fred

https://hpssjellis.github.io/fred/public/index.html

GRE and GMAT math problems

https://www.manhattanprep.com/gre/blog/hardest-gre-math-problems/

https://gmatclub.com/forum/25-hardest-questions-on-gmat-club-144023.html

https://gmatpractice.q-51.com/hard-math-gmat-sample-questions/gmat-maths-questions.shtml

https://www.prepscholar.com/gmat/blog/hardest-gmat-data-sufficiency-questions/

Let’s ask some LLM’s

For both test the math portion has a few very difficult questions that expect people to know some tricks for exponenets and series calculation. can you make a list of the math tricks that help students with the harder math questions.

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Here is bingChat’s answer:

Certainly! Here are the helpful math tricks formatted in markdown:

Squaring numbers ending in 5:

To square a two-digit number ending in 5, follow this rule:
For a number like (35^2), multiply the first digit (3) by itself plus one (3 * (3 + 1)), and then append 25 to the result.
Example: (35^2 = 3 \times 4 = 12), append 25 to get (1225). This works for any two-digit number ending in 5.

Multiplying by 11:

To multiply a two-digit number by 11, follow this rule:
Add the two digits and place the sum between them. If the sum is greater than 9, carry over the extra digit to the left.
Example: (47 \times 11 = 4 + 7 = 11), so place 11 between 4 and 7 to get (517).

Divisibility rules:

There are simple rules to check if a number is divisible by another number without doing long division:

• Divisible by 2 if it ends in an even digit
• Divisible by 3 if the sum of its digits is divisible by 3
• Divisible by 4 if the last two digits form a number divisible by 4
• Divisible by 5 if it ends in 0 or 5
• Divisible by 6 if it is divisible by both 2 and 3
• Divisible by 9 if the sum of its digits is divisible by 9
• Divisible by 10 if it ends in 0

Exponent rules:

There are basic rules for simplifying expressions involving exponents:

Series formulas:

And then ChatGPT added

Certainly! Here are a few additional math tricks in markdown format:

Square of Any Number:

To square a number close to a base number (b), you can use this formula: For example, to find (42^2), which is 2 more than 40 (a nice round number), use the formula: ((b + c) \times (b - c) + c^2), where (c) is the difference between the number and the base. For (42^2), it’s ((40 + 2) \times (40 - 2) + 2^2 = 1681).

Percentage Calculations:

To quickly find percentages of numbers, use shortcuts:

• To find 10% of a number, move the decimal point one place to the left.
• To find 1% of a number, move the decimal point two places to the left.
• To find 50% of a number, simply divide the number by 2.
• To find 25% of a number, divide it by 4.

Finding Multiples:

For finding multiples of numbers:

• To find multiples of 5, take the last digit and double it.
• To find multiples of 9, the sum of the digits should be divisible by 9.

Checking Prime Numbers:

To quickly check if a number is a prime number:

• Check divisibility by numbers up to the square root of the number. If it’s not divisible by any of these numbers, it’s likely prime.

Divisibility by 11:

If the difference between the sum of the digits at odd places and the sum of the digits at even places is 0 or divisible by 11, the number is divisible by 11.

Square Root Approximation:

To approximate the square root of a number, start with an initial guess and then refine it using the formula: (x_{n+1} = \frac{1}{2} \times (x_n + \frac{number}{x_n})). Iterate this formula, where (x_0) is the initial guess and (x_{n+1}) is the refined approximation.

These tricks can help make mental math and problem-solving more efficient across various mathematical operations.