Problem Solving

Hello all

Can I say 0 is a multiple of 5??


Thanks!!!!!

technically speaking, yes..zero would be a multiple of all the numbers..
1 x 0 = 0
2 x 0 = 0
3 x 0 = 0
4 x 0 = 0
5 x 0 = 0
..and so on...

but i am not sure if you would face such situation in GMAT. why dont you PM the experts and ask them and let us know too??

thnx..

Great question - and, yes, 0 is a multiple of all numbers. That's pretty important to know, as 0 is a great equalizer on a lot of problems that could ask:

x is an even number...

x is an integer that is a multiple of both 3 and 5...

x is a nonnegative integer such that...

If you think about 0, it's unique in so many of its applications:

0x = 0
0/x = 0
x^0 = 1
x/0 = undefined

That if 0 is a permissible option for a variable, it's a huge gamechanger, so the GMAT has an incentive to keep 0 in play for Data Sufficiency questions in particular. On DS questions, if there's just one "No" answer and all the others are "Yes", that renders the statement insufficient. So knowing that DS questions often feature that one exception-to-the-rule, special-case number, you should be alert for the potential of 0 since 0 is such a unique number that it's quite likely to be that exception to the rule when the GMAT needs one.

Just to respond to Ian's point...

The OG is a great study resource but GMAC itself will tell you that it's not designed to reflect proportional content coverage of the GMAT and that, because its questions have all been retired for quite some time now, the current test probably looks at least substantially different. High-scoring students also tend to report that the OG lacks a high concentration of the advanced-difficulty questions that they see on the official exam and on the official practice tests.

And that all makes perfect sense. GMAC has a responsibility to show people the general scope of content coverage and question type for the exam so that no one has to completely fly blind into the test, but it also has a responsibility to the business school community to keep it from being a test of how well you can memorize the question setups in the OG - it has to require you to think, too.

When we create advanced questions and evolve our lesson materials, we incorporate what we learn from the official www.mba.com practice tests - on which number theory, abstract algebra, etc. seem to have a higher rate of occurrence than they do in the OG - and the qualitative reports of students and instructors regarding their experience with the official test. To that, many have similarly mentioned that they wish they had seen more of the number theory type preparation and that they saw a higher rate of data sufficiency questions than problem solving.

So with that in mind, and knowing that:

-Unique number properties are clearly in play, and questions that feature 0 do appear on the official practice tests
-Data sufficiency questions tend to feature the "most of the time the answer is A but in a few unique cases it's B, so you need to be careful" logic
-When we do pose questions like those that feature 0 to students, they tend to miss them
-The GMAT quantitative section needs to evolve to become more difficult given the glut of scores at 49-50-51

It's pretty logical to infer that items like "properties of zero" will appear on the GMAT, and that, if unaware of them, students have a high likelihood of missing them.

Wayne Gretzky is famous for saying that he was successful in hockey because he didn't go to where the puck was, but instead went to where the puck would be by the time he got there. Our goal is to prepare students for the test that they'll take on test day, and test is known to not be limited to questions that appear in the Official Guide.

Ian Stewart wrote:

Brian@VeritasPrep wrote:
The OG is a great study resource but GMAC itself will tell you that it's not designed to reflect proportional content coverage of the GMAT and that, because its questions have all been retired for quite some time now, the current test probably looks at least substantially different. High-scoring students also tend to report that the OG lacks a high concentration of the advanced-difficulty questions that they see on the official exam and on the official practice tests.

And that all makes perfect sense. GMAC has a responsibility to show people the general scope of content coverage and question type for the exam so that no one has to completely fly blind into the test, but it also has a responsibility to the business school community to keep it from being a test of how well you can memorize the question setups in the OG - it has to require you to think, too.

When we create advanced questions and evolve our lesson materials, we incorporate what we learn from the official www.mba.com practice tests - on which number theory, abstract algebra, etc. seem to have a higher rate of occurrence than they do in the OG - and the qualitative reports of students and instructors regarding their experience with the official test. To that, many have similarly mentioned that they wish they had seen more of the number theory type preparation and that they saw a higher rate of data sufficiency questions than problem solving.

So with that in mind, and knowing that:

-Unique number properties are clearly in play, and questions that feature 0 do appear on the official practice tests
-Data sufficiency questions tend to feature the "most of the time the answer is A but in a few unique cases it's B, so you need to be careful" logic
-When we do pose questions like those that feature 0 to students, they tend to miss them
-The GMAT quantitative section needs to evolve to become more difficult given the glut of scores at 49-50-51

It's pretty logical to infer that items like "properties of zero" will appear on the GMAT, and that, if unaware of them, students have a high likelihood of missing them.

Wayne Gretzky is famous for saying that he was successful in hockey because he didn't go to where the puck was, but instead went to where the puck would be by the time he got there. Our goal is to prepare students for the test that they'll take on test day, and test is known to not be limited to questions that appear in the Official Guide.

First, I wasn't discussing any particular company when I mentioned prep company questions; I was just describing a general impression I've gained from questions posted on forums. You seem to have interpreted my comments as an indictment of one particular company, and I meant no such implication.

Second, if you're going to argue that it's 'pretty logical' that special exceptions about zero will appear on the GMAT in the future, and if you'll dismiss any actual evidence about how zero has been tested on the GMAT in the past, we're simply going to have to disagree. I don't base my impressions of the test solely on the content of the Official Guides; that was just an easy reference that anyone interested could check. While this may not matter to you, I did just go over about 60 DS questions from GMATFocus and 300 DS questions from GMATPrep, and found exactly one in which zero was a relevant 'special case'. That question was the following:

If z^n =1, what is the value of z ?

1) n is a non­zero integer.
2) z>0


and you'll notice that Statement 1 even alerts you to the fact that it is important to consider the case that n might be zero. So I've looked at about 600 official DS questions and found just one where zero was, in some sense, an 'exception' that was important to consider. Take from that what you will.

It obviously cannot do any harm to know the properties of zero, but, as I pointed out in my last post, there are very few situations where some special property of zero can even be tested; in most GMAT subjects, zero is irrelevant. While there are many 'traps' on the GMAT, they're normally based on how categories of numbers behave (negatives vs. positives, or "fractions" between 0 and 1 vs. numbers bigger than 1) or on misapplications of mathematical rules (dividing by an unknown in an inequality without knowing its sign, counting equations and unknowns when you shouldn't, etc), and not on special properties of a single number.

Thank you guys!!!

I have another questions, can I say 5 is factor of 0? although I know 0 is a multiple of 5