lnm87 wrote:
I have a question and it's about the strategy to solve this question in less time - i solved it in 2:04. The question arises from St.2 which gives us a condition too open to test and most likely leading to both YES and NO cases. So, i started solving statement 1 and found that it's not sufficient. Then, statement 2 which is easy to say insufficient. Together they again leaves a wide area to cover up, leading to both YES and NO possibilities. I didn't test numbers.
What i thought, afterwards, is that i should have solved St.2 first as its easy and then St.1. Had i done so, i would have atleast known that x is dependent on y, eventually, what St.1 defines. So, together the two statements give us 2 conditions which lead us to two different answers. But i think approaching in this manner would not have made much difference time-wise.
OR
Could i have just solved St.1 and straight went to solving both statements together as st.2, independently, is nothing. But, still it leaves one with slight questions of whether all things have been checked.
OR
Do you think that number picking would have been best to do.
Thanks in advance.
First, a general comment if you're trying to reach conclusions about strategy: you should only make inferences from official questions. I can guarantee that if a prep company teaches, say, 'backsolving', then backsolving will be far more useful on that company's questions than it is on the real GMAT (on the real test, it's almost worthless as a strategy on higher-level questions). So you risk reaching incorrect conclusions if you focus on anything besides official problems.
This question is clearly not an official question. For one thing, if you pick numbers, then using the simplest numbers (positive integers) you're going to get a "no" answer to the original question. In most (not all, but most) real GMAT yes/no DS questions, if you can answer the question you'll usually get a "yes" answer, and when you can't answer (when information is not sufficient) it's the "no" answer that's normally the harder one to get. And if this question were official, I'd normally expect the answer to turn out to be C. Normally you'd have two cases from Statement 1 that might give two different answers, and the perhaps useless-looking inequality in Statement 2 would either rule out one case, or would ensure that regardless of which case you have, you get the same answer to the question. If the inequality in Statement 2 were reversed, that's exactly what would happen here - the answer would be C, because whether x = y or x = 2y, either way the answer to the question is "no".
I point that out just to emphasize why these unofficial questions can be counterproductive to look at, because if you studied official problems set up in a similar way, you'd learn how these questions are typically patterned, and learn how to guess more successfully at similar official DS questions (of course not every official question will fit a pattern you observe, but you can raise your chances). Prep company questions often don't match those patterns.
To your question: under normal circumstances, when you intend to solve a question properly (so you're not racing to beat the clock at the end of a test, and feel you understand the content of a question well enough that you have a chance to answer properly) it's normally a waste of time to think about which statement to consider alone first. It's true that in some cases, technically you'd save a bit of time by looking at Statement 2 first instead of Statement 1, but you'd spend a lot more time trying to identify those situations than you'll save when you notice them. Since you need to consider each Statement alone regardless, you might as well just look at S1 first, then S2.
The situation is different if you're desperately short on time, or don't feel you understand the question perfectly (but understand something about it). Then I'd always look at the simpler Statement first, since at least then you'll be certain to eliminate some answer choices quickly, and if you end up forced to guess because, say, you have 3 seconds left, you won't need to do so purely randomly.
As for when to test numbers, and when to do other things, that's a complex question. It depends partly on the nature of the question -- on some questions, number-picking is a good strategy (in fact, to prove statements are *not* sufficient, sometimes it's the only strategy), and on some it's a very bad strategy. But it also depends on the abilities of the test taker. On a question like this, say:
If k is a positive integer greater than 10, what is the remainder when k^2 is divided by 8?
1. k is a prime number
2. k < 20
then a test taker who is both comfortable with algebra, and who has a good foundation in number theory, shouldn't pick numbers. Using Statement 1, if k is prime, then k is odd, so k = 2m + 1 for some integer m. So k^2 = (2m + 1)^2 = 4m^2 + 4m + 1 = 4(m^2 + m) + 1 = 4(m)(m+1) + 1, and since m and m+1 are consecutive integers, one of them is even, and 4(m)(m+1) is divisible by 8 for sure. So k^2 is exactly 1 greater than a multiple of 8, which means k^2 gives us a remainder of 1 when we divide it by 8, and Statement 1 is sufficient alone. Statement 2 is not (since k can be even or odd, which will produce different answers to the question), so the answer is A.
The test taker capable of solving that way will save a lot of time, compared to the test taker who chooses numbers, particularly because k^2 ends up being quite large here. But a test taker who wouldn't be comfortable solving that way should definitely test numbers. Trying a few values of k, both less than and greater than 20, using Statement 1, one will always find that k^2 produces a remainder of 1. That's no proof that any mathematician would accept that the answer is 1, because it's impossible to test every prime number. But it's persuasive evidence that the answer is always the same, so by testing numbers, you at least can get a basis for a 'guess' that has a high probability of being correct.
For higher level test takers, I'd normally recommend the following: if you think a statement is sufficient, try to prove it. If you think a statement is not sufficient, and can see two simple situations that you'd expect would produce two different answers, then pick numbers. If neither of those things are true, try to do a bit of work first (some algebra, say, or some conceptual thinking) and then decide. Number picking is a very good fallback though no matter what, since picking numbers at least gives you a good basis for a guess most of the time, and sometimes will prove the statements aren't sufficient when the answer is E.
In the question in this thread, I solved without picking numbers at first. But because (for the reasons I pointed out above - it is not structured like an official question) the answer wasn't what I expected, I generated some simple numbers to confirm that I hadn't accidentally flipped an inequality around and made a careless error. That's something I'd suggest doing to a test taker who is prone to making careless errors; if spending an extra 20 seconds lets you notice mistakes a quarter of the time, that's a very wise time investment. For a test taker who has difficulty with pacing overall (that's most test takers!) and who does not make many careless errors, I'd probably recommend skipping that confirmation step though, since in that case saving the time would be more important.
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