Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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2
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2answers
31 views

What inequality does the units digit of a two digit number less than $40$ satisfy if the sum of the units digit and tens digit equals $8$?

For a two digit number , the sum of the "units digit" and "tens digit" is $8$ and the two-digit number is less than $40$. Denoting that the "units digit" of the two-digit number to be $x$, form an ...
1
vote
1answer
43 views

Existence of subsequences in square roots

For any sequence of decimal digits $x_1x_2 \ldots x_m$ there exists $n \in \mathbb{N} $ such that this seqence occurs (as a substring) in the decimal expansion of the fractional part of $ \sqrt{n} $ ...
1
vote
0answers
59 views

Theorem of two squares. Proving $p$ can be written as a sum of two squares.

Hi I'm having trouble with this problem. Let $p$ be a prime number such that $p\equiv 1\pmod4$. We want to prove that we can write it as a sum of two squares. Let $S:=\{(a,b,c)\in\mathbb N^2 \times ...
0
votes
0answers
30 views

Cases of the Erdos-Selfridge Theorem

I'm having a difficult time trying to understand/proceed with this problem. Problem: The goal of this problem is to study particular cases of the Erdos-Selfridge theorem which says that: . We call ...
0
votes
3answers
108 views

Is it possible to build a formula that prevents negative numbers? [closed]

I have a calculation that goes like this: $$\text{<any positive number>} - 100$$ As long as the result is a positive number it is acceptable. However, if the result is a negative number, I ...
2
votes
2answers
69 views

Deducing an integer from $0$-$15$ and lying

I'm interested in reducing the upperbound of the number of questions needed and in finding alternate solutions to solve the following question: Suppose I have thought up an integer between $0$ and ...
3
votes
1answer
47 views

Determining which number pair has greater product - without multiplying.

This is a 5x5 multiplication table. ...
-2
votes
4answers
100 views

If the sum of $m$ and $n$ is odd then exactly one of them is odd. [closed]

Let $m,n$ be integers. Prove that if $m + n$ is odd, then exactly one of $m$ or $n$ is odd. What is the approach to prove this?
-2
votes
1answer
57 views

Which branch of mathematics deals with errors? [closed]

Maths is a concrete language which is definite in terms of it's accuracy. But, it seems mathematics also has it's flaws. Consider an example such as: seeing this we can only say that the whole ...
3
votes
2answers
57 views

Does the term “selling price” mean the “cost price” or the “sale price” of a product/commodity?

I have been told that the idiom "selling price" is the same as the cost price of an item, that is the amount which a seller pays to, e.g. a wholesale merchant. The seller later sells the commodity at ...
1
vote
5answers
35 views

How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is The price of a mobile phone is $8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price ...
0
votes
3answers
27 views

Factorising large numbers

Can I get some hint for this question, please? I'm told to find the value of $p$ in the following equation $$\dfrac{1}{(2p-1)^4} = \dfrac{1-2p}{32}$$ Here's my thought process ... I can't ...
0
votes
1answer
14 views

Inverse proportion

I am not sure how to approach this question, can I get some help? This is an inverse proportion question. $y$ is inversely proportional to the square of $x$. Find the percentage change of $x$ when ...
3
votes
3answers
48 views

From a set of positive consecutive integers starting with $1$, one number is erased and the AM of the remaining numbers is $\frac{602}{17}$

A set of positive consecutive integers starting with one is written on a blackboard. One number is erased and the AM of the remaining numbers is $\frac{602}{17}$. The erased number is 6 7 8 9 ...
2
votes
2answers
18 views

Proportion understanding

49 Painters are required to complete a painting job in 12 days . However, due to unforeseen circumstances , there was a delay and only one third of the job was completed in 5 days . Assuming that all ...
2
votes
4answers
120 views

Prove or disprove: If $n^3$ is odd then $n$ is odd.

If $n^3$ is odd, then $n$ is odd. I need to prove or disprove by means of counterexample why this is true or false. $\forall x P(x) = x^3$, $x = 1,3,5,7,9$ I am having a very difficult time ...
0
votes
1answer
27 views

Proportions question

I do not know how to approach this qn properly .. Qn - 6 workers working 8 Hours per day were tasked to complete a building project in 5 days . After working for 3 days , 2 of the workers were sick ...
3
votes
7answers
114 views

What do the square brackets mean in $[5-(6-7(2-6)+2)]+4$?

While watching a youtube video about a Simpsons math episode at 1:27 there's a puzzle that includes square brackets. $$[5-(6-7(2-6)+2)]+4$$ Apparently the answer is $-27$ which I can't figure out ...
0
votes
0answers
29 views

Percents question [duplicate]

A vacuum is priced at \$$340$ with an allowed trade-in of \$$135$ on an old unit. If the sales tax of $4$ $3/4$% is charged on the price of the new vacuum unit before the trade-in, find the total cost ...
-1
votes
1answer
32 views

Percent story problem [closed]

A vacuum is priced at \$$340$ with an allowed trade-in of \$$135$ on an old unit. If the sales tax of $4$ $3/4$% is charged on the price of the new vacuum unit before the trade-in, find the total cost ...
1
vote
1answer
50 views

simple arithmatic

in sexagesimal method 1 rtangle =90 degrees then 0.942387rtangle =? actually in unitary method 1 is the least count but if we get something like .95,.88.How to calculate this?
0
votes
1answer
33 views

Indices solving for $x$

Sorry this is a simple question but I'm having difficulty with it . $$2(16^{3x+2}) = 1 / 8^{5x-4}$$ I'm told to solve for $x$. My working - $$2(16^{3x+2}) = 1 / 8^{5x-4}$$ $$32^{3x+2} = ...
1
vote
1answer
22 views

Proportion problems

Tension T, newtons , of a string is inversely proportional to the square of the frequency, f Hz , of the note produced . When the tension is 80N , the string produces a note with frequency of 400 Hz . ...
4
votes
5answers
111 views

What is the value of $3-3\times 6+2$?

Please could someone help me and my brother settle our dispute? We have been looking at the following equation: $$3-3\times 6+2=$$ This may look familiar but I have yet to find a fully conclusive ...
2
votes
4answers
71 views

Proving $a \leq \frac{a+b}{2} \leq b$

I want to prove the following $a \leq \frac{a+b}{2} \leq b$, where we know that $0 \leq a \leq b$. My proof goes as follows. Suppose $a \leq \frac{a+b}{2} \leq b$, then we know $a \leq \frac{a+b}{2}$ ...
2
votes
1answer
36 views

Division by rational (decimal) number meaning

When I say, that I exchanged 42 CZK into 1,5 euro. Why do I get the rate for one euro by dividing? 1) How do you explain this division in words. Like when you say when doing integer division, that ...
2
votes
1answer
59 views

What word to use to describe the mathematical objects and axioms of a branch of math

I'm trying to write a paragraph which describes the objects and rules of a branch of mathematics. But I'm stuck as to what word I should use here. Example: (fill the blank) Arithmetic is an ...
0
votes
3answers
56 views

How to solve 'a÷b(c+d)'? [duplicate]

How to solve $a÷b(c+d)$? For example, $2÷4(8+16)$. Is it $($$\frac{2}{4}$$)(8+16)$ = $\frac{1}{2}$(8+16) = $\frac{1}{2}$(24) = 12? or $\frac{2}{4(8+16)}$ = $\frac{2}{4*24}$ = $\frac{2}{96}$ = ...
1
vote
4answers
150 views

Finding remainder of the big integer?

The value of the expression $\mathrm{13^{99}(mod 17)}$, in the range $0$ to $16$, is_______? My attempt : Somewhere it explain as: Note: for remainder cycle $\mathrm{13^1mod17=13, ...
7
votes
0answers
59 views

To what extent can the fondamental theorem of arithmetic be used to give a canonical form to non-integer numbers?

The fundamental theorem of arithmetic gives us a unique way of writing any non-zero integer. For any $n \in \mathbb{Z}^*$, we have a unique decomposition : $$n = (-1)^\epsilon \prod\limits_{i \in ...
1
vote
1answer
36 views

Encoding 2 numbers into 1

Say we have two integers, $a$ and $b$. I need a way to combine these numbers into one unique number $x$, such that they can both be recovered from $x$ and no other numbers can be recovered from $x$ ...
2
votes
3answers
75 views

Prove that if $ 2^n $ divides $ 3^m-1 $ then $ 2^{n-2} $ divides $ m $ [closed]

I got a difficult problem. It's kind of difficult to prove. Can you do it? Let $ m,n\geq 3 $ be two positive integers. Prove that if $ 2^n $ divides $ 3^m -1$ then $ 2^{n-2} $ divides $ m $ Thanks ...
0
votes
2answers
77 views

Formula to find the first intersection of two arithmetic progressions

Formula to find the first intersection of two arithmetic progressions I am not good in math, but I need to determine if two generic arithmetic progressions have an intersection point and, in that ...
1
vote
2answers
55 views

Arrangement of points in a circle

From the 2015 Moscow Mathematical Olympiad: The numbers $1$ to $1000$ are arranged on a circle such that each number divides the sum of its two neighbors. Suppose that the number $k$ has two odd ...
1
vote
3answers
99 views

Computing shortest path including specific edge

Consider the weighted undirected graph with $4$ vertices, where the weight of edge $\{i, j\}$ is given by the entry $W_{i, j}$ in the matrix $W$. $$W = \begin{bmatrix} 0&2&8&5\\ ...
1
vote
1answer
36 views

Simplifying sum of sort

I want to know that simple method of sqrt sum I have 10 values of some information. Let these be $d_1 , ... , d_{10}$ And I want to calculate $\frac {\sqrt d_1+...+\sqrt d_{10}}{10}$ in computer ...
8
votes
4answers
140 views

Is there $n$ such that $n,n^2,n^3$ start with the same digit ($\neq 1)$

From the 2015 Moscow Mathematical Olympiad: Is there some $n>2$ such that $n,n^2$ and $n^3$ start with the same digit (this digit being different from $1$) Using a computer I found that $99$ ...
0
votes
1answer
104 views

Finding square of cube? [closed]

A cube is built using $64$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after ...
1
vote
1answer
34 views

Problem on Time and Work

$A$ can do a piece of work in $10$ days, $B$ can do in $20$ days and $C$ can do in $30$ days. If $A$ is assisted by $B$ and $C$ turn by turn in alternate days respectively, in how many days the work ...
3
votes
2answers
94 views

Fraction Sum Series

This question was asked in (selection) IMO for 8th graders. $1/2 + 1/6 + 1/12+ 1/20 + 1/30 + 1/42 +1/56 + 1/72 + 1/90 + 1/110 +1/132$ I have noticed that it can be written as $1/(1*2) + 1/(2*3) ...
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votes
1answer
30 views

How to subtract fractional numbers using complements.

I know how $10$'s and $9$'s complements are used, but I don't know how to use complements to subtract two fractional numbers. For example $108.32-26.30$ . How will we solve it using $10$'s and $9$'s ...
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votes
2answers
56 views

How calculate the rest of the division 2/7 [closed]

How can I calculate the rest of division about two / seven? According to this video (https://youtu.be/Nu-lW-Ifyec?t=113) the result of this division is two. But how can I know that? In calculator the ...
0
votes
3answers
46 views

Complex Addition

Solving a question, I need to find the value of following in between the solution. $$(\frac{i+\sqrt3}{2})^{200} + (\frac{i-\sqrt3}{2})^{200}$$ The only useful thing I got was ...
0
votes
2answers
39 views

A reduction of $10\%$…

A reduction of $10\%$ in the price of sugar would enable a man to buy $2\,\rm{kg}$ of sugar more for Rs. $125$. Find the reduced price per kg. My attempt: Let the initial price of sugar be Rs. $x$ ...
0
votes
2answers
39 views

How is unique factorization of integers related to computing greatest common divisors?

Source: Discrete Mathematics with Applications, Susanna S. Epp. What does the unique factorization of integers have to do with gcd $2^{10}$ of ($10^{20}, 6^{30}$) in Example 4.8.5.b? ...
7
votes
4answers
231 views

What is the sum of all the natural numbers between $500$ and $1000$.

What is the sum of all the natural numbers between $500$ and $1000$ (extremes included) that are multiples of $2$ but not of $7$?
0
votes
1answer
36 views

Solve this simple problem of Simplification [closed]

Simplify $14-\frac{21}{7}+4*2$ Answer given is $3$ but mine is $19$. Where am I doing wrong?
0
votes
3answers
47 views

Which of the following integers cannot be expressed as the sum of two prime numbers? [closed]

Please help me with this problem. I'm stumped! which of the following integers cannot be expressed as the sum of two prime numbers? A) $8$ B) $9$ C) $10$ D) $11$ E) $12$ According to the GRE ...
0
votes
0answers
46 views

Standard name or notation for the “even part” of an integer?

\begin{align} 0 & \mapsto 0 \\ 1 & \mapsto 0 \\[6pt] 2 & \mapsto 2 \\ 3 & \mapsto 2 \\[6pt] 4 & \mapsto 4 \\ 5 & \mapsto 4 \\[6pt] 6 & \mapsto 6 \\ 7 & \mapsto 6 \\ ...
1
vote
1answer
55 views

Why does lattice multiplication work?

My brother (who is currently in 4th grade) is learning a technique called Lattice multiplication in school. It is a technique that involves taking two numbers, placing them on the outside of a square, ...