Backdoor strategies

Posted on October 23, 2009 by GRE Tutor

Sometimes applying common sense or backdoor strategies will get you to the correct answer more quickly and easily. The key is to be open to creative approaches. Often this involves taking advantage of the question format. These three methods are extremely useful when you don’t see – or would rather not use – the textbook appraoch to solving a question.

Picking Numbers
Picking numbers is a handy strategy for “abstract” problems – ones using variables either expressed or implied – rather than numbers. An expressed variable appears in the question (”Jane had x apples and 3 oranges…”). Questions with implied variables describe a problem using just numbers, but the only way to solve the problem is by setting up an equation that uses variables.

Problems that lend themselves to the picking numbers strategy involve simple math, but the variables make the problem complex. They include those where both the question and the answer choices have variables, expressed or implied; where the problem tests a number property you don’t recall; or where the problem and the answer choices deal with percents or fractions

Step 1. Pick Simple Numbers
These will stand in for the variables.

Step 2. Try Them Out
Try out all the answer choices using the numbers you picked, eliminating those that gave you a different result.

Step 3. Try Different Values
If more than one answer choice works, use different values and start again.

Backsolving
Some math problems don’t have variables that let you substitute picked numbers, or they require an unusually complex equation to find the answer. In cases like these, try backsolving: Simply plug the given answer choices back into the question until you find the one that works. Unfortunately, there are no hard-and-fast rules that identify a picking numbers question from a backsolving problem. You have to rely on two things: The experience you gain from answering practice questions, and your instinct. Combining these two skills will point you to the fastest solution for answering a problem. If you do this using the system outlined below, it shouldn’t take long.

Step 1. Estimate Whether the Answer Will Be Small or Large
Eyeball the question and predict whether the answer will be small or large. Your estimate needn’t (and shouldn’t) be precise; it just has to reflect your ‘feel’ for the relative size of the answer.

Step 2. Start with B or D
For small-quantitty answers, start backsolving with answer choice B; for large-quantity answers, start with D. By starting with B or D, you have a 40% chance of getting the correct answer in a single try because GRE answers are listed in order of ascending size. For example, if you start with B, you have these three possibilities: B is right, A is right (because B is too big), or B is too small.

Step 3. Test the Choice That You Did Not Start With
If B is too small or D is too large, you’ll have three choices left. In either case, testing the middle remaining choice immediately reveals the correct answer.

Elimination
How quickly can you solve this problem?

Jenny has 228 more marbles than Jack. If Bob gave each of them 133 marbles, she will have twice as many marbles as Jack. How many marbles does Jenny have?
a. 95
b. 190
c. 228
d. 323
e. 456

If you know a bit about number properties, you can solve it without doing any calculations. If Jenny and Jack each had 133 more marbles (an odd number), Jenny would have twice as many (an even number) as Jack. Since an even number minus an odd number is an odd number, Jenny must have an odd number of marbles. That allows us to eliminate B, C and E. Since Jenny has 228 more marbles than Jack, you to eliminate A as well. Therefore, the correct answer has to be (D) and you didn’t have to do any math to get it!

Elimination works on fewer problems than either picking numbers or backsolving. Where you can apply it, it’s very fast. When you can’t, the other two methods and even the straightforward math are good fallback strategies. You should use elimination if:

• the gap between the answer choices is wide and the problem is easy to estimate, or
• you recognize the number property the test maker is really testing

Number properties – the inherent relationshps between numbers (odd/even, percent/whole, prime/composite) – are what allow you to eliminate in correct answers in number property problems without doing the math.

Math content on the GRE
Arithmetic – about a third of all questions
Algebra – about a sixth of all questions
Geometry – about a third of all questions
Graphs – about a sixth of all questions

About a quarter of all questions are presented in the form of word problems.