Strategies to solve Data sufficiency problems

Biggie Smalls Strategy #1: Biggie SmallsConsider this Data Sufficiency problem: What is the value of integer z? 1) z is the remainder when positive integer y is divided by positive integer (y – 1) 2) y is not a prime number Statistically, more than 50% of respondents in the practice tests incorrectly choose answer choice A, that Statement 1 alone is sufficient but Statement 2 alone is not sufficient. Why? Because they’re not quite sure “what numbers to dial.” People know that they need to test numbers – Statement 1 is very abstract and difficult to visualize with variables – so they test a few numbers that come to mind: If y = 5, y – 1 = 4, and the problem is then 5/4 which leads to 1, remainder 1. If y = 10, y – 1 = 9, so the problem is then 10/9 which also leads to 1, remainder 1. If they keep choosing random integers that happen to come to mind, they’ll see that pattern hold – the answer is ALMOST always 1 remainder 1, with exactly one exception. If y = 2, then y – 1 = 1, and 2 divided by 1 is 2 with no remainder. This is the only case where z does not equal 1, but that one exception shows that Statement 1 is not sufficient. The question then becomes, “If there’s only one exception, how the heck does the CAT expect me to stumble on that needle in a haystack?” You need to test “Biggie Smalls,” meaning that you need to test the biggest number they’ll let you use (here it can be infinite, so just test a couple of really big numbers like 1,000 and 1,000,000) and you need to test the smallest number they’ll let you use. Here, that’s y = 2 and y – 1 = 1, since y – 1 must be a positive integer, and the smallest of those is 1. The problem is that people tend to simply test numbers that come to mind (again, over half of all respondents think that Statement 1 is sufficient, which means that they very likely never considered the pairing of 2 and 1) and don’t push the limits. Data Sufficiency tends to play to the edge cases – if you get a statement like 5 < x < 12, you can’t just test 8, 9, and 10 – you’ll want to consider 5.00001 and 11.9999. When the CAT gives you a range, use the entire range – and a good way to remind yourself of that is to just remember “Biggie Smalls.” Biggie Smalls Strategy #2:   Consider this example: a, b, c, and d are consecutive integers such that the product abcd = 5,040. What is the value of d? 1) d is prime 2) a>b>c>d This problem exemplifies why keeping Big’s words top of mind is so crucial – difficult problems will often “satisfy your intellect” with interesting math…and then beat you with negative/positive ideology. Here it takes some time to factor 5040 into the consecutive integers 7 x 8 x 9 x 10, but once you do, you can see that Statement 1 is sufficient: 7 is the only prime number. But then when you carry that over to Statement 2, it’s very, very easy to see 7, 8, 9, and 10 as the only choices and again see that d = 7. But wait! If d doesn’t have to be prime – primes can only be positive – that allows for a possibility of negative numbers: -10, -9, -8, and -7. In that case, d could be either 7 or -10, so Statement 2 is actually not sufficient. You’ll like the life you live much better if you go from negative to positive (or in most cases, vice versa since your mind usually thinks positive first), and if you don’t know (is that sufficient?) now, after checking for both positive and negative and for the biggest and smallest numbers they’ll let you pick, now you know.