All I know about geometry in GMAT PS is that “figures are drawn as accurately as possible” (unless otherwise stated, which is rare). The arc, a little more than 3/2, looks only a bit smaller than the radius. So only B and C are feasible. C looks to big, so I’m going with B.

For the record: I know all about all of the math on the GMAT, including geometry. In fact, I quickly did the calculations in my head to make sure that B was in fact the correct answer. But this should not detract from the idea that figures in problem-solving are indeed drawn to scale and so can be carefully(!) eyeballed when one is stuck.

Personally, I’ve been known to put my fingers right up to the screen to make my careful eyeball estimations. Who cares how I get to the answer as long as I do so in under two minutes.

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That used to be true in the old days. The test instructions still say that, but if you look at this official GMATPrep question:

https://gmatclub.com/forum/in-the-figur ... 85154.html

the diagram is not to scale (and is very misleading), but the question doesn't say the diagram is not to scale. So I'm not sure these days to what extent test takers should trust GMAT PS diagrams (to be fair, that's the only misleading official diagram I've seen, so they're likely trustworthy the vast majority of the time).

It definitely can be useful to estimate answers from diagrams, but because of the question I linked to above, the safest thing to do is to draw the diagrams yourself, and estimate based on what you've drawn. Of course in this particular question, it won't matter at all, since the diagram is clearly to scale (we'd only need to redraw it if the 45 degree angle didn't look like a 45 degree angle). And if we wanted to solve this question properly, a 45 degree angle is 1/8 of a circle (180 is half, 90 is a quarter, 45 is an eighth), so π/2 is one eighth of the circumference, and the circumference is 4π, and since 2πr is the circumference, r = 2.
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\(2 π\frac{45r}{360} = \frac{π}{2}\)

Or, \(\frac{πr}{4} = \frac{π}{2}\)

Or, \(r = 2\), Answer will be (B)
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You’re not wrong about that figure you provided. It’s been around for a few years on the prep tests.

But undoubtedly the rule still holds because it’s explicitly stated in the directions.

Choosing between the directions that been consistent for decades and a one-off question from a practice test? Got to go with the former, especially because making educated guesses on this test are an absolute requirement to maximize one’s scores.

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Length of arc = \(\frac{central angle }{ 360}\) * 2πr

=> \(\frac{π}{2} = \frac{45}{360} * 2 * π * r\)

=> \(\frac{1}{2} = \frac{r}{4} \)

=> r = 2

Answer B
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Your not-wrong reply really bugged me (that’s a compliment by the way). I think I found an explanation: GMAT geometry has NOT always been drawn to scale. In addition, GMAC’s official tests include some very old material.

I actually found a link that provides past GMAT instructions: https://www.gmatix.com/history_of_gmat.htm

Note how the Quant directions only introduced “figures are drawn as accurately as possible” in the 80s. I suspect the question you provided has been around for a very long time, before the figures were drawn to scale.

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