source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38897 | & \frac 12 x & + 5 \\ \hline \end{array}$$ The ask what you have to multiply $4x^2$ by to get $4x^2$, then multiply, then subtract.....
The following is multiple choice question (with options) to answer.
Evaluate: 50 - 12÷4×2 = | [
"44",
"54",
"16",
"27"
] | A | According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right
12÷4×2 = 3 × 2 = 6
Hence
50 - 12÷4×2 = 50 - 6 = 44
correct answer A)44 |
AQUA-RAT | AQUA-RAT-38898 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"$2000",
"$2500",
"$2400",
"$3120"
] | C | 115% of cost - 110% of cost = $120
5% of cost = $120
cost = 120*100/5 = $2400
Answer is C |
AQUA-RAT | AQUA-RAT-38899 | # Permutations of the word $\text{TRIANGLE}$ with no vowels together.
First of all, $$\text{TRIANGLE}$$ has $$8$$ distinct letters, $$3$$ of which are vowels($$\text{I, A, E}$$) and rest are consonants($$\text{T, R, N, G, L}$$).
While attempting this, I came up with the idea of putting alternate vowels and consonants... | [
"6!/2!",
"3!*3!",
"4!/2!",
"4! *(3!/2!)"
] | D | In the word ABROAD , there are 3 vowels - 2 A's and O
Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide b... |
AQUA-RAT | AQUA-RAT-38900 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"15000",
"15002",
"15029",
"15329"
] | A | Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A |
AQUA-RAT | AQUA-RAT-38901 | ## anonymous one year ago Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small tank is initially full of water, and the water drains out a... | [
"50hrs",
"30hrs",
"70hrs",
"80hrs"
] | B | time taken to full the cistern=(1/10-1/15)hrs
=1/30
=30hrs
ANSWER:B |
AQUA-RAT | AQUA-RAT-38902 | Let one woman complete the job in $$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... | [
"25 days",
"24 days",
"22 days",
"27 days"
] | B | B
24 days
B = 1/8 – 1/2 = 1/24 => 24 days |
AQUA-RAT | AQUA-RAT-38903 | ### 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. 1200",
"Rs. 1300",
"Rs. 1500",
"Rs. 4000"
] | D | Explanation :
Interest on Rs.8000 at 5% per annum = ( 8000 × 5 × 1) / 100 = Rs. 400
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (8000 + x) × 6 × 1/100.
=> 400 + 2x/25 = (8000 + x) × 6 × 1/100.
=> 40000 + 8x = (800... |
AQUA-RAT | AQUA-RAT-38904 | EZ as pi
Featured 5 months ago
$\text{males : females } = 6 : 5$
#### Explanation:
When working with averages (means), remember that we can add sums and numbers, but we cannot add averages.
(An exception would be if there were the same number of males and females - in this case we may add the averages and divide by... | [
" 0.05",
" 0.0625",
" 0.2",
" 0.25"
] | C | Index for females = (20-8)/20 = 3/5 = 0.6
Index for males = (20-12/20 = 2/5 = 0.4
Index for females exceeds males by 0.6 - 0.4 = 0.2
Answer: C |
AQUA-RAT | AQUA-RAT-38905 | # Question on arithmetic (Percentages)
A machine depreciates in value each year at the rate of 10% of its previous value. However every second year there is some maintenance work so that in that particular year, depreciation is only 5% of its previous value. If at the end of fourth year, the value of the machine stand... | [
"Rs.2038",
"Rs.2073",
"Rs.2000",
"Rs.2027"
] | C | Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 2288
for 114.4 ---> 100 ; 2288 ... |
AQUA-RAT | AQUA-RAT-38906 | algorithms
Title: How many times can you pour milk among 3 buckets? This is a problem from usaco, which I solved, but I don't know how to estimate the number of times you can pour milk among the jugs, my solutions just uses a big enough number.
Here's the problem statement:
Farmer John has three milking buckets of ca... | [
"128",
"132.",
"146.",
"154."
] | A | Let the foam generators capacity be -
A = 10 lit/hr
B = 10 lit/hr
C = 18 lit/hr
Total foam generation in 1 hour will be 38 lit ( 10 + 10 + 18 ) ; since in 1 and 1/2 hr they will generate 38 + 19 => 57 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 10 lit/hr
C = 18 lit... |
AQUA-RAT | AQUA-RAT-38907 | # 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... | [
"80%",
"105%",
"120%",
"112%"
] | D | 0,112R = x/100*0.1R
Answer D |
AQUA-RAT | AQUA-RAT-38908 | (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.
30 percent of Andrea's living room floor is covered by a carpet that is 4 feet by 9 feet. What is the area of her living room floor? | [
"14.4",
"120",
"50.4",
"60"
] | B | 30% of Area of the floor = 4*9 square feet = 36 square feet
i.e. 100% Area of Floor = (36/30)*100 = 120 square feet
Answer: Option B |
AQUA-RAT | AQUA-RAT-38909 | # 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... | [
"10",
"20",
"40",
"60"
] | A | Method 1:
Take the first amateur. He plays a game with each of the other four i.e. 4 games.
Now take the second one. He has already played a game with the first one. He plays 3 games with the rest of the 3 amateurs i.e. 3 more games are played.
Now take the third amateur. He has already played a game each with the firs... |
AQUA-RAT | AQUA-RAT-38910 | # If $28a + 30b + 31c = 365$, then what is the value of $a +b +c$?
Question: For 3 non negative integers $a, b, c$; if $28a + 30b + 31c = 365$ what is the value of $a +b +c$ ?
How I approached it : I started immediately breaking it onto this form on seeing it :
$28(a +b +c) +2b +3c = 365 .......(1)$ $30(a +b +c) -2a... | [
"14",
"8",
"6",
"9"
] | A | have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*6 + 31*7..
hence values of a,b and c are 1, 6 and 7 respectively..
a+b+c=14
ANSWER:A |
AQUA-RAT | AQUA-RAT-38911 | ## 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... | [
"88hours",
"38hours",
"78hours",
"28hours"
] | D | 2/7 - 1/x
= 1/4
x = 28
Answer:D |
AQUA-RAT | AQUA-RAT-38912 | $$3 = (321)(-18+41k) + (123)(47-107k) \text{ for any } k$$
so for instance we also get ($k=1$):
$$3 = (321)(23) + (123)(-60)$$
-
The following is multiple choice question (with options) to answer.
What is the place value of 3 in the numeral 53468? | [
"3000",
"30",
"3",
"330"
] | A | place value of 3 = 3 * 1000 = 3000
Answer is A |
AQUA-RAT | AQUA-RAT-38913 | # Given an Alphabet, how many words can you make with these restrictions.
I'm trying to understand from a combinatoric point of view why a particular answer is wrong. I'm given the alphabet $\Sigma = \{ 0,1,2 \}$ and the set of 8 letter words made from that alphabet, $\Sigma_8$ . There are $3^8 =6561$ such 8 letter wo... | [
"2!",
"3!",
"4!",
"5!"
] | C | There are 6 letter blocks to be arranged. Note that the letter P occurs twice. 2 'P' blocks can be arranged only in one way, since the two blocks are exactly the same(PP is same as PP). So we can consider PP as one letter and proceed to find the arrangement of 4 letters, A, PP, L, E. These four blocks can be arranged i... |
AQUA-RAT | AQUA-RAT-38914 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"6",
"8",
"10",
"12"
] | D | Let the weight of the package be X.
2X + 6= 30
X = 12
The answer is D. |
AQUA-RAT | AQUA-RAT-38915 | Q 4.Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:
If same pair of coins is tossed at random, find the probability of getting:
SOLUTION:
Number of trials = 500
Number of outcomes of two heads (HH) = 105
Number of outcomes of one head (HT or TH) = 275
Number of outcomes of... | [
"3/8",
"6/11",
"2/5",
"4/5"
] | A | Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer : A |
AQUA-RAT | AQUA-RAT-38916 | Hint: You may suppose, w.l.o.g. that $$|x-2|<\frac12$$, in which case $$|x-1|>\frac12$$, so that $$\left|\frac{x-2}{x - 1}\right| <2|x-2|.$$
$$\delta<\min(1,\varepsilon)/2$$ should do the job.
The following is multiple choice question (with options) to answer.
If 0.75: x :: 5:9, then x is equal to: | [
"1.12",
"1.16",
"1.2",
"1.35"
] | D | Explanation:
(x * 5) = (0.75 *9)
X=6.75/5 = 1.35
Answer: D |
AQUA-RAT | AQUA-RAT-38917 | only effective. Share, and after five years it earned you$ 15 in income 2 years or decreases ) in! A certain period of time that an investment over time as a percentage of investment. Zijn bidirectioneel, wat wil zeggen dat je woorden gelijktijdig in beide talen kan.! Are returned to you not reinvest would have $40 per... | [
"Rs. 5640",
"Rs. 5760",
"Rs. 7500",
"Rs. 8600"
] | B | To earn Rs. 50/3 , investment = Rs. 64.
To earn Rs. 1500, investment = Rs.64 x 3/50x 1500 = Rs. 5760.
ANSWER :B |
AQUA-RAT | AQUA-RAT-38918 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"15%",
"25%",
"38.9%",
"45%"
] | C | Explanation:
720 --- 280
100 --- ? => 38.9%
Answer: C |
AQUA-RAT | AQUA-RAT-38919 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"240",
"288",
"665",
"199"
] | A | S = 600/40 = 15 mps
S = 3600/15 = 240 sec
= 4 min
Answer: A |
AQUA-RAT | AQUA-RAT-38920 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"123",
"480",
"266",
"1251"
] | B | SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480Answer: B |
AQUA-RAT | AQUA-RAT-38921 | # 3 balls are drawn from a bag contains 6 white balls and 4 red balls, what is the probability that 2 balls are white and 1 ball is red?
A bag contains 6 white balls and 4 red balls. If 3 balls are drawn one by one with replacement, then what is the probability that 2 balls are white and 1 ball is red?
$$\frac{18}{12... | [
"64",
"128",
"132",
"222"
] | A | Explanation:
From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that
at least one black ball should be there.
Hence we have 3 choices
All three are black
Two are black and one is non black
One is black and two are non black
Total number of ways
= 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because ... |
AQUA-RAT | AQUA-RAT-38922 | I am pretty sure that I am wrong.
Could someone help me?
Thanks
The answer is ${6 \over 25 \pi}$ ft /min according to the answer sheet
You can't take $r=12$ in $$v={1 \over 3} \pi r^2 h\\ {dv \over dm} = {2 \over 3} \pi (12){dh \over dm}$$ because the radius of the water is changing as it drains. What you can do, h... | [
"67",
"58",
"54",
"46"
] | C | let T be the total capacity of the reservoir.
Now we can equate before cases i.e 79/100(T) = 118.
Lets take approximate values for easy calculation 80/100(T) = 120 => T = 150 MG.
We need to subtract total - after drought case = 150 - 96 = 54 MG..
Option C is correct answer... |
AQUA-RAT | AQUA-RAT-38923 | c#, strings, converting
// assert
inchDimension.Millimeters.Should().Be(architecturalDimension.Millimeters);
copiedDimension.ShouldBeEquivalentTo(architecturalDimension);
}
/// <summary>
/// Tests mathmatical operators we will test the properties at the same time.
/// </summary>
[T... | [
"986000",
"968000",
"978000",
"987000"
] | A | 986 x 137 + 986 x 863 = 986 x (137 + 863) = 986 x 1000 = 986000.
Answer is A. |
AQUA-RAT | AQUA-RAT-38924 | # an exam has 50 multiple choice questions with 5 options
An exam has 50 multiple choice questions. Each question has five answer options and each question has 2 grades A-. Assuming that "a student" has no prior knowledge and randomly guess on all questions exam,
1. Compute the expected mean for the student score
2. ... | [
"20",
"31",
"45",
"90"
] | A | 1SD from the mean ranges from 35 to 65, where 65 is within SD above the mean and 35 within 1SD below the mean
2SD=15 TWICE=30 from the the mean, which is 80 to 20, where 80 is within 2 SD above the mean AND 20 is within 2 SD below the mean.
Answer = A |
AQUA-RAT | AQUA-RAT-38925 | 12n + 7 7, 19, 31, 43, 67, 79, 103, 127, 139, 151, ... A068229
12n + 11 11, 23, 47, 59, 71, 83, 107, 131, 167, 179, ... A068231
The following is multiple choice question (with options) to answer.
256, 225, 196, 169, 144, ? | [
"49",
"64",
"81",
"121"
] | D | Explanation :
The pattern is 16^2, 15^2, 14^2, 13^2, 12^2, ...
So next number is 11^2 = 121
Answer : Option D |
AQUA-RAT | AQUA-RAT-38926 | Case 1 : A pair of socks are present, hence exactly 2 draws for the socks to match. Case 2 : 2 pair of socks are present in the drawer. How?
To start with, instead of looking for a matching pair, let's find the probability that both socks are red.
The Sock Drawer: Probability and Statistics Problem A drawer contains ... | [
"100",
"80",
"60",
"50"
] | A | I'll prefer to solve this with plug n play method.
As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks Z has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.
100 fits perfectly after relevant calculations. Hence answer A. |
AQUA-RAT | AQUA-RAT-38927 | This one is different: there are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.
What is the probability of choosing ANY sibling from junior class? 60/1000 (as there are 60 of them).
What i... | [
"1/40000",
"1/3600",
"9/2000",
"1/60"
] | A | Let's see
Pick 60/3000 first
Then we can only pick 1 other pair from the 800
So total will be 60 / 800 *3000
Simplify and you get 1/40000
Answer is A |
AQUA-RAT | AQUA-RAT-38928 | P = principal = $50,000 here. r = rate of interest = 0.055 here. n = number of years In compounded annually, A = P(1+r)^n After year 1, A = P(1+r) Atfer withdrawal of X, A = P(1+r) -X After year 2, A = [P(1+r) -X](1+r) = P(1+r)^2 -X(1+r) After withdrawal of X, A = P(1+r)^2 -X(1+r) -X After year 3, A = [P(1+r)^2 -X(1+r)... | [
"Rs.4000",
"Rs.5000",
"Rs.4500",
"Rs.4800"
] | A | CI=4410,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
4410=P[21/20]^2
4410[20/21]^2
4000
ANSWER:A |
AQUA-RAT | AQUA-RAT-38929 | 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... | [
"1/3",
"2/3",
"2/5",
"3/5"
] | B | Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x =... |
AQUA-RAT | AQUA-RAT-38930 | # 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... | [
"3:16.",
"2:3.",
"5:3.",
"3:4."
] | C | 1st statement : ratio of pants
Store A : Store B
50x : 40x
5X:4X
Price :
4y:3y
Total revenue
20xy : 12xy
5:3
Answer is C |
AQUA-RAT | AQUA-RAT-38931 | to calculate area, perimeter or volume of a figure. Find the area of the face we are looking directly at. A (rectangular) cuboid is a closed box which comprises of 3 pairs of rectangular faces that are parallel to each other and joined at right angles. The Surface Area of a cuboid is the total of all the areas on each ... | [
"1350",
"1750",
"1150",
"1450"
] | A | Surface area = 6 a(power)2 sq. units
6 a(power)2 = 6 × 225 = 1350 m(power)2
Answer is A. |
AQUA-RAT | AQUA-RAT-38932 | 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",
"10 sec",
"12 sec",
"14 sec"
] | C | Explanation:
Speed of the train relative to man = (59 + 7) kmph
= 66 ×5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man = Time taken by it to cover 220 m
at (55/3) m / sec = (220 ×3/55) sec = 12 sec
Answer: Option C |
AQUA-RAT | AQUA-RAT-38933 | 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... | [
"175kmph",
"150kmph",
"162kmph",
"145kmph"
] | A | Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
500/[(x+5)*5/18] = 10
10(x+5) = 1800
x = 175kmph
Answer is A |
AQUA-RAT | AQUA-RAT-38934 | It would help of you reported some descriptive statistics or a histogram of your age and height data, such as mean, variance, skewness, kurtosis.
• Thank you for your help, can you tell me how to know that the certain data comes from normal distribution for example in your answer stated that age can not be from normal... | [
"8",
"16",
"17",
"18"
] | C | Minimum age = Average - 1 Standard deviation = 20 - 8 = 12
Maximum age = average + 1 Standard deviation = 20+ 8 = 28
Maximum number of different ages of the applicants = 28 - 12 + 1 = 17
Answer C |
AQUA-RAT | AQUA-RAT-38935 | Since he did not score 45, he lost an average of 4.5 upon the total number of innings, which includes the latest innings as well.
So 45 runs upon x innings will give an average of 4.5
Hence 45/x = 4.5 i.e. x = 10. (Remember, x includes the latest inning as well)
Problem 6:
The average of 8 scores is 87. Of these, t... | [
"39",
"35",
"42",
"40.5"
] | A | let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+87
then average run after 17th inning=(16x+87)/17
(16x+87)/17=x+3;
x=36;
average after 17th inning =36+3=39
ANSWER:A |
AQUA-RAT | AQUA-RAT-38936 | 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, ... | [
"28",
"32",
"36",
"40"
] | D | The average of the numbers in set S is 12.
If we increase the mean by 25%, the new mean is 15.
Thus, on average, 5 numbers increase by 5.
Therefore n = 15+25 = 40
The answer is D. |
AQUA-RAT | AQUA-RAT-38937 | In total, there are $$6! = 720$$ ways for all the people to sit on the chairs.
1. First there are $$6$$ ways for you to take a seat, $$2$$ ways for your friend to sit next to you. Now with $$4$$ people left with $$4$$ chairs, there are $$4!=24$$ ways for them to sit. So the probability would be $$\frac {24 \times 2 \t... | [
"360",
"500",
"420",
"720"
] | D | number of ways =6! = 720
Answer is D |
AQUA-RAT | AQUA-RAT-38938 | to calculate area, perimeter or volume of a figure. Find the area of the face we are looking directly at. A (rectangular) cuboid is a closed box which comprises of 3 pairs of rectangular faces that are parallel to each other and joined at right angles. The Surface Area of a cuboid is the total of all the areas on each ... | [
"228",
"148",
"992",
"772"
] | B | 2(4*5 + 5*6 + 4*6) = 148
Answer: B |
AQUA-RAT | AQUA-RAT-38939 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"89",
"90",
"92",
"99"
] | D | The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (wh... |
AQUA-RAT | AQUA-RAT-38940 | # Another probability question from my textbook
Suppose that we have a tennis tournament with 32 players. Players are matched in a completely random fashion, and we assume that each player always has probability 1/2 to win a match. What is the probability that two given players meet each other during the tournament.
... | [
"90 matches",
"95 matches",
"99 matches",
"85 matches"
] | D | D 85 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 85 matches were played. |
AQUA-RAT | AQUA-RAT-38941 | # 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... | [
"14",
"16",
"18",
"20"
] | D | The speed of the boat downstream = 15 + 3 = 18 km/hr
18 km/hr * 5/18 = 5 m/s
The time taken to cover 100 meters = 100/5 = 20 seconds.
The answer is D. |
AQUA-RAT | AQUA-RAT-38942 | Problem #2: A box contains 18 tennis balls, 8 new 10 old. 3 balls are picked randomly and played with (so if any of them were new, they become 'old'), and returned to the box. If we pick 3 balls for the second time (after this condition), what is P that they are all new? I broke this down into 4 pieces: P(3 new second ... | [
"7",
"8",
"9",
"10"
] | A | Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(18-x)+x+2=30
37-2x+x=30
37-x=30
x=7
So 7 members play both badminton and tennis.
A |
AQUA-RAT | AQUA-RAT-38943 | Since this is a quadratic equation, and the leading coefficient is $+1$, we have
$$\Delta < 0$$
Whence the equation is always strictly positive (that is, it's always $>0$).
• I think it's worth to note that we need the leading coefficient to be positive too, even if it's trivial. Jun 28 '18 at 7:56
• @Botond You're ... | [
"0 and 0.5",
"0.5 and 1",
"1 and 1.5",
"1.5 and 2"
] | B | Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4... |
AQUA-RAT | AQUA-RAT-38944 | For $N = 5$, $2A$ looks like:
$$\begin{array}{ccccc} &0 &1 &0 &0 &1 \\ &1 &0 &1 &0 &0 \\ &0 &1 &0 &1 &0 \\ &0 &0 &1 &0 &1 \\ &1 &0 &0 &1 &0 \end{array}$$
Solving this equation system for $\mathbf{x}$ with $N = 10$ and $\mathbf{b} = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]$ gives
$x_6 = 1$.
6. For her to announce an average ... | [
"6",
"8",
"9",
"5"
] | A | Average = 2(1 + 2 + 3 + 4 + 5)/5
= 30/5
= 6.
Answer:A |
AQUA-RAT | AQUA-RAT-38945 | Math Help - N positive integer problem with a + exponent
1. N positive integer problem with a + exponent
Here it is a problem that is driving me nuts...
Note: ^ means the exponent, in this case the exponent is "+".
If n is a positive integer, then n^+ denotes a number such that n < n^+ < n+1.
So decide which of the ... | [
"11",
"44",
"24",
"25"
] | D | the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44
0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.
Only option A-11 satisfies this
for remainder 11,
A=236 and B=25
Ans - D |
AQUA-RAT | AQUA-RAT-38946 | ### 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... | [
"2400",
"1600",
"2980",
"2707"
] | B | First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 3600 = 1600
Answer:B |
AQUA-RAT | AQUA-RAT-38947 | There are 3 crates of apples A, B and C. The ratio of the number of apples in crate A to crate B to crate C is 8 : 5 : 3. David removed 42 apples from crate A and placed them into crate C. as such, there are 2 more apples in crate C than crate B. How many apples are there altogether?
2. HINT: 3k + 42 = 5k + 2
4. Orig... | [
"5",
"10",
"15",
"20"
] | D | Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20
Answer: D |
AQUA-RAT | AQUA-RAT-38948 | However, this includes the solution when $$x_1,x_2,x_3,x_4,x_5=0$$, which is explicitly stated in the problem to be excluded. Hence our final answer is $$\boxed{6187}$$.
Questions like this are often worded ambiguously, forcing you to figure out a sensible interpretation. In this case, you aren't told whether differen... | [
"8",
"7",
"6",
"5"
] | D | Back-solving is the best way to solve this problem.
You basically need 12 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - D |
AQUA-RAT | AQUA-RAT-38949 | 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 ... | [
"Rs.140",
"Rs.120",
"Rs.130",
"Rs.110"
] | B | When compounded annually, interest
= 12000[1 + 20/100]1 - 12000 = Rs.2400
When compounded semi-annually, interest
= 12000[1 + 10/100]2 - 12000 = Rs.2520
Required difference = 2520 - 2400 = Rs.120
ANSWER:B |
AQUA-RAT | AQUA-RAT-38950 | 5,224 views
In a certain town, the probability that it will rain in the afternoon is known to be $0.6$. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to $25°C$, the probability that it will rain in the afternoon is $0.4$. The temperature at noon is equally likely to be a... | [
"8/125",
"2/25",
"5/16",
"8/25"
] | C | 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
E= 5/16
Answer - C |
AQUA-RAT | AQUA-RAT-38951 | meters (m), centimeters (cm) & millimeters (mm). This packet covers all you need to know about sectors of a circle. The curved part of the sector is of the circumference of the circle but to find the perimeter of the sector we must add (the radius of the circle is) so the perimeter of the sector is. A worksheet where y... | [
"100 cm",
"85 cm",
"75 cm",
"95 cm"
] | A | Perimeter of the sector = length of the arc + 2(radius)
= (90/360 * 2 * 22/7 * 21) + 2(28)
= 44 + 56 = 100 cm
Answer: A |
AQUA-RAT | AQUA-RAT-38952 | $$\frac{(12)(9)}{2}$$ = 54
Answer A
_________________
In the depths of winter, I finally learned
that within me there lay an invincible summer.
-- Albert Camus, "Return to Tipasa"
CEO
Joined: 12 Sep 2015
Posts: 2561
Location: Canada
Re: A polygon has 12 edges. How many different diagonals does it have? [#permalink]... | [
"25",
"27",
"40",
"56"
] | B | Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 9
No. of diagonals = 9(9 - 3)/2
= 27
Ans B |
AQUA-RAT | AQUA-RAT-38953 | 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.
. .... | [
"112",
"64",
"96",
"80"
] | D | Explanation:
Increase in ratio for 3 classes is 6 - 3 = 8 - 5 = 11 - 8 = 3.
Given, 15 more students are admitted to each class.
Therefore, 3 :: 15 ⇒ 1 :: 5
Therefore, 3 + 5 + 8 = 16 :: 16 x 5 = 80.
Hence, total students in the beginning were 80.
Correct Option: D |
AQUA-RAT | AQUA-RAT-38954 | electric-circuits, voltage
Title: Unsatisfactory explanation for the EMF measurement of a battery Experimentally, I have seen how hooking up a battery to a simple circuit just with a high-resistance voltmeter raises the voltage reading (allegedly to a level equal to the EMF of the battery).
However, I find the explan... | [
"22",
"266",
"27",
"26"
] | C | Explanation:
Answer: Option C |
AQUA-RAT | AQUA-RAT-38955 | # Difference between revisions of "2017 AMC 10A Problems/Problem 25"
## Problem
How many integers between $100$ and $999$, inclusive, have the property that some permutation of its digits is a multiple of $11$ between $100$ and $999?$ For example, both $121$ and $211$ have this property.
$\mathrm{\textbf{(A)} \ }226... | [
" 90",
" 82",
" 80",
" 45"
] | A | Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way)... |
AQUA-RAT | AQUA-RAT-38956 | 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.... | [
"126",
"120",
"119",
"126"
] | A | A 126
add 6, 12,18,24,..... |
AQUA-RAT | AQUA-RAT-38957 | Assuming the girls have sat down, they leave 3 gaps between them. 1 for each boy. Thus the first boy can pick between 3 chairs, the second boy 2 chairs, and the third doesn't get to pick. So there are $3\cdot 2=3!=6$ ways the boys can sit. Now the girls are a little bit more tricky. Notice that it isn't specified how t... | [
"120",
"360",
"420",
"720"
] | D | Number of arrangements possible = (7-1)!
= 6!
= 6*5*4*3*2*1
=720
Ans -D |
AQUA-RAT | AQUA-RAT-38958 | ### 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... | [
"4991",
"4992",
"2777",
"2977"
] | A | Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer: A |
AQUA-RAT | AQUA-RAT-38959 | only effective. Share, and after five years it earned you$ 15 in income 2 years or decreases ) in! A certain period of time that an investment over time as a percentage of investment. Zijn bidirectioneel, wat wil zeggen dat je woorden gelijktijdig in beide talen kan.! Are returned to you not reinvest would have $40 per... | [
"3:2",
"9:2",
"18:20",
"1:2"
] | D | A: B = 10000 : 20000 = 1 : 2
ANSWER:D |
AQUA-RAT | AQUA-RAT-38960 | # Making Friends around a Circular Table
I have $n$ people seated around a circular table, initially in arbitrary order. At each step, I choose two people and switch their seats. What is the minimum number of steps required such that every person has sat either to the right or to the left of everyone else?
To be spec... | [
"30",
"20",
"15",
"10"
] | B | if total seats N = 5 in a circular arrangement ( _ _ M _ _ M ) where first ( _ ) is connected with last Man(M), then min no of persons required= 2.
similarly If N = 9, Man required = 3 i.e,( _ _ M _ _ M _ _ M )
If N= 12, Man required = 4 i.e, ( _ _ M _ _ M _ _ M _ _ M)
have u got any relation??
the no of man required i... |
AQUA-RAT | AQUA-RAT-38961 | 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... | [
"10",
"40",
"30",
"20"
] | B | Suppose a worker remained ideal for x days then he worked for 60-x days
20*(60-x)-3x=280
1200-23x=280
23x=920
x=40
Answer is B. |
AQUA-RAT | AQUA-RAT-38962 | # Math Help - Finding the values of a and b
1. ## Finding the values of a and b
Hello everyone. This question is apparently unsolvable:
If $x = 3$ or $-4$ are the solutions of the equation $x^2+ax+b=0$, find the values of $a$ and $b$.
The keyword in this irksome question would be the word 'or'. So it denotes that t... | [
"2",
"4",
"6",
"8"
] | A | Factor the left side of the equation:
t2 – 6t + 8 = 0
(t – 2)(t – 4) = 0
Split this equation into two equations and solve:
t – 2 = 0 t – 4 = 0
t = 2 t = 4
Thus, a = 4 and b = 2. So a – b = 4 – 2 = 2.
correct answer A)2 |
AQUA-RAT | AQUA-RAT-38963 | 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}$$ job/day... | [
"15.5 days",
"19.5 days",
"17.5 days",
"9.2 days"
] | D | C = 1/5 – 1/11 = 6/55 => 9.2 days
ANSWER:D |
AQUA-RAT | AQUA-RAT-38964 | 3. How many numbers that are not divisible by 6 divide evenly into 264,600?
(A) 9
(B) 36
(C) 51
(D) 63
(E) 72
4.A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60,... | [
"Rs. 15",
"Rs. 12.10",
"Rs. 19.70",
"Rs. 16.80"
] | C | Explanation :
Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25 − (30/100) − x)(6/100) = 30/100
⇒ 6(25 − 0.3 − x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 ... |
AQUA-RAT | AQUA-RAT-38965 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"384",
"826",
"240",
"269"
] | C | Average mark scored by all the three boys =
[64/100 (500) + 36/100 (500) + 44/100 (500)] / 3
= 240
Answer: C |
AQUA-RAT | AQUA-RAT-38966 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"30",
"36",
"42",
"48"
] | C | The cost of Annie's ride was 2.5+5+(0.25*22) = $13
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 13
0.25*x = 10.5
x = 42 miles
The answer is C. |
AQUA-RAT | AQUA-RAT-38967 | ## Dinner Party Seating
A host invites $$n$$ guests to a party (guest #1, guest #2, … , guest #n). Each guest brings with them their best friend. At the party there is a large circular table with \2n\) seats. All of the $$n$$ invited guests and their best friends sit in a random seat.
1. What is the probability that ... | [
"1.35",
"2.None of these",
"3.12",
"4.126"
] | B | 9 managers, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two managers in it. That would mean selecting 5, from the remaining 7 which is 7C5 = 21
2. Meeting with one of the two managers. select 1 manager from two, and then select 4 from the remaining 7, whi... |
AQUA-RAT | AQUA-RAT-38968 | # 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... | [
"50 years",
"25 years",
"62 years 6 months",
"37 years 6 months"
] | C | Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $600.
Therefore, the Simple Interest earned = 600 - 100 = $500.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 500 = (100 * ... |
AQUA-RAT | AQUA-RAT-38969 | # 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... | [
"113000",
"114000",
"115000",
"116000"
] | B | let costs of cow and horse are x,y so x+y=300000------(1)
(x*120/100)+(y*90/100)=304200
120x+90y=30420000------(2).
solve equations (1) and (2)
x=114000
ANSWER:B |
AQUA-RAT | AQUA-RAT-38970 | ## A committee of 2 people is to be selected out of
##### This topic has expert replies
Legendary Member
Posts: 1892
Joined: 14 Oct 2017
Followed by:3 members
### A committee of 2 people is to be selected out of
by VJesus12 » Thu Mar 15, 2018 4:23 am
A committee of 2 people is to be selected out of 3 teachers and 4 ... | [
"1/10",
"1/5",
"3/10",
"2/5"
] | C | We have three units - Tom (T), Mary (M) & the Rest (R).
Total ways of making a community of 3 from 6 people = 6 x 5 x 4 = 120
Now ways the community can be formed with Tom in it and Mary NOT in it:
TRR
RTR
RRT
TRR posb = 1 (way of picking Tom) x 4 (4 people left excluding Tom and Mary) x 3 (3 people left after excludin... |
AQUA-RAT | AQUA-RAT-38971 | 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... | [
"40",
"28",
"26",
"27"
] | A | Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A |
AQUA-RAT | AQUA-RAT-38972 | # 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... | [
"127",
"688",
"400",
"121"
] | C | Let C.P. be Rs. x.
Then, 5% of x = 360 - 340 = 20
x/20 = 20 => x = 400
Answer: C |
AQUA-RAT | AQUA-RAT-38973 | 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... | [
"1400 m^2",
"2500 m^2",
"2520 m^2",
"1800 m^2"
] | D | Solving the two equations, we get: l = 45 and b = 40.
Area = (l x b) = (45 x 40) m2 = 1800 m^2
D |
AQUA-RAT | AQUA-RAT-38974 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"2",
"14",
"3",
"5"
] | D | D
75% --- 8
125% --- ?
75/125 * 8 = 5 |
AQUA-RAT | AQUA-RAT-38975 | for full-screen mode. TRIG WHEEL 1. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. Interested in seeing how well you grasp a specific area of trigonometry? Take Study. 11 mm into kilometers and divided. They are going to start the chapter on graphing trigonometric functions on ... | [
"16.8",
"26",
"14",
"12"
] | A | 2 * 22/7 * 10 * x = 1056 => x
= 16.8
Answer: A |
AQUA-RAT | AQUA-RAT-38976 | Let us take another mixture problem:
Question 2:
Two types of rice costing $60 per kg and$40 per kg are mixed in a ratio 2: 3. What will be the cost per kg of mixed rice?
Solution:
• Can we apply alligation to this question?
• Can we assume the price of the mixed rice to be $x per kg and make this diagram? • Now do... | [
"25",
"62",
"27",
"19"
] | A | Explanation:
Let original consumption = 100 kg and consumption = y kg.
So, 100 x 6 = y x 8
y = 75 kg
Reduction in consumption = 25 %.
ANSWER: A |
AQUA-RAT | AQUA-RAT-38977 | 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 ... | [
"22",
"88",
"99",
"66"
] | B | 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88.Answer:B |
AQUA-RAT | AQUA-RAT-38978 | that is y=???abc
#### Bacterius
##### Well-known member
MHB Math Helper
Re: find the value of x and y
$$x^2 \equiv x \pmod{1000} \tag{1}$$
[JUSTIFY]Clearly for $x$ coprime to $1000$, the only solutions are the trivial $x = 0$ and $x = 1$, so all nontrivial solutions for $x$ must be divisible by either $2$ or $5$, or... | [
"0",
"1",
"2",
"3"
] | B | x^2*y^3 + y^2*x^3=25
=> x^2*y^2*(y+x)=25
=> x^2*y^2*25=25 [given, x+y=25]
=> (xy)^2 = 1
=> xy = 1
ANSWER:B |
AQUA-RAT | AQUA-RAT-38979 | 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... | [
"25",
"20",
"24",
"32"
] | D | Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 15c + 15d = 10*x.
=> a + b + 3(c+d) = 2 * x . -----------------------------(i)
Since, a + b = 4.5+5.5 =10.
And,
=> c + d = 8+10=18
Putting these values in (i), we get :-
=> 10+ 3 * 18 = 2 * x.
=>... |
AQUA-RAT | AQUA-RAT-38980 | evolution, population-dynamics
Title: How many humans have been in my lineage? Is it almost the same for every human currently living? If I were to count my father, my grandfather, my great-grandfather, and so on up till, say chimps, or the most common ancestor, or whatever that suits the more accurate answer, how man... | [
"38 5/7 years",
"31 5/7 years",
"81 5/7 years",
"31 9/7 years"
] | B | Required Average
= [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7 = 31 5/7 years.
Answer:B |
AQUA-RAT | AQUA-RAT-38981 | # 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... | [
"V=2/5",
"V=3/5",
"1/5",
"1/2"
] | A | P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on y... |
AQUA-RAT | AQUA-RAT-38982 | So total sales for the year, 30000, cash sales 6000. Thus the yearly proportion of cash sales is $\dfrac{6000}{30000}=20\%$. This is the correct percentage.
Now let's compute the monthly averages. For January through October, they are $50\%$. For each of November and December, they are $5\%$.
To find the average of t... | [
"$ 18,687",
"$ 22,000",
"$ 24,000",
"$ 26,000"
] | A | Let x be the total sales in $.
For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$
For the remaining (x-11000) $, you get 32% ---> 0.32*(x-11000)
Thus, 0.32*(x-11000) + 2200 = 7300 ----> x= 18,687 $
A is thus the correct answer. |
AQUA-RAT | AQUA-RAT-38983 | Kudos [?]: 132821 [4], given: 12378
Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink] 13 Nov 2014, 13:09
Display posts from previous: Sort by
The following is multiple choice question (with options) to answer.
If the perimeter of a rectangular garden is 600 m, its length when i... | [
"299 m",
"777 m",
"200 m",
"100 m"
] | D | 2(l + 200) = 600 => l
= 100 m
Answer:D |
AQUA-RAT | AQUA-RAT-38984 | 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... | [
"41.1 sec",
"20.2 sec",
"31.8 sec",
"43.2 sec"
] | D | Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 140 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 660 m
Time = Distance / Speed
= 660 x 18 / (5 x 55)
= 43.2 sec
Ans is :D |
AQUA-RAT | AQUA-RAT-38985 | # 99 Consecutive Positive Integers whose sum is a perfect cube?
What is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube?
• What have you tried? What do you know about the sum of $99$ consecutive integers? If the first is $n$, what is the sum? – Ross Millikan Au... | [
"I",
"IV",
"II",
"III"
] | B | Since we summarize the reciprocals from 80 to 71, we can say also that we add ten numbers who are all (with one exception 1/80) greater than 1/80, so that the sum must be greater than 1/8.
On the other side we can say that we add the reciprocals from 71 to 80, so that the sum has to be less than the sum of ten times 1/... |
AQUA-RAT | AQUA-RAT-38986 | Related Rate Prob - Ships sailing in different directions
• November 5th 2010, 09:15 PM
dbakeg00
Related Rate Prob - Ships sailing in different directions
Ship A is 15 miles east of point O and moving west at 20mi/h. Ship B is 60 miles south of O and moving north at 15mi/h. a)Are they approaching or seperating after 1... | [
"STARTED WITH EQUATOR",
"STARTER WITH NORTH POLE",
"STARTER WITH SOUTH POLE",
"STARTER WITH 80 DEGREE NORTH POLE"
] | A | Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 19 = -11
And x = 0. |
AQUA-RAT | AQUA-RAT-38987 | # How many numbers made out of 5 distinct digits contain 4 and are even
This is an exercise from a book on combinatorics and I can't seem to wrap my head around it: How many numbers are there, made out of 5 distinct digits, which contain '4' and are even. The answer according to the book is 7686.
I distinguished some... | [
"6",
"12",
"24",
"36"
] | C | The main question here is how can you arrange 4 different digits E. We don't even need to find the number. from the question itself we know that there are 4 different digits and none of them is 0 as the product is non-zero.
Therefore no of ways to arrange 4 diff. digits is 4! which is 24
hence C |
AQUA-RAT | AQUA-RAT-38988 | Since he did not score 45, he lost an average of 4.5 upon the total number of innings, which includes the latest innings as well.
So 45 runs upon x innings will give an average of 4.5
Hence 45/x = 4.5 i.e. x = 10. (Remember, x includes the latest inning as well)
Problem 6:
The average of 8 scores is 87. Of these, t... | [
"48 runs",
"50 runs",
"70 runs",
"75 runs"
] | A | Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 6
= 11x + 66 = 10x + 108
= x = 42.
New average = (x + 6) = 48 runs.
ANSWER A |
AQUA-RAT | AQUA-RAT-38989 | RonL
Quite right!
I have made a picture of how could these streets look like.
There is also second question.
How many there are areas which are edged with streets from every side?
I have counted from picture that there are 15, I must say that I can't think another way at the moment. :D
• Apr 24th 2006, 05:50 PM
ThePe... | [
"1/21",
"1/7",
"4/21",
"10/21"
] | C | She choose a route which allows her to walk fewest number of blocks
there are 2 blocks she will cross towards east moves represented by E,E and there will be 5 blocks she will cross towards south represented by S,S,S,S,S
total number of ways 7!5!2!7!5!2!
there are 4 ways she can cross 2 blocks on av.1 as shown in attac... |
AQUA-RAT | AQUA-RAT-38990 | # Math Help - counting
1. ## counting
arrange 12 people into 4 teams of 3 people
would u choose the team first then the players: 4C1 x 12C3 first team
3C1 x 9C3 second team and carry on for third and fourth then multiply all of ur results together?
2. Originally Posted by qwerty10
arrange 12 people into 4 teams of ... | [
" 20",
" 24",
" 36",
" 48"
] | B | We are given that at lovely gym class can be divided into 8 teams or 12 teams, with an equal number of players on each team. Translating this into two mathematical expressions we can say, where G is the total number of students in the gym class, that:
G/8 = integer and G/12 = integer
This means that G is a multiple of ... |
AQUA-RAT | AQUA-RAT-38991 | Show Tags
18 Jun 2014, 06:09
Thanks much Bunuel
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The perimeter of square S is 40. Square T is inscribed in square S. [#permalink]
Show Tags
... | [
"3p/4",
"3p^2/4",
"12p/5",
"3p^2"
] | C | Area of square, (side)^2 = (3p/5)^2
Therefore side of the square = 3p/5
Perimeter of square = 4*side = 4* (3p/5) = 12p/5
Answer is C. |
AQUA-RAT | AQUA-RAT-38992 | # Remainder on division with $22$
What is the remainder obtained when $$14^{16}$$ is divided with $$22$$?
Is there a general method for this, without using number theory? I wish to solve this question using binomial theorem only - maybe expressing the numerator as a summation in which most terms are divisible by $$22... | [
"1",
"3",
"4",
"6"
] | C | Explanation:
35 + 25 = 60/15 = 4 (Remainder)
C |
AQUA-RAT | AQUA-RAT-38993 | How do you solve this?
There is this kind of question in our test and I don't know how will I do it.
You're working in a company. Your starting income is 5000. Every year, the income will increase by 5%. What is your total income on your 25th year in the company?
Related Precalculus Mathematics Homework Help News on ... | [
"12.5%",
"20%",
"25%",
"50%"
] | A | Explanation :
Given, Ritesh and Co. generated revenue of Rs. 2,500 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 2500 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×2500.
=>20,000.
Hence, the total revenue by end of 2007 is Rs. 10,000. In 2006, revenue grew by Rs. 2500. This is a ... |
AQUA-RAT | AQUA-RAT-38994 | Hello Matty R!
No, that doesn't mean anything, does it?
Hint: what will Bea's age be when Claire is as old as Dawn is now?
3. Feb 27, 2010
### HallsofIvy
Staff Emeritus
"When Claire is as old as Dawn is now, Bea will be twice as old as Ann currently is.
Claire is older than Bea."
Claire will be as old as Dawn is no... | [
"7 years",
"10 years",
"12 years",
"13 years"
] | A | Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.
(2x + 2) + 2x + x = 37
5x = 35
x = 7
Hence, Chris's age =7 years.
Answer : A |
AQUA-RAT | AQUA-RAT-38995 | ## Wednesday, August 12, 2015
### The angle between the hour and minute hands of a clock.
Q. The time shown in the clock is 7:35 what is the angle between the hour and minute hands of a clock?
A. Consider the simpler problem if the time is 7:00. As there are 12 hours in a complete revolution of the hour hand, one ho... | [
"45 minutes",
"55 minutes",
"35 minutes",
"30 minutes"
] | D | there are 6 hours in between 12 a.m. to 6 p.m.
6*5=30 minutes.
ANSWER:D |
AQUA-RAT | AQUA-RAT-38996 | 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... | [
"1288",
"1299",
"1000",
"10000"
] | D | 100 * 100 = 10000
125 * 80 = 10000
Answer: D |
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