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diegocuenca: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Thu Feb 24, 2011 1:17 pm

by diegocuenca » Wed Jul 06, 2011 5:39 pm

When positive integer x is divided by positive integer y, the reminder is 9. If x/y = 96.12, what is the value of y? Are there any alternative explanations besides the answer in the book?

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Source: Beat The GMAT — Problem Solving | Wed Jul 06, 2011 5:39 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jul 06, 2011 6:21 pm

diegocuenca wrote:When positive integer x is divided by positive integer y, the reminder is 9. If x/y = 96.12, what is the value of y? Are there any alternative explanations besides the answer in the book?

I posted a solution here:

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Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Wed Jul 06, 2011 6:54 pm

diegocuenca wrote:When positive integer x is divided by positive integer y, the reminder is 9. If x/y = 96.12, what is the value of y? Are there any alternative explanations besides the answer in the book?

Hey!

This is pretty analagous to the post that's already been linked to, but maybe I'll use a few different words

Whenever you're doing a long division problem and the divisor doesn't divide cleanly into the dividend, you have three options when it comes to expressing what's left over: (1) remainders, (2) fractions, and (3) decimals. For instance 5/3 can be expressed as "1 with a remainder of 2," or "1 and 2/3," or 1.66666.

(The remainder, when used by itself, is pretty clearly the least informative of these modes of expression, which is why we more or less abandon it after third grade, but the GMAT likes to throw it back into the mix

.) So, when you've got a remainder and want to transition into one of the other forms of expression, the fractional equivalent of that remainder is the same as remainder/divisor (and the decimal equivalent is just the decimal equivalent of that fraction). Here we know that the divisor is y and the remainder is 9, so the fractional equivalent must be 9/y, which apparently also equals .12 (in other words, the entire whole number component--in this case 96--is totally irrelevant to the problem).

9/y = .12 --> .12y = 9 --> y = 9/.12 = 900/12 = 75.

Ashley Newman-Owens
GMAT Instructor
Veritas Prep

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Thu Jul 07, 2011 12:14 am

x= qy +9

x/y = 96.12

qy+9/y = 96.12

qy+9 = 96y + 0.12y

0.12y = 9

y = 75

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diegocuenca: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Thu Feb 24, 2011 1:17 pm

by diegocuenca » Thu Jul 07, 2011 11:59 am

Thanks guys, I really like that short cut Ashley. So right away if they give you the divisor and the remainder and the decimal equal. you can figure it out straight from there. I def had to look at this one a few different times.

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