Using 1 vs 2 Smart Numbers.

[b.shmorhun]

Hello,

Could anyone explain when we can use 2 Smart Numbers to solve a problem and when we can only use 1?

Here is an example I made up where you can use two smart numbers:

1) Hoses A and B fill 600 gallons in z minutes. Hose A fills 600 gallons in a minutes. In terms of z and a, how many minutes does it take hose B to fill 600 gallons?

A) a/(z+a) B) az/(z-a) C)az/(a-z)

-->The answer here is to pick any 2 smart numbers where z<a, preferably that are both factors of 600.

I noticed in FDPs, normally only one smart number can be used, but with Rates and Work -- doesn't seem to be a problem.

[RonPurewal]

You have to think about each problem individually, and determine whether the quantities depend on each other.
If you have two unknowns but they have to satisfy some kind of relationship, then you can probably pick only one of them. If they can vary independently of each other (like the ones here), then you can pick both of them.

[b.shmorhun]

Thanks for the help! You guys are awesome.

[RonPurewal]

You're welcome.

(Two months later... ?)

[PaulN139]

Hi there, it took me a while to find this topic. So glad to have found it as I am having issue understanding "Using 1 vs 2 Smart Numbers" on GMAT OG questions.

In the Study Guide, it says I can only pick 1 smart number per question. Then I found comments (as below) , explaining that so long as the question doesn't give a concrete value, and that the relationship to the unknown value cannot provide you with one, you can pick a smart number.

But I have seen answers picking 2 smart numbers in a single question that seem to be dependent.

Allow me to start with a question that's similar to the OG question I am having trouble with...

During a trip, Tom travelled y percent of the total distance at an average speed of 20mph, and the rest of the distance at 40mph. In terms of y, what was Tom's average speed for the whole trip?

My thoughts:
I would have picked a number for y as the total distance.

Or

I would have pick y as a percentage OF the total distance. the "OF the total distance" part is ANOTHER smart number (i.e. 100 miles). That would mean I have picked 2 smart number in a single questions.

I then get confused about picking smart number that might give me false/incorrect information.

Can you maybe help me understand where I am missing the point here? Or further elaborate what you have explained below?

Thank you very much. Very much appreciated.

[tim]

My thoughts:
I would have picked a number for y as the total distance.

Or

I would have pick y as a percentage OF the total distance. the "OF the total distance" part is ANOTHER smart number (i.e. 100 miles). That would mean I have picked 2 smart number in a single questions.

I then get confused about picking smart number that might give me false/incorrect information.

Can you maybe help me understand where I am missing the point here? Or further elaborate what you have explained below?

As near as I can tell, the only place where you appear to be missing the point is where you said you could choose option A *or* option B and then concluded that this meant you would pick two smart numbers. If you picked one of those options *or* the other, you would end up only picking one smart number. In most cases, you should stick to one smart number, so it sounds like you had the right idea here as long as you took your own advice and implemented only one of those options. :)

Let us know if you have further questions. I'm not convinced I fully addressed your concerns, but it was a little tough to figure out exactly what your real question was.

[PaulN139]

My thoughts:
I would have picked a number for y as the total distance.

Or

I would have pick y as a percentage OF the total distance. the "OF the total distance" part is ANOTHER smart number (i.e. 100 miles). That would mean I have picked 2 smart number in a single questions.

I then get confused about picking smart number that might give me false/incorrect information.

Can you maybe help me understand where I am missing the point here? Or further elaborate what you have explained below?

As near as I can tell, the only place where you appear to be missing the point is where you said you could choose option A *or* option B and then concluded that this meant you would pick two smart numbers. If you picked one of those options *or* the other, you would end up only picking one smart number. In most cases, you should stick to one smart number, so it sounds like you had the right idea here as long as you took your own advice and implemented only one of those options. :)

Let us know if you have further questions. I'm not convinced I fully addressed your concerns, but it was a little tough to figure out exactly what your real question was.

Hi Tim,

thanks for your prompt reply. Sorry I wasn't clearer with my question as I am trying to get my head around it.

You mentioned that for either option, I am actually only picking 1 smart number. Here's what I was thinking, kindly bear with me...

For this particular question (OG13-PS162), the MGMAT explanation says I can either pick a smart number for the actual Total Distance *or* for y (percentage of total distance)

For option A: I am sure I am only choosing 1 smart number (y=100 for Total Distance)
For option B: It seems like I am choosing 2 smart numbers. Allow me to explain.

For option B (pick y as a percentage OF the total distance): say I am picking y (1st smart number) as 20%, then I am picking Total Distance (2nd smart number) as 100 miles. Which makes y=20miles. But if the 2nd smart number is 120miles, then y=24miles.

This issues came to me as I was looking thru the explanation on the NAVIGATOR and it says "We can choose a smart number for y, if y=40, then in the first leg of the trip, Tom traveled 40% of 100 miles". Where did this 100 miles come from? Isn' this another smart number?

I hope my question isn't confusing you.

Thanks again.

[tim]

I see. First, you don't *have* to pick a second smart number; you could just use 40% as the distance for the first part rather than 40, then the total distance is 100% (which should be obvious because of the word "total"). The method you described just dropped the % sign. Of course, you *can* pick a second smart number (100) if you want to; please refer to Ron's post above about how you can pick two smart numbers (as long as you're comfortable doing so), provided they are independent of each other.

[RonPurewal]

basically, the deal is this:
if you have a relationship involving N number of quantities, you can generally pick (N - 1) smart numbers.

in the example at the head of this thread, there is a relationship involving three quantities: "a", "z", and the answer to the problem (which doesn't have a name). so, you can pick two quantities.

(this observation doesn't apply when more than one relationship is presented. in that case, you'll just have to think about how much freedom you have to choose things in whatever particular situation is at hand.)