davidbeckham wrote:
could someone please explain the logic behind writing 81.2 in form 81 + 0.2 or 81 + 1/5?
Everything you learn about remainders will be about integers, so you generally would always want to rewrite a question like this using integers instead of decimals. From the definition of a quotient and a remainder, then when we divide integer n by integer d,
n = qd + r
where integer q is the quotient, and integer r is the remainder. The remainder must be between 0 and d-1 inclusive, so r < d is always true. If you divide by d on both sides, you get
n/d = q + (r/d)
Since r < d, then r/d must be between 0 and 1. So when you divide n by d, the quotient q is the whole number part of the result, and r/d is the decimal or fractional part of the result. If we use that for this question (and I'm going to change the letters, because whoever designed this question did something profoundly annoying -- they're using "n" where "d" is normally used in a quotient/remainder definition, and using "k" where "n" would normally be used) :
When the positive integer n is divided by the positive integer d , the remainder is 11. If n/d = 81.2 , what is the value of d?then 81 is the whole number part of the result, so is the quotient, and 0.2 = 1/5 is the decimal part of the result, so equals r/d. Since r = 11, and r/d = 1/5, we have 11/d = 1/5 and d = 55.
So if you replace 0.2 with a fraction of integers, and you know how to use the definition of a remainder, it's a one-line solution. It's true that you can solve this question in other ways, as the post above mine suggests, but if you're doing something like testing answers here, you're spending far more time on this question than you need to.
_________________
GMAT Tutor in Montreal
Contact me for online GMAT math tutoring, or about my higher-level GMAT Quant books and problem sets, at ianstewartgmat at gmail.com
ianstewartgmat.com