Need help with remainder problem

[apc2012]

A question from the Manhattan GMAT number properties book asks:

If x and y are positive integers and x/y has a remainder of 5, what is the smallest possible value of xy?

the answer is 30, but I don't understand why it's not 66. They calculate x and y to be 5 and 6 respectively, where as i got 11 and 6. I don't understand how 5/6 has a remainder of 5. Please help.

Thanks!

[Patrick_GMATFix]

Hi Ana

As you probably know (since you're studying from MGMAT) the algebraic equation that ties the numerator (n), denominator (d), quotient (q) and remainder (r) is n = dq+r. For instance when 13 is divided by 5, the quotient is 2 and the remainder is 3 >> 13 = 5*2 + 3.

When the numerator is smaller than the denominator the integer part of the result of the division is 0. for instance, 5/6 = 0.833. The integer part of the result is another name for the quotient. 5 divided by 6 has a quotient of 0 and a remainder of 5 >> 5 = 6*0 + 5.

In any integer division for which the top is smaller than the bottom, the remainder is the top.

Examples
5/6 has a remainder of 5.
3/12 has a remainder of 3.

To create timed drills with remainder questions, set topic='Number Properties' and difficulty='700+' in the Drill Generator. You can also practice just remainder questions by searching for the keyword 'remainder' in the GMATPrep solutions search page.

Hope that helped,
-Patrick

[dinesh19aug]

Here's a simpler way:

x= qy + 5 ........ q is quotient
What should the value of a so that x is minimum??
If q =0 (q cannot be negative, becuase you never get negative quotient)
Hence X = 5
If X =5, that what will be min. the value of Y so that remainder is 5
So Y = 6 (Plugin the values .... if it is difficult to visualize)

Hence XY = 30.

[Testtrainer]

Remainder questions can be a real pain. Most test-takers should either plug in answers or pick numbers. In this particular case, plugging in answer choices (which I didn't see) would probably be a snap. When possible, picking numbers is also quite easy (I believe an example can be found in the OG quant book).

For advanced (85th percentile+) test-takers, knowing certain formulas can be a help, but again, they're a pain to memorize (especially considering everything else you need to know).

Hope this helps...