Bunuel wrote:
Ergenekon wrote:
Bunuel, you wrote that we shoud start by middle option. Can you explain the reason? Thanks.
Good question. +1.
On the GMAT, answer choices are always in ascending/descending order, so trying option C firsts gives an idea which direction to go next if C is not correct.
Two things about this - in a question like this one, there's no way to know, if you test an answer choice and find that it produces an answer that is too small, whether you should try out a larger or smaller answer choice. There isn't a strong relationship, when numbers are fairly similar in size, between the size of a number and the size of its 'prime sum'. The prime sum of 1,000,000,000, for example, is smaller than the prime sum of 67.
But when you
would know, after testing a wrong answer choice, whether the right answer is smaller or larger, you also should not test C first. I wouldn't test answer choices at all for a question like the one below (I'd use a quick estimate and units digits), but it illustrates how best to proceed if that's the strategy you decide to use:
If x is positive, and x^2 + x = 5112, what is the value of x?
A) 68
B) 70
C) 71
D) 72
E) 74
In this question, if x > 0, the larger the value of x, the larger the value of x^2 + x. So if we test an answer choice, and x^2 + x is smaller than 5112, we'll know the right answer is larger than the one we tested. If you decided then to test answer C first:
• 1/5 of the time you'll get lucky, and C will be correct
• 4/5 of the time, C will be wrong, and then you will need to test precisely one other answer choice (e.g. if C is too large, you could test A, say, and that will either be right, or if it's wrong, you'll know B is right)
But if you decide to test B or D first -- say we test B:
• 1/5 of the time you'll get lucky, and B will be correct
• 1/5 of the time, B will be too large, and you will know A is correct without testing any other answer choice
• 3/5 of the time, B will be too small, and then you only need to test D. If that's right, you're done, if D is too large then C is right, and if D is too small, then E is right
So in questions like this, you never need to test more than two answer choices, but you if you test B or D first, rather than C, you need to test only one choice twice as often (2/5 of the time instead of 1/5).
Testing answers isn't a very useful strategy anyway on the GMAT, at least for higher-level test takers, so this isn't as useful to understand as it might seem, but if someone is going to do it, it probably makes sense to know how to do it optimally.
And I'd add that there is a myth I've seen repeated in some prep materials that on "which of the following" questions, the GMAT typically makes the right answer D or E more often, so test takers working in order from A through E spend more time on the question. If you actually look at this empirically -- look at published official questions of this type to see how often each answer choice is correct -- you'll find there's no truth to that myth.