Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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-1
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2answers
13 views

A shopkeeper gives rebate a% and b% successively to buyers.Then what's the total rebate buyers should get? [on hold]

(please help me with some kind of explanation) i'm trying to learn maths, Any help will be welcomed
0
votes
2answers
55 views

How to find minutes?

Need help solving this real life problem, I have an SD Card of $4$GB(gigabyte), and a $32$ second video occupies $6.12$MB(megabyte), I need to know how many minutes or seconds can this $4$GB SD Card ...
1
vote
1answer
27 views

Variations in the successor fuction from Peano's axioms

Concerning the successor function in Peano's axioms, what prevents me from defining it in the following way: 0 to 2, 2 to 1, 1 to 4, 4 to 3, 3 to 6, 6 to 5, 5 to 8, 8 to 7 ... and so on. It seems ...
0
votes
2answers
36 views

Simplifying Square Roots Frustration

Okay, I'm really frustrated with this. So, when you have $3 \sqrt 5 + 5 \sqrt 5$, you get $8\sqrt5$, right? Okay, so what do I do for here: $\sqrt{11} - 3 \sqrt{11}$ Is it just $-3 \sqrt{11}$ ? ...
1
vote
1answer
24 views

Interval arithmetic - faster version

As per the below question picked from self training exercise: Q4: In passing, Ben also cryptically comments, "By testing the signs of the endpoints of the intervals, it is possible to break ...
-2
votes
1answer
22 views

question from real numbers [on hold]

a man has 1044 candels after burning he can make a new candal from 9 stubs left behind .the maximum numbers of candals that can be made are?
0
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1answer
34 views

order of operations in different cultures?

Are there any cultures or countries around the world that use a different convention for order of operations than the BEDMAS convention? i.e.: Parentheses Exponents & Roots Multiplication & ...
-7
votes
0answers
45 views

A simple arithmetic puzzle [on hold]

$_+_+_=30$ You can use the numbers $1,3,5,7,9,11,13,15$ to fill the gaps.
1
vote
2answers
49 views

How many numbers smaller that $N$ can be written as a sum of two square numbers?

We define $$a_N =\# \{ n \leq N, \exists (n_1,n_2) \in \mathbb{N}^2, n = n_1^2 + n_2^2 \}.$$ Can we have the exact value of $a_N$, or at least an asymptotic behavior such as $$ \alpha N \leq a_N \leq ...
0
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0answers
13 views

solving Multi operation equations correctly

Is it possible to solve an equation with different operations in it correctly without using orders of operation? I was having a discussion with my friend who believes you can solve an equation from ...
-4
votes
1answer
32 views

A policeman is 834 feet behind a car travling 25 mph [closed]

A policeman is 834 feet behind a car travling 25 mph, how fast does the policeman need to go to catch up to the car before the car travels 1500 more feet?
7
votes
8answers
136 views

Which is larger, $\sqrt{3} + \sqrt{5}$ or $\sqrt{2} + \sqrt{6}$?

The clue given by the text is to "use the fact that $\sqrt{x}$ is increasing." I was able to get the correct answer here by squaring both expressions. But I don't think I made use of the text-prided ...
0
votes
1answer
19 views

Profit-Loss : Discount

On an order of 5 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of: 15% 97/6% 50/3% 20% I don't know how to put these ...
1
vote
1answer
17 views

Profit and Loss : Manufacturer

A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to its estimates, even if 5% fail to pass the quality tests, then he will make a profit of ...
3
votes
1answer
42 views

Finding all possible pairs of positive integer values

The ratio of the sum of two positive integers to their difference is $7:5$. If the the sum of the two numbers is at most $25$, find all possible values for the pair of numbers. Let $m$ be the first ...
2
votes
3answers
68 views

Solve $x + y + z = xyz$ such that $x , y , z \neq0$

I came across the equation $x+y+z=xyz$ such that $x , y , z \neq 0$. I set $x=1, y=2, z=3$ but how can i reach formal mathematical solution without " guessing " the answer ? Thank you
0
votes
1answer
16 views

modular problem in arithmetic

hello can someone please help me to solve this problem: 2008 mod 71, 9 square mod 41, 34 suare mod 71 b)determine all a and b that verify a square mod 41=40 b square mod 71=20 ...
0
votes
1answer
17 views

a tax Deferred keogh account

Suppose you contribute $20,000 in an account at the end of the year.How much would you have at the end of 20 years if the account pays 8% annual interest.
1
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3answers
49 views

How do I compute $-6(-4)^{n-1} + 8(-4)^{n-2}$?

How do I compute $-6(-4)^{n-1}$ + $8(-4)^{n-2}$ ? I recall that as long as the number from both operands (in this case: -4) are the same, I can actually "add" them together. But the problem is the -6 ...
0
votes
1answer
28 views

Tricks to simplify basic arithmetic expressions?

I am doing a problem set and have several formulas that are quite ugly such as $$b=\left(\frac{3p_b}{2p_r}\right)^{\frac{1}{\rho-1}} \left(\frac{m}{p_r + p_b ...
3
votes
3answers
73 views

A doubt concerning the fundamental theorem of arithmetic

Will a prime $p^{0}$ be considered a unique prime in prime decomposition of a number? If the answer to the above question is yes then it breaks the uniqueness which the Fundamental Theorem of ...
0
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1answer
70 views

Which one of the following logical propositions is to be preferred?

I'm trying to update the symbolism of Giuseppe Peano's "Arithmetices Principia", to make the translation freely available. Might I ask you, which of the following might be a correct mathematical ...
4
votes
1answer
58 views

Time and distance: Police and a thief with a twist.

A thief was given a head-start of 15 hour. The velocity of the thief being 4 km/hr and the police chasing after him be 5 Km/hr. A dog is moving to and fro between the police and the thief, starting ...
0
votes
1answer
31 views

Tree addtion has to do with Pascal's Triangle, why?

Let me define tree addition of a list of numbers as follows: 4 3 2 1 7 5 3 12 8 20 I conjecture that it is true that the tree addition of n numbers ...
3
votes
3answers
67 views

Find the largest $k$ such that $3^k$ divides the product of the first $100$ odd integers

Let $P$ be the product of the first 100 positive odd integers. Find the largest integer $k$ such that $P$ is divisible by $3^k$. There are $50$ odd numbers and $50$ even numbers between $0$ and ...
0
votes
3answers
25 views

Complex values of the cube root

I just learned that the cube root has 2 complex roots. For example, the cube root of 8 has : 2 , -1 plus or minus square root of 3 *i I was wondering, how do you find those conjugate complex values ...
0
votes
2answers
38 views

simplifiying an expression $(n + 1)! − 1 + (n + 1) \cdot (n + 1)!$

I've been stuck on this one problem and I have a problem on the process simplifying this equation so that it is $(n + 2)! − 1.$ $$(n + 1)! − 1 + (n + 1) \cdot (n + 1)!$$ If anyone could shed some ...
0
votes
1answer
15 views

10% fraud, while purchasing and selling. Whats the overall profit?

Ok, so the answer i find logical is $21$%. Like : 100 bucks paid, 110 items got. (10% profit). Then, 110 items you sell at 10% profit, you get 121 items worth of bucks. So, 100 bucks investment, 121 ...
6
votes
5answers
135 views

Show that $2^{105} + 3^{105}$ is divisible by $7$

I know that $$\frac{(ak \pm 1)^n}{a}$$ gives remainder $a - 1$ is n is odd or $1$ is n is even. So, I wrote $ 2^{105} + 3^{105}$ as $8^{35} + 27^{35}$ and then as $(7\cdot 1+1)^{35} + (7\cdot ...
0
votes
1answer
38 views

How to calculate $\binom{17}6 21$? [closed]

$\dbinom{17}{6}21$ I understand most of this, where you use $$C(n,r) = \dfrac{n!}{r! (n - r)!}$$ but I am not sure how to calculate with the $21$ and the $17$ choose $6$.
2
votes
3answers
51 views

Number in tens place

A number in tens place in result of $4^{2015} \cdot 9^{2016}$ is? Obviously without using calculator, though I doubt it could count with those high numbers. By tens place I mean, for example if you ...
1
vote
2answers
44 views

Number of boys in school

We have $400$ students in a school. Every $20^{th}$ student failed at the end of the school year. Which was $2\%$ of schools girls and $10\%$ of schools boys. The number of all boys attending the ...
1
vote
2answers
64 views

Number addition riddle

I got this math "riddle" in one of my math test, and I would love to know how to solve it. If $$S = 1 + 2 + 3 + 4 + \ldots + 2015,$$ then a sum of $$1 + 2 + 3 + \ldots + 2015 + 2016 + \ldots + 4030$$ ...
1
vote
1answer
27 views

Number of apples in a basket riddle

You have six baskets with apples - 10,12,15,20,22,25 (this is how many apples there were in them - 10 in first, 12 in second..). Some of the apples are red and some are green. After one basket was ...
0
votes
1answer
31 views

What is the difference between the largest and smallest possible positive roots?

I am faced with the following question: What is the difference between the largest and the smallest possible positive roots of $4x^5 + 3x^3 -5x^2 + 7x - 12$? Now, my first attempt was to try ...
0
votes
3answers
18 views

Is it possible to convert fraction to decimal using only addition and subtraction?

I am working on a programming challenge that requires me to implement addition, division, and modulo using only addition and subtraction. Cool, simple enough: ...
1
vote
3answers
80 views

Easy inequality going wrong

Question to solve: $$\frac{3}{x+1} + \frac{7}{x+2} \leq \frac{6}{x-1}$$ My method: $$\implies \frac{10x + 13}{(x+1)(x+2)} - \frac{6}{x-1} \leq 0$$ $$\implies \frac{4x^2 -15x-25}{(x-1)(x+1)(x+2)} ...
3
votes
3answers
37 views

Find point of passing of two racers. [closed]

Two contestants run a 3-kilometre race along a circular course of length 300 metres. If their speeds are in the ratio 4:3, how often and where would the winner pass the other? (The initial start-off ...
0
votes
2answers
39 views

Generalized formula for sum of products.

Q:The sum of all possible products of the first n natural numbers taken two by two is? I did not understand the question as it is.What exactly is being asked?I'd really appreciate an answer ...
0
votes
1answer
20 views

Find the kind of progression

The four positive numbers a,b,c,d are in arithmetic progression.What is the progression sequence of abc,abd,bcd? I found out the common difference b-a,c-b.. but that does not seem to be of much use.
1
vote
1answer
42 views

Number of the term

If the sum of n terms in AP is $3(n^2)+5$.What is the number of the term which equals $159$? My attempt: $3(n)^2-3(n-1)^2=159$.I got $n=27$ but the answer given is $21$.
2
votes
3answers
27 views

Theory behind multiplying decimals

When multiplying two decimal numbers, you first ignore the decimals, find the product, then count the number of decimal places that need to be in the answer by taking the sum of the original decimal ...
0
votes
1answer
17 views

How to Normalize the Sum of Two Gaussians

I have the following function: $I(\theta_i) = I_0 + I_1\exp(\mu(\cos(\theta_i - \theta_s) - 1))$. Suppose I have two implementations of this function, whose parameters match with the exception of ...
2
votes
1answer
28 views

How do I find the sum of first N numbers common to 2 APs?

Here is the question - Certain numbers appear in both arithmetic progressions 17, 21, 25, ... and 16, 21, 26, ... . Find the sum of first 100 numbers appearing in both progressions. The ...
4
votes
0answers
80 views

Minimum number of real multiplications to multiply two quaternions

Karatsuba multiplication of two complex numbers can be performed with just three real multiplications (instead of four) as follows: $$(a+bi)(c+di) = (ac-bd) + i ((a+b)(c+d) - ac-bd)$$ We only need the ...
5
votes
1answer
67 views

Find prime numbers $p,q$ such that $p^n+p^{n-1}+…+p+1=q^2+q+1$

Let $p,q$ are prime numbers and $n$ is a even number such that : $p^n+p^{n-1}+...+p+1=q^2+q+1$ Find $p,q$? I think : $p^n+p^{n-1}+...+p+1=q^2+q+1\Rightarrow p^n+p^{n-1}+...+p=q(q+1)\Rightarrow ...
2
votes
1answer
54 views

Small integral representation as $x^2-2y^2$ in Pell's equation

Let $k$ be a "representable" positive integer, in the sense that $k=|x^2-2y^2|$ for some integers $x,y$. Does it necessarily follow that $k$ can also be represented with small parameters, i.e. ...
1
vote
1answer
23 views

Does using the syntax X%% make sense?

I know percentages can be multiplied, as they're basically just fractions, so it makes sense to ask what 50% of 72% of 10 is, for example. But would anybody use an expression like 3%% as shorthand for ...
3
votes
2answers
25 views

Calculating the value of numbers with different operations

Calculate the value of: $$-14 + 49 \times 21 - 63 + 56 \div 35 \div 28 \times 70 - 42 \div 7$$ I noticed the numbers are a factor of $7$, so I took out $7$ as a common factor: $$7[-2 + (7 \times 3) ...
1
vote
0answers
23 views

Simple Interest Problem Ambiguity in Conventions

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on. In what time does sum of money become 4 times ...