MGMAT ADVANCED QUANT 2ND EDITION Q106

[MridulG275]

in MGMAT advanced quant guide Problem 106.

the radius of a circle is r yards.is the area of circle at least r square yards?

(1 yard=3 feet)

(1) the diameter of circle is more than 2 feet.

(2) if the radius of the same circle is f feet,the are of the circle is more than 2f square feet.

i think there is some issue with the solution.

when we rephrase question it is given:

Is 3.14r^2>=r? there seems to be an omission of unit square yard while solving the question.

the question has been rephrased to is r>=1/(3.14) yards ? whereas in my opinion it should be square yards.
And that we need to consider that 1yard^2=9 feet^2 while solving the question.

please correct me if i' m wrong.

[cgentry]

Huh. This is an interesting issue.

We need to keep in mind that "r" is a numerical value for yards, and that number exists independently of the units. The units only come into play when we try to convert between units.

So the question should really be

is 3.14*r^2 square yards >= r square yards? The unit exists only in that we are working with numerical values for area. If you have a science background (my undergrad degree is chemical engineering), this is probably a little bit irritating. I was always taught to track my units. But keep in mind that was for real-life applications. And while the GMAT allows real-life assumptions (more on that in a moment), GMAT problems are not meant to exactly mimic a real-life mathematical issue.

So in this case, if you're tracking units, both units would cancel. So then the question becomes "is 3.14 r^2 >= r?"

So here we get to the real life assumptions the GMAT will allow. We don't deal with negative dimensions. And also, since the problem states that the circle exists, r =/= 0.

So we can divide both sides of this inequality by r, and get

is 3.14 r >= 1?

And you can divide both sides by 3.14, to get

is r >=1/3.14 ?

Notice that I haven't done any unit conversions yet. Now, when we get to the idea of unit conversions, we need to put the units back into the question. Essentially, we're asking if the radius is greater than 1/3 of a yard.

[MridulG275]

Hi cgentry,

MY first instinct while solving this question was to look at the two statements(which were in feet) and therefore rephrase my question in feet form.However,since this problem involved areas i complicated the issue by in introducing the unit^2 issue.From all the similar problems i have encountered on GMATprep i had not yet been tricked by this issue yet.Great information about the constraint though that since a circle exists therefore r>0 ? i missed this and this could have simplified my calculations a lot.

Thanks for the help.

[RonPurewal]

Hi cgentry,

MY first instinct while solving this question was to look at the two statements(which were in feet) and therefore rephrase my question in feet form

^^ but you can't do this, since the QUESTION is phrased in terms of YARDS.

the question doesn't work anymore if you try to convert away from yards (since 1 linear yard = 3 linear feet, but 1 square yard = 9 square feet).
so, you need to convert the feet INTO YARDS instead.

does that make sense?