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Re: When x/8 the remainder is 3 ... [#permalink]
You can also "square the remainder" - it's a shortcut that will save you time on questions like this.

The "square the remainder rule" isn't a universally applicable rule in math, but it's a handy shortcut in this specific scenario. It applies when:

1) We're dealing with remainders after dividing by a number containing a 2 (like 8, 16, 32)
2) We're raising the term (x) to an even power (x^2, x^4, etc.)

Here's how we would solve the problem using this shortcut:

When the exponent is even (e.g. x^4) and the divisor is a multiple of 2 (such as 8), the remainder when dividing the power (x^4) by 8 will be the same as dividing the square of the remainder (3) by the divisor (8).

Therefore, (3^2)/8 = remainder 1

If you were familiar with this rule, the only computation you would do is 9/8 = remainder 1.
As soon as you spot 8 as a multiple of 2, and (x^4) as an even exponent, you would recognise that this is a "square the remainder" question. You would reduce the time spent answering this question from 45-70 seconds to 15-20 seconds.

The GRE throws predictable questions with predictable time saving opportunities. I would recommend familiarising yourself with these time saving techniques! Ultimate Tuition has a GRE Quant Cheat Sheet that has over 160 pages of rules and patterns to know before the exam.

Check out the Ultimate GRE Quant Cheat Sheet
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