Questions tagged [mental-arithmetic]

Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.

91 questions
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Estimating square numbers

A large dice has a side length of 9.2 cm. Estimate the surface area of the cube. What I did: 6× $9^2$ = 6 × 81 = 6 × 80 = 480 But the answer says that $9.2^2$ is 85 as an estimate. How do I get ...
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How do people do calculation in mind for large numbers? [closed]

I can easily tell the answer of the following questions in few seconds: 2500+2500 2500x2 5000/5 These are easy, because of small numbers. But how do people do calculation of large numbers in mind ...
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What would be the best way to memorize the 10 by 10 multiplication table?

Hear me out before you start downvoting please. I have a learning disability so no matter how hard I try I can’t memorize the table. Please give some tips/hints on how to memorize the table. Thanks in ...
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Approximating values while calculating percentage changes

At times, in certain types of data interpretation questions that usually get asked in aptitude examinations, some techniques are employed to cut time on calculation and get a near perfect answer. One ...
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Mental approximations of 1) log, 2) non-integer power

I am currently preparing for a interview that is notorious for asking mental approximations. Two example questions came up: 1) $\ln 514$ and 2) $3^{3.6}$. What are some of the best ways to calculate ...
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What method for mentally computing 2-digit multiplication problems, minimizes the amount of mental steps?

So I've been practicing alot of mental math recently and ofcourse as a part of that, multiplying a double-digit number by another double-digit number. I have been doing some research into what the ...
171 views

Vinculum number of 989?

To find vinculum number I was subtracting finding the complement of 989 and cosidering the number to be 0989 I raised the 0 to 1 so my answer was 1011 , but why was the answer given 1111 ? Do I also ...
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Age questions: How to approach solving this?

Completely foxed by this question: Moses is twice as old as Methusaleh was when Methusaleh was one-third as old as Moses will be when Moses is as old as Methuselah is now. The difference in their ...
55 views

Generating “random” mental calculation exercises?

I recently tried to come up with "random" mental calculation exercises in an attempt to fight traffic jam boredom. Unfortunately, I quickly got bored by the lack of creativity of the problems I can ...
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This quantity (see question) will end with how many zeros?

I have this GRE practice question, asking me to find the quantity $$3^{3}4^{4}5^{5}6^{6} - 3^{6}4^{5}5^{4}6^{3}$$ will end in how many zeros? The answer given is $4$, but I don't quite understand ...
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How to find a volume of this figure (which is $3080 \text{ cm}^3$) in a few seconds?

I was watching this Japanese game show and came across this question: The contestants were told that each small cube is 2cm on its side and were asked to find the volume of the above figure. The ...
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Multiplication tables: up to what number should I memorise? [closed]

I never memorised them and suffered immensely through school as a result. Eg. I calculated 7x8 as (7x10=70) minus 7 using my fingers (63) then minus again on my fingers (56). In Australia children ...
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Why is it so good to know that $(1+x)^n \approx 1+nx$ for $nx \ll 1$?

I’ve often heard that it’s good to memorize the fact that $(1+x)^n \approx 1+nx$ for $nx \ll 1$ (most recently here), especially for mental arithmetic or making quick approximations. But why? Could ...
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Pandigital strings that end in $0$ and available to mental arithmetic?

I'm looking for a sequence that includes every number from $1$-$9$ and then ends with $0$. It should look random on first glance (or as random as possible given the mental arithmetic constraint) but ...
228 views

Mentally calculate the first 9 terms of this Fibonacci sequence.

There was a question in a mental math test and it expected me to calculate the first 9 terms of the following Fibonacci sequence (Note that this is how the problem was exactly given.): The sum of ...
62 views

Problems on Trains

A train Leaves station $x$ at $5 AM$ and reaches station $y$ at $9AM$. Another train leaves station $y$ at $7AM$ and reaches station $x$ at $10.30 AM$ . At what time do the two trains cross each other?...
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Mental Arithmetic Problems

The speed of a Motor - Boat is that of the current of water as 36:5.The boat goes along with the current in 5 hours 10 Minutes,It will Come Back in which time? I have Tried: Speed of Motor : Speed of ...
183 views

Divison In Mental ArithMatic

The nearest number to $99548$ which is divisible by $687$ is? How can I find the answer quickly, is there any short cut to check if a number is divisible by $687$?
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Boats and Streams [closed]

A boat can travel with a speed of $13$ km/hr in still water. If the speed of the stream is $4$ km/hr, find the time taken by the boat to go $68$ km downstream. Can you Explain the Difference between ...
193 views

Simplifying this fraction in a different base

Note: I would appreciate a solution that DOES NOT convert back to base 10. How would one simplify $\frac{43}{70}_8$? I assume, like in decimal, I must recognize a common factor and divide by that ...
207 views

Faster mental calculations

Currently I am preparing for trading exams which tests faster arithmetic skills. For ex- 80 questions (like calculating 0.abc* 0.cd) to be done in 8 minutes. I am trying to memorize the squares and ...
519 views

Shortcut for finding cube of the Numbers

Is there a shortcut for finding cube of a particular number like $68^3$ ? If anyone knows how to solve for two- and three digit numbers, can you please share the answer?
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Nice approximation to pattern

Does anyone know a good general approximation (within 5 percent) for the sum of the products of two numbers such that the sum of one number of one product and another of another product is equal two ...
508 views

What is the fastest method to find which of $\frac {3\sqrt {3}-4}{7-2\sqrt {3}}$ and $\frac {3\sqrt {3}-8}{1-2\sqrt {3}}$ is bigger manually?

What is the fastest method to find which number is bigger manually? $\frac {3\sqrt {3}-4}{7-2\sqrt {3}}$ or $\frac {3\sqrt {3}-8}{1-2\sqrt {3}}$
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Is there a simple way of computing when $a^n=b^m$

I don't want exact equality just close enough to be useful in approximation. i.e. $2^{10 }= 10^3$ is very useful and used daily for an approximation. Is there a do this efficiently? Is there a way ...
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