source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-39197 | Spoiler:
The middle number is the average of the other two.
$\frac{47+63}{2} \:=\:55,\quad \frac{85+99}{2} \:=\:92,\quad \frac{73+25}{2} \:=\:{\color{red}49}$
3. ## Re: Math puzzles questions?
Originally Posted by amrithaa
1. What number should replace the question mark?
Each row is 8 times the immediate row above.... | [
"49",
"37",
"70",
"17"
] | D | D
17
The sequence progresses -18, -17, -18, -17. |
AQUA-RAT | AQUA-RAT-39198 | 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... | [
"650 meter",
"555 meter",
"500 meter",
"458 meter"
] | C | Explanation:
Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
=>800+x=65/3∗60
=>800+x=20∗65=1300
=>x=1300−800=500
So the length of the tunnel is 500 meters.
Option C |
AQUA-RAT | AQUA-RAT-39199 | Show Tags
25 Nov 2010, 21:43
2
shrive555 wrote:
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt?
20
40
216
720
729
Or out of 6 children, choose 3 in 6C3 ways = 20 ways.
Note: When you choose 3 children say, A, B... | [
"7209",
"4059659",
"2169",
"20"
] | D | How to solve:
1st Person: 6 has options
2nd Person: 5 has options…
Therefore, for all people: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the reds are identical, we divide by 3! Since the greens are identical, we divide by another 3!
So: in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: D) |
AQUA-RAT | AQUA-RAT-39200 | 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... | [
"18.6 sec",
"14.9 sec",
"12.4 sec",
"16.8 sec"
] | A | A
18.6 sec
D = 110 + 200 = 310 m
S = 60 * 5/18 = 50/3
T = 310 * 3/50 = 18.6 sec
Answer is A |
AQUA-RAT | AQUA-RAT-39201 | "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... | [
"3/8",
"8/15",
"9/16",
"12/25"
] | C | 6a/100 = 8
a = 400/3
8b/100 = 6
b = 75
c = b/a = 75*3/ 400 = 9/16
The answer is C. |
AQUA-RAT | AQUA-RAT-39202 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"d = p/1.06 - 0.18",
"d= (p-0.18)/1.06",
"d = (p-0.06)/1.18",
"d = p-0.24"
] | B | Let dealers price (d) be 1. so adding 6% to dealers price is d+ 6% of d. i.e. 1 + 6% of 1 which is1 + 0.06. then add 0.18 to the value.
Now 1.06 + 0.18. this is now 1.24. you have the gasoline stations price (p) as 1.24 dollars.
Now sub 1.24 in the options to know which option gave you d = 1. d must equal 1 because you... |
AQUA-RAT | AQUA-RAT-39203 | # 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... | [
"42 6/8%",
"42 8/7%",
"72 6/7%",
"42 6/7%"
] | D | SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D |
AQUA-RAT | AQUA-RAT-39204 | They settle and use the first price that comes to mind, copy competitors, or (even worse) guess. Prove that the product of three consecutive positive integer is divisible by 6. gl/9WZjCW prove that the product of three consecutive positive integers is divisible by 6. Therefore, n = 3p or 3p + 1 or 3p + 2 , where p is s... | [
"7",
"14",
"21",
"28"
] | C | 1029 = 7 x 7 x 7 x 3
N must include at least 7, 2*7, and 3*7.
The answer is C. |
AQUA-RAT | AQUA-RAT-39205 | Originally Posted by Archie
Because the question talks about all possible pairs of integers, not just 2 and 3.
I can see that every word in word problems is important.
8. ## Re: Positive Integers x & y
Originally Posted by Plato
To harpazo, I cannot understand how this can be so mysterious.
Learn this:
1. The sum of ... | [
"3, 16, 25",
"9, 25, 24",
"2, 81, 32",
"2, 9, 16"
] | C | This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*81*32 = 2*9*9*8*4 = 9*9*8*8
ans C |
AQUA-RAT | AQUA-RAT-39206 | ### 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... | [
" $0.25",
" $0.50",
" $0.75",
" $3.9"
] | D | 9x+6y=20
9x+8y=30
subtracting 1 from 2
-2y=-10
y=5
therefore
x=1.1
difference in price =3.9
D |
AQUA-RAT | AQUA-RAT-39207 | This online aptitude test on Compound Interest is useful for candidates preparing for banking exams - Bank PO, IBPS PO, SBI PO, RRB PO, RBI Assistant, LIC,SSC, MBA - MAT, XAT, CAT, NMAT, UPSC, NET etc. COMPOUND INTEREST TABLES 561 1 / 2 %Compound Interest Factors 1 2 Single Payment Uniform Payment Series Arithmetic Gra... | [
"Rs.600",
"Rs.630",
"Rs.660",
"Rs.680"
] | D | amt=2000(1+r/2/100)^2n formulae as it is half yearlly
amt=2000(1+1/20)^4
amt=2680.19
ci= 2680.19-2000 = 680.00
ANSWER:D |
AQUA-RAT | AQUA-RAT-39208 | newtonian-mechanics, drag, relative-motion
Title: Relative motion-Acceleration My first post here and I'm a complete beginner on this. So please excuse if I'm asking too-basic a question. This question is about the classical boat and river problem.
Say a boat travels at 10 m/s in a water channel.
the water speed rela... | [
"15",
"8",
"9",
"12"
] | A | US = 35
DS = 65
M = (65- 35)/2
= 15
Answer:A |
AQUA-RAT | AQUA-RAT-39209 | Let P=[$(\sqrt{n}+0.7)^2$]
Second Hint
given $n \geq 1$, put n=1 gives P=2
n=2 gives P=4
n=3 gives P=5
n=4 gives P=7
n-5 gives P=8
n=6 gives P=9
n=7 gives P=11
Final Step
here missing number are
1,3,6,10,… which is following a certain pattern
1, 1+2, 3+3, 6+4, 10+5, 15+6, 21+7, 28+8, 36+9, 45+10, 55+11, 66+... | [
"10 & 19",
"8 & 17",
"9 & 18",
"11 & 20"
] | A | 1+3=4
4+3=7
7+3=10
10+3=13
13+3=16
16+3=19
ANSWER:A |
AQUA-RAT | AQUA-RAT-39210 | 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... | [
"3",
"6",
"8",
"9"
] | B | the choices give away the answer..
36 machines take 4 hours to fill 4 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 4*48/72*12/4 = 6
Ans B |
AQUA-RAT | AQUA-RAT-39211 | Example: Take $k=2002$, then $n=63$ and hence $2002$ lies in $(T_{63}-2002+1,63+2002-T_{63})=(15,49)$.
መለሰ
The following is multiple choice question (with options) to answer.
N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? | [
"1 1/2",
"1 1/3",
"5/3",
"3/2"
] | B | "N is such that when multiplied by 0.75 gives 1" is written mathematically as
N * 0.75 = 1
Solve for N
N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3
correct answer B |
AQUA-RAT | AQUA-RAT-39212 | # Geometry
Two cylinders have the same volume. If the radius of cylinder I is 3 times the radius of cylinder II, then the height of cylinder II is how many times the height of cylinder I?
A. 12
B. 9
C. 6
D. 3
1. 👍 0
2. 👎 0
3. 👁 96
1. Cylinder 1 has nine times the base area of cylinder 2.
Volume is (base area) x (h... | [
"25%",
"50%",
"68%",
"80%"
] | C | Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 8/9
New cylinder 3/5
So 3/5/8/9 = 3/5 * 9/8 = 12/15 = 4/5 = 0.680 or 68%.
Answer C |
AQUA-RAT | AQUA-RAT-39213 | 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... | [
"10 m",
"16 m",
"245 m",
"19 m"
] | C | Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C |
AQUA-RAT | AQUA-RAT-39214 | (A) 10
(B) 45
(C) 50
(D) 55
(E) 65
OG 2019 PS07712
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: Of the 150 houses in a certain development, 60 percent have [#permalink]
### Show Tags
15 Nov 2017, 16:22
9
3
ganan... | [
"33 1/3%",
"51 23/27%",
"50%",
"62 1/2%"
] | B | P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27%
Answer B |
AQUA-RAT | AQUA-RAT-39215 | Arrange $2$ red books. Arrange the $5$ black books in any of the three positions as [bbb] [bb]. Take $3$ blue books and separate the adjacent bbb and bb. Remaining $3$ books can be arranged in remaining $5$ positions. So,
$\dbinom{3}{1}\dbinom{2}{1}\dbinom{5}{3}=60$
Arrange $2$ red books. Arrange the $5$ black books i... | [
"14",
"18",
"24",
"28"
] | B | Binders Books Days
15 1400 21
x 1600 20
x/15 = (1600/1400) * (21/20) => x = 18
ANSWER:B |
AQUA-RAT | AQUA-RAT-39216 | harpazo
#### harpazo
##### Pure Mathematics
Sure you do...you know that the number $$54$$ has a value of $$5\cdot10+4$$, right?
Yes but???
#### MarkFL
##### La Villa Strangiato
Staff member
Moderator
Math Helper
Yes but???
But what? If a number has the two digits from left to right as x and y, then the value of the... | [
"4",
"6",
"3",
"Cannot be determined"
] | B | Let the two-digit no. be l0x + y.
Then, (10x + y) – (10y + x) = 36
or, 9(x – y) = 54
or, x – y = 6
Answer B |
AQUA-RAT | AQUA-RAT-39217 | In this case, you have the digits $3$ and $2$, each of them $25$ times, so the remainder when dividing by $8$ is the same as the remainder of $(2+3)\times 25 = 125$ when divided by $8$, which is $5$.
(More generally, the remainder of dividing the number $(b_1b_2\cdots b_k)_b$ by $b-1$ is the same as the remainder of d... | [
"0",
"3",
"5",
"11"
] | C | Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x = 5k + 3
x2 = (5k + 3)2 = (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
ANSWER:C |
AQUA-RAT | AQUA-RAT-39218 | Digital Sum Rule of Multiplication: The digital sum of the product of two numbers is equal to the digital sum of the product of the digital sums of the two numbers.
Example: The product of 129 and 35 is 4515.
Digital sum of 129 = 3 and digital sum 35 = 8. Product of the digital sums = 3 × 8 = 24 Digital sum = 6.
Digit... | [
"24",
"73",
"26",
"82"
] | A | Explanation:
Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
Answer: A |
AQUA-RAT | AQUA-RAT-39219 | # Given a bag of 3 red marbles, 5 black, and 8 green, what is the probability that?
A bag has:
$3$ red
$5$ black
$8$ green
marbles.
Total of 16 marbles.
You select a marble, and then another one right after. (without replacement).
What is the probability that $both$ are red?
Probability that first pick is red:... | [
"1/2",
"12/21",
"7/12",
"2/3"
] | B | Total selection ways: 7C2=7!/3!4!=21
Selecting one blue chip out of two: 3C1=3!/2!1!=3
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (3C1*4C1)/7C2=(3*4)/21=12/21=B |
AQUA-RAT | AQUA-RAT-39220 | 27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14... | [
"226.623",
"224.777",
"233.523",
"414.637"
] | A | Solution
Given expression = 894.7 - (573.07 + 95.007) = 894.7 - 668.077 = 226.623. Answer A |
AQUA-RAT | AQUA-RAT-39221 | kmph. com/2016/01/01/speed-distance-timeVideos, worksheets, 5-a-day and much more. If a car traveled 50 miles over the course of one hour then its average speed will be 50 mph. Distance, Time and Speed Word Problems | GMAT GRE Maths. Exercise: Problems on Speed Time and Distance. org/time-speed-distanceTime, Speed and ... | [
"70 km",
"76 km",
"85 km",
"90 km"
] | D | Explanation :
Solution: Difference between timings = 30 min. = 30/60 hr = 1/2 hr.
Let the length of the journey be x km.
Then, x/45 - x/60 = 1/2
=> 4x -3x = 180/2
=> x = 90 km.
Answer : D |
AQUA-RAT | AQUA-RAT-39222 | Just need to verify if this one needs to be subtracted or no.
jaytheseer
New member
Mr. Gates owns 3/8 of Macrohard. After selling 1/3 of his share, how much more of Macrohard does Mr. Gates still own?
MarkFL
Staff member
Yes, I would view the subtraction in the form:
If Mr. Gates sold 1/3 of his share, how much o... | [
"782",
"276",
"727",
"205"
] | D | A:B:C = 100:65:40
= 20:13:8
8 ---- 40
41 ---- ? => Rs.205
Answer:D |
AQUA-RAT | AQUA-RAT-39223 | 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... | [
"8 sec",
"7 sec",
"2 sec",
"6 sec"
] | D | T = 60/36 * 18/5
= 6 sec
Answer:D |
AQUA-RAT | AQUA-RAT-39224 | # 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.2166.67",
"Rs.2224",
"Rs.2270.72",
"Rs.2145"
] | A | Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % o... |
AQUA-RAT | AQUA-RAT-39225 | 7. Originally Posted by HallsofIvy
Skeeters method, find the roots to the original equation, take the reciprocal, and create the new equation from that is the obvious and simplest method.
Here is a little more "sophisticated" method. Look at the general product (x- a)(x- b)= x^2- (a+b)x+ ab. If, instead, we have (x- 1... | [
"a=b",
"a-bc",
"c=a",
"c=b"
] | C | based on the problem 1/k will be the other root of the given equation. root equation = c/a. k*1/k=c/a. c/a= 1 or a = c[multiplying on both sides].
the roots of the equation axsquared + bc + c= 0 will be reciprocal if a= c. correct answer: (C) |
AQUA-RAT | AQUA-RAT-39226 | 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... | [
"396/60+k",
"376/60+k",
"386/60+k",
"366/60+k"
] | A | k=96+300
tot distance= 396 miles
tot time= 1min + k
avg speed= 396/60+k
ANSWER:A |
AQUA-RAT | AQUA-RAT-39227 | # How to distribute $k$ prizes in $p$ student with each student would receive $(k-1)$ prizes at most?
A teacher decided to encourage the kids by distributing prizes to them. Each of the prizes was different from the other. The total number of prize was $k$, and total number of kids was $p$. To encourage the kids, the ... | [
"25",
"30",
"64",
"70"
] | A | Ans.(A)
Sol. In this case, repetitions are allowed, so all the two prizes can be given in 5 ways, i.e. (5 x 5) ways = 52 ways = 25 ways Or nr ways = 52 ways = 25 ways |
AQUA-RAT | AQUA-RAT-39228 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"20 kmph",
"13 kmph",
"65 kmph",
"55 kmph"
] | A | Speed of the boat in still water
= (40+80)/2
= 60 kmph. Speed of the stream
= (80-40)/2
= 20 kmph.
Answer: A |
AQUA-RAT | AQUA-RAT-39229 | algorithms, scheduling, algorithm-design
Title: Schedule two trains whose tracks overlap so they don't crash I've encountered scheduling problems in my algorithms class before like the type we use vertex cover to solve.
Recently I was asked this question and did not even know what algorithmic technique to use to answe... | [
"108",
"112",
"126",
"140"
] | C | Explanation :
Initially, let's remove the 4 stopping stations
Then we are left with 8 non-stopping stations (=12-4) as shown below
(non-stopping stations are marked as 1,2 ... 8)
Now there are 9 positions (as marked by * in the above figure) to place the 4 stopping stations
such that no two stopping stations are consec... |
AQUA-RAT | AQUA-RAT-39230 | $38k - (2*38 - 7)l = 34$
$38(k-2l) + 7l = 34$. Let $m=k-2l$
$38m + 7l = 34$.
$(3+ 5*7)m + 7l = 34$
$3m + 7(5m + l) = 34$. Let $n = 5m+l$.
$3m + 7n = 34$
$3m + 2*3n + n = 34$
$3(m + 2n) + n = 34$. Let $a = m+2n$.
$3a + n = 34$.
Let $a=11; n = 1$. So $a=m+2n; 11=m + 2; m = 9$. and $n= 5m + l; 1=5*9 +l; l = -44$.... | [
"65",
"59",
"72",
"80"
] | B | (9 * 6) + 5 = 59
B |
AQUA-RAT | AQUA-RAT-39231 | (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 - ... | [
"138687",
"142587",
"144487",
"142667"
] | B | B
142587
142587*2=285174
These type of numbers are called cyclic numbers where a number multiplied by any digit the result will contain all the digit in the original number and no other digit.
cyclic numbers are generated by full reptend prime 7,17,19,23 etc.
where 1/7=0.142857……
1/17=0.058823529411764 |
AQUA-RAT | AQUA-RAT-39232 | # Project Euler #5 - Lowest common multiple of 1 through 20
This is my code. All comments welcome. Last time run it only took 335 milliseconds:
static bool CheckMultiples(int val)
{
for (int i = 1; i <= 20; i++)
{
if (val % i != 0)
return false;
}
return true;
}
static void Main(string[] args)
{
Stopwatch s = new S... | [
"350",
"420",
"510",
"320"
] | A | LCM=2*5*5*7=350.
Answer is A |
AQUA-RAT | AQUA-RAT-39233 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"20 hours",
"15 hours",
"10 hours",
"12 hours"
] | A | Part filled by A in 1 hour = 1/36
Part filled by B in 1 hour = 1/45
Part filled by (A+B) in 1 hour = 1/36 + 1/45 = 9/180 = 1/20
Both the pipes together fill the tank in 20 hours
Answer is A |
AQUA-RAT | AQUA-RAT-39234 | # 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... | [
"60%",
"37%",
"30%",
"80%"
] | C | Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer & Answer:C |
AQUA-RAT | AQUA-RAT-39235 | 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... | [
"7/4",
"4/3",
"14/5",
"10/3"
] | C | Rate(1)=1/5
Rate(2)=1/8
Combined = 13/40
Work done in 2 days=13/20
Work left = 7/20
Rate * Time = Work left
1/8 * Time = 7/20
Time=14/5
C |
AQUA-RAT | AQUA-RAT-39236 | ### 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... | [
" 11",
" 13",
" 15",
" 17"
] | A | (x+5)*150 +x*85=1455
=>x=3
total lens=3+(3+5)= 11
Answer A |
AQUA-RAT | AQUA-RAT-39237 | 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 ... | [
"610.25",
"573.85",
"563.75",
"420.5"
] | C | CI=P[(1+(R/100))^T-1]
=5500*[(1+(5/100))^2-1]
=5500*[(1.05)^2-1]
=5500*0.1025
=Rs.563.75
Option C |
AQUA-RAT | AQUA-RAT-39238 | I see from your profile that you’re a programmer. Extreme cases like these are analogous to testing boundary conditions in your code (things like loops that execute 0 times).
Let x to be your gross salary and y = 1600 to be your net salary. Because tax is 20% of gross salary then we have
x = y + tax = 1600 + 0.2x
=> ... | [
"15%",
"20%",
"25%",
"69%"
] | D | Initially 92% and 8% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗92
so, the required % is [(3/4)∗92/100]∗100 = 69%
ANSWER:D |
AQUA-RAT | AQUA-RAT-39239 | homework-and-exercises, pressure, fluid-statics
Title: Which tank fills up first? Which tank would fill first. My first guess was 3 and 4 simultaneously due to Pascal's Law of pressure distribution. Then tank 2 and then 1. Could you please help? This is my first question ever on Stack Exchange. Tank 1 will to the lev... | [
"3",
"6",
"9",
"12"
] | A | The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15
Since the rate is negative, the tank will be emptied.
A full tank would take 15 minutes to empty.
Since the tank is only one-fifth full, the time is (1/5) * 15 = 3 minutes
The answer is A. |
AQUA-RAT | AQUA-RAT-39240 | ### 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... | [
"1300",
"1100",
"1000",
"1200"
] | D | Let the price of a pant and a t-shirt be Rs. x and Rs. y respectively.
Then, 3x + 6y = 2250 .... (i)
and x + 12y = 2250 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 750. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 2250 (-)
x + 2y = 750
----------------
10y = 1500
----------------
y= 15... |
AQUA-RAT | AQUA-RAT-39241 | Notice carefully, the sign of the net increase is negative, clearly indicating the after the successive decrease the value of the original number, decreased instead of increasing. And what was the magnitude??? Right 28%. The net decrease is 28%.
So, before we use this approach to give you an official answer for the ab... | [
"26% increase",
"44% decrease",
"60% increase",
"66% increase"
] | A | if n items are sold for $p each, revenue is $np. If we reduce the price by 30%, the new price is 0.7p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.7p)(1.8n) = 1.26np, which is 1.26 times the old revenue, so is 26% greater.
ANSWER:A |
AQUA-RAT | AQUA-RAT-39242 | ### 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... | [
"180",
"100",
"112",
"110"
] | C | Income of 10 months = (10 × 85) – debt
= 850 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 1120
Average monthly income = 1120 ÷ 10 = 112
Answer C |
AQUA-RAT | AQUA-RAT-39243 | 4,8),(3,5,8),(2,6,8),(1,7,8),(1,9,8),(9,0,9),(8,1,9),(7,2,9),(6,3,9),(5,4,9),(4,5,9),(3,6,9),(2,7,9),(1,8,9)]
The following is multiple choice question (with options) to answer.
How many terms are there in 2, 4, 8, 16,..., 512? | [
"14",
"11",
"12",
"9"
] | D | 2, 4, 8, 16, ..., 512 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 512
or 2^n-1 = 256 = 2^8
Thus n - 1 =8
n= 9
ANSWER:D |
AQUA-RAT | AQUA-RAT-39244 | # Math Help - word problem.
1. ## word problem.
hi ! im having a difficult time answering this word problem.
"Alvin set out from a certain point and travelled at the rate of 6 kph. After Alvin had gone for two hours, Ben set on to overtake him and went 4km the first hour, 5 km the second hour, 6 km the third hour an... | [
"233",
"552",
"376",
"287"
] | B | Given that distance travelled in 1st hour = 35 km
and speed of the bus increases by 2 km after every one hour
Hence distance travelled in 2nd hour = 37 km
Hence distance travelled in 3rd hour = 39 km
...
Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term, a=... |
AQUA-RAT | AQUA-RAT-39245 | circle, ellipse, trapezoid, cube, sphere, cylinder and cone. 2πrh=πrl [r is radius of. A cylinder is a solid figure, with a circular or oval base or cross section and straight and parallel sides. ' and find homework help for other Math questions. Derive the formula for the surface area of a cone of radius r and height ... | [
"2:5",
"2:6",
"2:3",
"2:4"
] | A | The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2
=2:5
Answer: A |
AQUA-RAT | AQUA-RAT-39246 | # Number of ways in which they can be seated if the $2$ girls are together and the other two are also together but separate from the first two
$5$ boys and $4$ girls sit in a straight line. Find the number of ways in which they can be seated if $2$ girls are together and the other two are also together but separate fr... | [
"120",
"130",
"150",
"195"
] | D | The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different way... |
AQUA-RAT | AQUA-RAT-39247 | "Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4959 Location: Canada GMAT 1: 770 Q49 V46 When a positive integer n is divided by 5... | [
" 0",
" 1",
" 2",
" 3"
] | B | the equation that can be formed r is 13x+2=8y+5..
13x-3=8y...
as we can see x can take only odd values as the RHS will always be even..
Also x can take values till 13 as 13*14>180..
now we have to substitue x as 1,3,5,7,9,11,13...
once we find 7 fitting in , any other value need not be checked as every 4th value will g... |
AQUA-RAT | AQUA-RAT-39248 | Example $$\PageIndex{6}$$:
A student’s grade point average is the average of his grades in 30 courses. The grades are based on 100 possible points and are recorded as integers. Assume that, in each course, the instructor makes an error in grading of $$k$$ with probability $$|p/k|$$, where $$k = \pm1$$$$\pm2$$, $$\pm3$... | [
"15%",
"20%",
"25%",
"66 2/3%"
] | D | 0.4*75 + 0.6x = 105
30 + 0.6x=107
0.6x = 75
x= 125
125/75= 1.66666...
Ans:D |
AQUA-RAT | AQUA-RAT-39249 | (A) 1
(B) 2
(C) 4
(D) 6
(E) 8
11. What is the area of the shaded region of the given 8 X 5 rectangle?
The following is multiple choice question (with options) to answer.
A block of wood has dimensions 10cm x 10cm x 50cm. The block is painted red and then cut evenly at the 25 cm mark, parallel to the sides, to form two... | [
"5.5%",
"8.3%",
"11.6%",
"14.2%"
] | B | The area of each half is 100+4(250)+100 = 1200
The area that is not painted is 100.
The fraction that is not painted is 100/1200 = 1/12 = 8.3%
The answer is B. |
AQUA-RAT | AQUA-RAT-39250 | 10. A $$2$$-foot brick border is constructed around a square cement slab. If the total area, including the border, is $$121$$ square feet, then what are the dimensions of the slab?
11. The area of a picture frame including a $$2$$-inch wide border is $$99$$ square inches. If the width of the inner area is $$2$$ inches... | [
"2 FT 7 IN",
"1 FT 7 IN",
"2 FT 6 IN",
"3 FT 7 IN"
] | A | Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
ANSWER A |
AQUA-RAT | AQUA-RAT-39251 | Let one woman complete the job in $$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}$$ job/day... | [
" 32",
" 64",
" 50",
" 144"
] | A | (10/100)Workers = 16 = > number of workers = 160
(20/100)*Workers = x+16 = > x = 32
Answer A |
AQUA-RAT | AQUA-RAT-39252 | Pre-checking the number $A$
Very quickly, 7 is found to be a factor of $A$. We have $A=7 \times B$ where $B$ is:
$B=$ 9636514689378269172619627962314350702683338048951
We then try to find small factors of $B$. The number 283 is found to be a factor of $B$. Then we have $A=7 \times 283 \times C$ where $C$ is the foll... | [
"3",
"4",
"5",
"6"
] | B | 484848 when divided by 4 gives the result 121212
CONCEPT: Rule of Divisibility of 4 isIf sum of the digits of the Number is divisible by 4 then the number will be divisible by 2
SUm of the digits of No. which is divisible by 4 hence the Number 121212 will be divisible by 4
B |
AQUA-RAT | AQUA-RAT-39253 | • Any triangle whose sides are in the ratio 3:4:5 is a right triangle. Such triangles that have their sides in the ratio of whole numbers are called Pythagorean Triples. There are an infinite number of them, and this is just the smallest. If you multiply the sides by any number, the result will still be a right triangl... | [
"64",
"49",
"96",
"81"
] | D | LET a= hypotenuse , b =base ,9 = perpendicular . therefore a^2 -b^2 =9^2 or (a+b)(a-b) = 81
a+b =81/a-b ' a-b cannot be zero ..therefore a+ b =81 where a-b is equal to 1
D |
AQUA-RAT | AQUA-RAT-39254 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"10 sec",
"8 sec",
"5 sec",
"6 sec"
] | D | T = 60/36 * 18/5 = 6 sec
ANSWER D |
AQUA-RAT | AQUA-RAT-39255 | Question
# In a school, there are $$1000$$ student, out of which $$430$$ are girls. It is known that out of $$430, 10$$% of the girls study in class $$XII$$. What is the probability that a student chosen randomly studies in class $$XII$$ given that the chosen student is a girl?.
Solution
## Total number of students ... | [
"A)0.9",
"B)0.6",
"C)0.45",
"D)0.3"
] | B | Percent of students who are 25 years old or older is 0.4*48+0.3*52=~34, so percent of people who are less than 25 years old is 100-34=66.
Answer: B. |
AQUA-RAT | AQUA-RAT-39256 | So, we can always stop when we reach the largest prime number smaller than the square root of the limit -- in this case, when we reach the largest prime number smaller than $\sqrt{200}$. (The square root, say $a$ has the property that $a\times a = 200$ so any other combination of factors must have one larger, one small... | [
" 1",
" 2",
" 3",
" 4"
] | A | My friend, every single odd number greater than can be written either as 4V+1 or as 4V+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.
The 6V+1 or 6V-1 rule is basically every odd number that is not divisible by three, so it narrows the ... |
AQUA-RAT | AQUA-RAT-39257 | 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... | [
"1/4",
"2/7",
"5/9",
"1/2"
] | C | Total Savings = S
Amount spent on stereo = (1/3)S
Amount spent on television = (1-1/3)(1/3)S = (2/3)*(1/3)*S = (2/9)S
(Stereo + TV)/Total Savings = S(1/3 + 2/9)/S = 5/9
Answer: C |
AQUA-RAT | AQUA-RAT-39258 | Hint: Find the square of $1+\sqrt{3}$. ${}{}{}{}{}{}{}{}{}$
-
Since $(4+2\sqrt3)(4-2\sqrt3)=16-12=4$, try squaring: \begin{align} \left(\sqrt{4+2\sqrt3}+\sqrt{4-2\sqrt3}\right)^2 &=(4+2\sqrt3)+(4-2\sqrt3)+2\sqrt{(4+2\sqrt3)(4-2\sqrt3)}\\ &=8+2\sqrt{16-12}\\[6pt] &=12 \end{align} Therefore, $\sqrt{4+2\sqrt3}+\sqrt{4-2... | [
"76",
"5776",
"304",
"2704"
] | D | Answer
Let √N/13= 4
Then √N = 13 x 4 = 52
∴ N = 52 x 52 = 2704.
Correct Option: D |
AQUA-RAT | AQUA-RAT-39259 | # Probability - analyzing "randomness" of data
Forgive me, I am a probability novice and am looking for a little guidance. My question is based on real-world data. I have obscured it a bit for confidentiality reasons but the spirit of the question is the same. Okay, here is the setup: Suppose that 100 students from 37... | [
"1/2",
"3/4",
"5/8",
"7/8"
] | D | Since the probability of Karen's being accepted to each individual project is 50%, the probability of her not being accepted to each project is 50%. The probability that she will be accepted to none is, therefore, (1/2)*(1/2)*(1/2)=1/8.
P(Karen will be accepted to at least one project) = 1 - (1/8) = 7/8.
The answer is ... |
AQUA-RAT | AQUA-RAT-39260 | • I am also stuck at this point. If the first rose is $Red$ then the Bride enters the Church and in that case the probability is $\frac{10}{20}$. But now come the cases when the first rose is $White$: $WRR$, $WWRRR$, $WRWRR$ and so on. No matter what, if the first rose is $White$, the last two roses must be $Red$. And ... | [
"20%",
"25%",
"62.5%",
"75%"
] | C | R + W + P = 120
S + L = 120
1/3 * 120 = 40
Short-Stemmed White = 15
Short-Stemmed Pink = 15
=> Short-Stemmed Red = 10
15/P =10/R
=> R = 2R/3
So Total Long Stemmed = 80
And Long Stemmed Red + Long Stemmed Pink = 80
So Long Stemmed Red/Long Stemmed = ?
Total White = 20 (As no Long stemmed white)
=> R + 2R/3 + 20 = 120
=>... |
AQUA-RAT | AQUA-RAT-39261 | Thus, it’s possible to make it into the second round with just $3$ wins.
With only $2$ wins, however, it’s impossible to get to the second round. The top three finishers cannot have more than $18$ wins altogether (either $7+6+5$ or $6+6+6$). That leaves $10$ wins amongst the remaining $5$ teams, so either each of the ... | [
"(a) $5,000",
"(b) $7,000",
"(c) $15,000",
"(d) $25,000"
] | C | The highest prize cannot possibly be less than 1/3rd of 24,000 (because in this case the sum of 3 prizes would be less than 24,000) and cannot be more than 24,000.
Answer: C. |
AQUA-RAT | AQUA-RAT-39262 | 36&14,9,9,9,9,10\\ 37&16,9,9,9,9,10\\ 38&16,9,9,9,9,12\\ 39&16,9,9,11,9,12\\ 40&16,9,9,11,11,12\\ 41&16,9,11,11,11,12\\ 42&16,11,11,11,11,12\\ 43&18,11,11,11,11,12\\ 44&18,11,11,11,11,14\\ 45&18,11,11,13,11,14\\ 46&18,11,11,13,13,14\\ 47&18,11,13,13,13,14\\ 48&18,13,13,13,13,14\\ 49&18,13,13,13,13,16\\ 50&18,13,13,15,1... | [
"385",
"429",
"671",
"264"
] | B | Solution
In each number except 429,the middle digit is the sum of the other two. Answer B |
AQUA-RAT | AQUA-RAT-39263 | # 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... | [
"2",
"4",
"6",
"8"
] | C | P ---- 2P ---- 8 years
6P ---- 24 years Answer: C |
AQUA-RAT | AQUA-RAT-39264 | 713, 731, 799, 841, 851, 899
Next come a pair of twins, a 99, then another pair of twins, then another 99! 713 and 731 are twins because they have the same digits, with the 1 and 3 reversed. 731 we have already seen: it is from the same 17-sequence as 527 and 629. 713 is $729 - 16 = 27^2 - 4^2 = (27-4)\cdot (27+4)$. 7... | [
"699990",
"99990",
"99980",
"69300"
] | D | Explanation:
Required Difference
= 70000 - 700 = 69300
Answer is D |
AQUA-RAT | AQUA-RAT-39265 | 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}$$ job/day... | [
" 520",
" 480",
" 392",
" 288"
] | D | total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =40% =400
Total male employees =48%=480
male employees working in research =400-208=192
male employees not working in research =480-192=288
Answer D |
AQUA-RAT | AQUA-RAT-39266 | $$12=2^2*3$$, so we should calculate how many 2-s and 3-s are in $$18!$$.
Calculating 2-s: $$\frac{18}{2}+\frac{18}{2^2}+\frac{18}{2^3}+\frac{18}{2^4}=9+4+2+1=16$$. So the power of $$2$$ (the highest power) in prime factorization of $$18!$$ is $$16$$.
Calculating 3-s: $$\frac{18}{3}+\frac{18}{3^2}=6+2=8$$. So the pow... | [
"2",
"3",
"4",
"5"
] | A | the number of 9s in 18!= 18/9=2..
ans A |
AQUA-RAT | AQUA-RAT-39267 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"13 km/hr",
"57.2 km/hr",
"17 km/hr",
"18 km/hr"
] | B | Speed of the train relative to man = (145/10) m/sec
= (14.5) m/sec. [(14.5) * (18/5)] km/hr
= 52.2 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 52.2 ==> x
= 57.2 km/hr.
Answer:B |
AQUA-RAT | AQUA-RAT-39268 | # Conceptual reason for why the volume of an ocahedron is four times the volume of a tetrahedron
The image below shows that a regular octahedron can be scaled by a factor of $$2$$ (resulting in a $$2^3$$ factor in volume) and decomposed as six octahedra and eight tetrahedra.
If $$V_o$$ and $$V_t$$ respectively repres... | [
"3.11545466",
"0.76678113",
"0.11785113",
"2.11785113"
] | C | The answer is sqr(2)/12 = 0.11785113
The following can be derived using the Pythagorean theorem:
The height of a face is 3.5/2.
The area of any face is 3.5/4.
The distance from any corner to the center of a joining face is 1/3.5.
The height of the tetrahedron is (2/3).5
The area is 1/3*base*height =
(1/3) * 3.5/4 * (2/... |
AQUA-RAT | AQUA-RAT-39269 | (A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres
let total qty be x liters
so milk 9x/100
9 liters is withdrawn so left with 9x/100- (9/100) * 9 which becomes equal to 6x/100
we have
9/100 * ( x-9) = 6x/100
3x-27 = 2x
x= 27 litres
OPTION B
Director
Joined: 25 Jul 2018
Posts: 731
A vessel is full o... | [
"10",
"20",
"21",
"25"
] | C | As A:B::7:5 ---> only option C is a multiple of 7 and hence it is a good place to start. Also A:B::7:5 means that , A = (712)*Total and B = (5/12)*Total
If A = 21 , B = 15 ---> remove 9 litres ---> you remove (7/12)*9 of A ---> A remaining = 21-(7/12)*9 = 63/4
Similarly, for B, you remove (5/12)*9 ---> B remaining = 15... |
AQUA-RAT | AQUA-RAT-39270 | Hint:
$$\frac{2\sqrt x-3x+x^2}{\sqrt x}=2-3\sqrt x+x^{3/2}$$
$\dfrac{-3x}{\sqrt{x}} = -3\sqrt{x}$, and $\dfrac{x^2}{\sqrt{x}} = x^{\frac{3}{2}}$
The following is multiple choice question (with options) to answer.
If x^2=x+2, then x^3=? | [
"3x+2",
"3x-2",
"2x+1",
"2x-3"
] | A | Given X^2 = X+2
X^3 = X*X^2 = x*(X+2)-- Substituted from above.
= X^2 + 2X = X+2+2X = 3X+2.
Hence A. |
AQUA-RAT | AQUA-RAT-39271 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"70%",
"80%",
"90%",
"100%"
] | A | Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage = (295/420) * 100
= 70%(approx)
Option A |
AQUA-RAT | AQUA-RAT-39272 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"56 hours",
"28 hours",
"35 hours",
"66 hours"
] | C | 1/A + 1/B + 1/C = 1/10 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/10
=> (1 + 2 + 4)/2B = 1/10
=> 2B/7 = 10
=> B = 35 hours.
Answer: C |
AQUA-RAT | AQUA-RAT-39273 | 10. A $$2$$-foot brick border is constructed around a square cement slab. If the total area, including the border, is $$121$$ square feet, then what are the dimensions of the slab?
11. The area of a picture frame including a $$2$$-inch wide border is $$99$$ square inches. If the width of the inner area is $$2$$ inches... | [
"16000",
"18000",
"20000",
"22000"
] | C | Explanation:
Number of bricks =Courtyard area /1 brick area
=(2500×1600 /20×10)=20000
Option C |
AQUA-RAT | AQUA-RAT-39274 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$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$$ (from the initial 90... | [
"3",
"5",
"9",
"4"
] | D | T = 40/36 * 18/5 = 4 sec
Answer:D |
AQUA-RAT | AQUA-RAT-39275 | First we choose two values, there are 13 values (2 to A), so $$13\choose2$$.
Then we want to choose two cards of the first value out of four cards, $$4\choose 2$$
Again, we want to choose two cards of the second value out of four cards, $$4\choose 2$$
And finally, choose one card not of the previously selected types... | [
" 71",
" 73",
" 76",
" 77"
] | D | Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x= 3p+2
x can take values 71 , 77
If the cards are counted 4 at a time , there is 1 left over
x= 4q+1
x can take values 73, 77
Therefore , x = 77
Answer D |
AQUA-RAT | AQUA-RAT-39276 | in n yrs and A 2 in (n+1) yrs, then Rate of compound interest =(A 2 - A 1)/A 1 *100% Sum = A 1 (A 1 /A 2) n. 596 APPENDIXC:COMPOUNDINTERESTTABLES 1/2% CompoundInterestFactors 1/2% SinglePayment UniformPaymentSeries ArithmeticGradient Compound Present Sinking Capital Compound Present Gradient Gradient Amount Worth Fund ... | [
"3388",
"3120",
"2177",
"1987"
] | B | Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B |
AQUA-RAT | AQUA-RAT-39277 | The next one up is $$2 \times 3\times 4=$$ 24. If you keep going, you should get this list:
$$1 \times 2 \times 3= 6$$
$$2 \times 3 \times 4= 24$$
$$3 \times 4 \times 5= 60$$
$$4 \times 5 \times 6= 120$$
$$5 \times 6 \times 7= 210$$
$$6 \times 7 \times 8= 336$$
$$7 \times 8 \times 9= 504$$
$$8 \times 9 \times 10= 720$... | [
"A)5",
"B)9",
"C)11",
"D)13"
] | C | Explanation:
x + y = 30
2x – 3y = 5
x = 19 y = 11
C) |
AQUA-RAT | AQUA-RAT-39278 | homework-and-exercises, kinematics
Title: Which approach can I use to find the total distance travelled by the car? I am really struggling with the following problem:
A car starts from rest with constant acceleration and moves in a
straight line. At some point the car passes two marked road sections
of length $L$... | [
" 250",
" 300",
" 800",
" 400"
] | C | Let D = total distance
Traci traveled 1/2 = D/2
i.e. remaining distance = D/2
She traveled 1/4 th of D/2 = D/8
Thus:
D = (D/2) + (D/8) + 200
D = 800
ANSWER: C |
AQUA-RAT | AQUA-RAT-39279 | 27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14... | [
"380",
"350",
"331",
"310"
] | C | Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9268)/28 = 331
Option C |
AQUA-RAT | AQUA-RAT-39280 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"50 min",
"60 min",
"90 min",
"80 min"
] | C | pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/180
x=90 min
ANSWER:C |
AQUA-RAT | AQUA-RAT-39281 | 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... | [
"267",
"766",
"810",
"868"
] | C | 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810
Answer:C |
AQUA-RAT | AQUA-RAT-39282 | 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... | [
"4",
"8",
"5",
"6"
] | D | Explanation:
(A+B) one day work =1/4
now A does half of the work in 3 days so A can complete the whole work in 6 days
A’s one day work =1/6
B’s one day work=1/4 - 1/6= 1/12
B alone can complete the work in 12 days so half of the work in 6 days
Answer: Option D |
AQUA-RAT | AQUA-RAT-39283 | 5%------------------20%
so ratio is 1:4 in final mixture
Earlier type 1 alcohol was 1
Now it is 1/5 ----> so loss of 4/5 = 80%...
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 56303
Re: Mixture problem-Can someone explain this [#permalink]
### Show Tags
02 Sep 2010, 08:52
11
14
zest4mba wrote:
I... | [
"1:2",
"3:7",
"3: 5",
"4:7"
] | A | Container 1 has 12 ounces in the ratio 1:2
or,
x+2x=12 gives x(alcohol)=4 and remaining water =8
container 2 has 9 ounces in the ratio 1:2
or,
x+2x=9 gives x(alcohol)=3 and remaining water =6
mixing both we have alcohol=4+3 and water =8+6
ratio thus alcohol/water =7/14=1/2
Answer A |
AQUA-RAT | AQUA-RAT-39284 | Alice speaks the truth with probability 3/4 and Bob speaks the truth with probability 2/3. A die is thrown and both Alice and Bob observe the number. Afterwards, Alice asserts to Carl (who does not know the number) that the number is 3 while Bob says (to Carl) the number is 1. Find the probability that the number is ac... | [
"1/4",
"2/3",
"3/5",
"2/5"
] | D | D) 2/5 |
AQUA-RAT | AQUA-RAT-39285 | of numbers in a data set from its mean value and can be represented using the sigma symbol (σ). deviation, standard error, sample variance). Next, add all the squared numbers together, and divide the sum by n minus 1, where n equals how many numbers are in your data set. The formula you'll type into the empty cell is =... | [
"12.0",
"13.5",
"17.0",
"23.5"
] | B | Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 21-7.5=13.5or more than 21+7.5=28.5.
Answer: B. |
AQUA-RAT | AQUA-RAT-39286 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"3 9/19 hrs",
"3 9/77 hrs",
"3 9/17 hrs",
"3 9/57 hrs"
] | C | Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.Answer: C |
AQUA-RAT | AQUA-RAT-39287 | # Find the remainder of $3^{333}$ divided by $100$
Find the remainder of $$3^{333}$$ divided by $$100$$
So I can find that $$100=2^2\cdot 5^2$$
Then I want to find $$3^{333}$$ mod $$4$$ and mod $$25$$ and use chinese remainder theorem to find a solution mod $$100$$.
I can find that $$3^{333}\equiv (-1)$$ mod $$4$$
... | [
"3",
"27",
"30",
"21"
] | A | take the remainder from each of 1024/33, 1047/33 and so on..
1024/33 gives remainder = 1
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e =1*24*27*30
break them into pairs 1*24/33 gives remainder 24
and 27*30/33 g... |
AQUA-RAT | AQUA-RAT-39288 | # Prove that the set of positive rational values that are less than $\sqrt{2}$ has no maximum value
Its been a while since I've written a proof and would appreciate some feedback on this one.
Question: Given the set of rational positive values, $\{q | q \in \mathbb{Q} \wedge 0 \lt q \lt \sqrt{2}\}$, show that there i... | [
"15",
"16",
"17",
"18"
] | D | A two-digit integer "ab" can be expressed algebraically as 10a+b.
Q-R=(10a+b)-(10b+a)=9(a-b)<20.
The greatest multiple of 9 which is less than 20 is 18.
The answer is D. |
AQUA-RAT | AQUA-RAT-39289 | Remark. The lemma shows that the least common multiple is not just "least" in terms of size. It's also "least" in the sense that it divides every other common multiple.
Theorem. Let m and n be positive integers. Then
Proof. I'll prove that each side is greater than or equal to the other side.
Note that and are integ... | [
"xy",
"x",
"y",
"xy - y"
] | D | The least common multiple of two positive integers cannot be less than either of them. Therefore, since xy - y is less than x, it cannot be the LCM of a x and y.
Answer: D |
AQUA-RAT | AQUA-RAT-39290 | the subarray [5,2], leaving us with [6,3] with sum 9. The sum of the digits in 21 is 3. As 59 is not wholly divisible by 3 the question is invalid. I'm trying to investigate this statement: The sum of n consecutive numbers is always divisible by n. Example 2 List all the factors of 32. The difference of the sum of odd ... | [
"x/16",
"x/36",
"x/25",
"x/46"
] | B | Prime factorization of 9 = 3^2
Prime factorization of 36= 3^2*2^2
LCM of 9 and 36 = 3^2 * 2^2 = 36
Therefore x/36 must be an integer
Answer B |
AQUA-RAT | AQUA-RAT-39291 | what I want to do is express the stuff in the parentheses as a sum of a perfect square and then some number over here. And I have x squared minus 4x. If I wanted this to be a perfect square, it would be a perfect square if I had a positive 4 over here. If I had a positive 4 over there, then this would be a perfect squa... | [
"0.02",
"0.2",
"0.04",
"0.4"
] | C | Given expression = (11.98)^2 + (0.02)^2 + 11.98 * x.
For the given expression to be a perfect square, we must have
11.98 * x = 2 * 11.98 * 0.02 or x = 0.04
Answer = C |
AQUA-RAT | AQUA-RAT-39292 | • #### 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... | [
"8",
"2",
"7",
"5"
] | D | Perimeter of rectangular yard = 2(l + b) = 18 --> l + b = 9
Area = l * b = 20
b = 9 - l
l(9 - l) = 20
29l - l^2 = 20
l^2 - 9l + 20 = 0
Upon simplifying we get l = 5 or 4. Only 5 is there in the answer choice.
Answer: D |
AQUA-RAT | AQUA-RAT-39293 | 7. wayki says:
Here you said there is a 2.9 thousandths of an inch curvature for each 100 feet of horizontal distance.....(heheh).
I hate imperial so please allow me to convert it to metric.
0.07366 mm = 30.480m
Multiply all of this up by 1000 =
73mm fall for every 30,000km. Are you mad? One would have nearly gone... | [
"5.2",
"7.4",
"13.7",
"21.2"
] | C | 28 miles represented by 1 inch
1 mile represented by (1/28) inch
383.6 miles represented by (1/28) * 383.6
approximately = 14
We should use estimation here as the answer options are not close .(28*10 =280 and 28*20 = 560 , hence we select the only option between 10 and 20 )
Answer C |
AQUA-RAT | AQUA-RAT-39294 | ## 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 -3 < x < 7 and -6 < y < 3, whi... | [
"-42 < xy < 21",
"-42 < xy < 18",
"-28 < xy < 18",
"-24 < xy < 21"
] | B | The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-3)*(-6)=18.
Therefore -42 < xy < 18.
Answer: B. |
AQUA-RAT | AQUA-RAT-39295 | I have to design a laboratory activity to answer the question, "What is the relationship between the diameter of a circle and the area of the circle?" My teacher said to use a previous activity as a templete to help me. For the
6. ### Math
Two perpendicular diamters(cutting each other at right angles) of a circle cut ... | [
"76",
"55",
"88",
"21"
] | C | the area of circle =pie* r^2 = 616 => r = 14
2 * 22/7 * 14 = 88
ANSWER:C |
AQUA-RAT | AQUA-RAT-39296 | (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 ... | [
" 4",
" 9",
" 12",
" 20"
] | B | let the no. of 5 liter bottles be x, so the no. of 20l bottles will be x/4 (to equate the vol.) since the total cost will be equal , 5x= 40+2*x/4 so x= 8.88 or 9. Answer is (B). |
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