RAT-39684 | int <- .1/100 # annual interest rate of 0.1%
inf <- 2/100 # annual inflation rate 2%
n <- 10 # number of years
The following is multiple choice question (with options) to answer.
At what rate percent per annum will the simple interest on a sum of money be 1/5 of the amount in 10 years? | [
"2%",
"7%",
"9%",
"3%"
] | A | Let sum = x. Then, S.I. = x/5, Time
= 10 years.
Rate = (100 * x) / (x * 5 * 10)
= 2%
Answer: A |
AQUA-RAT | AQUA-RAT-39685 | But $45 < \frac{\alpha}{2} < 90$. Therefore $\cos \left( \frac{\alpha}{2}\right) = \sqrt{0.02} = 0.1414$.
The following is multiple choice question (with options) to answer.
45 x ? = 35% of 900 | [
"16.2",
"7",
"5",
"500"
] | B | Answer
Let 45 x A = (35 x 900)/100
∴ A = (35 x 9)/45 = 7
Correct Option: B |
AQUA-RAT | AQUA-RAT-39686 | "How does this help me?" you say
I'm very glad you asked
Let's think about $8$ as our 100% and we want to find 2 parts of 8, so using what we just learned we say that "2 parts of 8 is the same as $\frac{2}{8}$." To turn $\frac{2}{8}$ into a percentage we just need the denominator to equal 100 since earlier we said tha... | [
"40000",
"45120",
"65200",
"32560"
] | A | a/100 * b = 8/9 * 450
xy = 400*100 = 40000
Answer is A |
AQUA-RAT | AQUA-RAT-39687 | (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 - ... | [
"480",
"475",
"485",
"490"
] | B | N=(4*5-1)*5*5=475
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 44 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
B |
AQUA-RAT | AQUA-RAT-39688 | 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.
. .... | [
"Rs. 4800",
"Rs. 3600",
"Rs. 3560",
"Rs. 4530"
] | D | Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
ANSWER:D |
AQUA-RAT | AQUA-RAT-39689 | 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 ... | [
"1600",
"2998",
"2778",
"2788"
] | A | 85%
120%
--------
25% ---- 400
100% ---- ? => Rs.1600
Answer:A |
AQUA-RAT | AQUA-RAT-39690 | # What is the next number in this sequence: $1, 2, 6, 24, 120$? [closed]
I was playing through No Man's Sky when I ran into a series of numbers and was asked what the next number would be.
$$1, 2, 6, 24, 120$$
This is for a terminal assess code in the game no mans sky. The 3 choices they give are; 720, 620, 180
• W... | [
"22",
"24",
"25",
"26"
] | C | Explanation: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
Answer: Option C |
AQUA-RAT | AQUA-RAT-39691 | 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, ... | [
"15",
"20",
"23",
"27"
] | D | The average falls between the 5th and 6th integers,
integer 5 = 22, integer 6 = 23.
Counting up to the tenth integer
we get 27.
ANSWER:D |
AQUA-RAT | AQUA-RAT-39692 | c++, beginner, calculator, reference
There are two problems with it. First, the movie name I gave was not Journey to Mars so that's a basic problem that comes from not passing that value into printReport. The second problem is more subtle. Notice that the gross amount is $954.50, but the sum of the donated amount a... | [
"Rs150",
"Rs112.50",
"Rs105",
"Rs120"
] | B | let the no. of tickets sold before = x
then the no. of tickets sold after = 1.5x
Collection Before = x*250
Collection after = 1.5x* = (250x*82.5)100
=137.5
change in price =250 - 137.5
=112.5
ANSWER:B |
AQUA-RAT | AQUA-RAT-39693 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"A)1055",
"B)1215",
"C)1065",
"D)1070"
] | B | Cost of 8 kg grapes = 90 × 8 = 720.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 720 + 495 = 1215.
B) |
AQUA-RAT | AQUA-RAT-39694 | # Combination Question
#### Swazination
##### New member
How many combinations can I make if I have 4 letters A,G,C,T and I want to make groups of 5. Yes, you can repeat the letters.
#### Denis
##### Senior Member
From AAAAA to TGCAA
or (if replaced by digits 1 to 4):
from 1111 to 43211
Yes?
#### ksdhart2
##### ... | [
"22",
"24",
"26",
"28"
] | D | 8C2=28.
The answer is D. |
AQUA-RAT | AQUA-RAT-39695 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"3:2.",
"2:1.",
"3:1.",
"4:3."
] | A | Price of 40 L juice= 3x
1L= 3x/40
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/40/4x/80= 3:2
A is the answer |
AQUA-RAT | AQUA-RAT-39696 | (1) The first $$n$$ people donated $$\dfrac1{16}$$ of the total amount donated.
(2) The total amount donated was $$\120,000.$$
Source: GMAT Prep
Target question: What was the value of n?
When I scan the two statements, it seems that statement 2 is easier, so I'll start with that one first...
Statement 2: The total a... | [
"dx/A(A - d)",
"dx",
"a",
"A-d"
] | A | Number of individuals = A
Amount paid by each individual = n
Total expected amount = Charity's goal = nA = x
n = x/A
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/A --> Additional amount
Number of individuals who are paying = A - d
Additional amount has to be divided... |
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