Basic GMAT Strategies Flashcards
Picking numbers is a good strategy when:
Picking numbers is a good strategy when:
- Variables, fractions or percentages in the question stem, no real numbers.
- Variables, fractions, or percents in the answer choices
- Must Be/Could Be/Cannot Be Questions
- Questions that are hard or complicated and fulfill all the above.
REMEMBER: Every high scorer on GMAT must know how to quickly pick smart numbers and when to apply that strategy in order to get through QUANT on time so practice!!!
How to pick numbers in Problem Solving:
How to pick numbers in Problem Solving:
- Pick permissible numbers, pay attention to the question, if asked for age don’t pick odd numbers if says x is odd pick an odd number for x.
- Pick manageable numbers, i.e. easy numbers or numbers that make equation easy. I.e. in d/12 don’t pick d=2 but rather d=12 or 24 etc. Look in question stem and answer choices for clues about what the most manageable numbers might be.
- VARIABLES: It’s just fine to pick 0 or 1 in questions with variables.
- If you get two correct answers after picking numbers for variables, pick a new set and test only the two or more correct answer to get the ultimate correct answer.
- Exception to having to re-pick numbers: For “could be” questions, e.g. “which of the following could be odd?” you can just pick first answer choice that works.
- FRACTIONS: If fractions are involved in the question stem, picking the lowest common denominators or numbers that appear frequently as denominators in answer choices are good picks. For instance if 1/3 and ¼ are in question stem then 12 would be the lowest common denominator and a good choice for the number to pick. If a frequent denomination in answer choices is 625, that’s a good number to pick.
- PERCENTS: Picking numbers also works well in questions where answer choices are in percent. Picking 100 is a good choice because it makes calculations and later-on expressing it in % easier.
- MUST BE/Could BE/Cannot Be: on these questions you can pick numbers and plug them into every answer choice or you can pick different numbers for each answer choice, trying either to eliminate or to confirm it. It works well in many cases to pick different numbers for each answer choice.
- Characterizing what you’re looking for in the answer choices will help you pick numbers.
- In Must Be and Cannot Be questions you have to go through all answer choices to make sure you found the one and only correct answer. But in a Could Be question you can safely pick the first answer choice that works. If none of the choices work you have to pick a new set of numbers. Think critically about what the question stems asks to pick the right numbers.
- Roman numeral questions often feature Must Be/Could Be/Cannot Be language in question stem. Here you can evaluate statements one at a time and eliminate answer choices as you go. Start with the statement that appears most frequently in answer choices so you can eliminate it quickly if it proves wrong.
Backsolving in Problem Solving:
Backsolving in Problem Solving:
- Backsolve by plugging numbers from answer choices into question stem, looking for answer choice that agrees with info in question. Plug in answer choice and solve arithmetically.
- Backsolve strategically, start with B or D. Numerical answer choices are in ascending or descending order, so if an answer is incorrect you can often see if it has to be larger or smaller.
- Backsolving works in word problems with ‘nice numbers’ (e.g. small integers, numbers ending in 0) and whenever you’re solving for a single variable in the question stem, e.g. the total sum of something.
- Backsolving only works well if it’s easy to know whether you must select an answer choice that is larger or smaller after one answer choice didn’t work out. If it isn’t it could potentially take too much time and not be the most efficient strategy.
- If you find correct answer you don’t have to test any more choices.
- High GMAT scorers must be trained in backsolving as you need to use the technique to get through quant on time. Practice to get faster and also to develop strategy to only have to test 2 answers because you can see the relationship and know if you need a much higher or smaller number right away.
WHEN not to use backsolving:
- when numbers are large or ugly (complicated)
- when more than one variable in question stem, e.g. instead of just the sum of something (as stated above) a combination of variables (e.g. V1 - V2). In these questions, solving the normal way is better.
Picking Numbers in Data Sufficiency:
Picking numbers in DS:
Can use this strategy in DS question for questions that contain variables, unknown quantities, or percents of an unknown whole. If question stem gives you an equation that results in a range (e.g. = > 3) then you can pick numbers.
⇒ Pick at least two different sets of numbers, trying to prove that the statements are insufficient by producing two different results. (it’s easier to prove insufficiency than sufficiency).
- Pick permissible and manageable numbers!
- Don’t hesitate to pick numbers 0 and 1 as they have unique properties that make them great candidates for the picking number strategy.
- When you pick your two sets of numbers it’s important that you try different sets of numbers that are likely to produce different results. Types of numbers that can produce different results: positive vs. negative, fractions vs. integers, odds vs. evens etc.
- If after picking two sets of numbers that have different properties (negative vs. positive, odd vs. even etc.) you get the same result each time, you can say with reasonable confidence that a statement is sufficient.
BASIC PRINCIPLES of NUMBER PICKING IN DS:
BASIC PRINCIPLES of NUMBER PICKING IN DS:
- To evaluate a statement (or the statements combined), you must pick at least two sets of numbers.
- When picking the second set of numbers, try to produce different answer than that given by first set to see if you have to determine it’s insufficient.
Combining Statements in DS:
Combining Statements in DS:
- Only if both statements on their own are insufficient do you then consider the statements together. You can then combine the two statements to make one long sentence essentially. So, at this stage you are solving the question like a Problem Solving question using all the information you are given. The difference is that you stop solving as soon as you know you CAN solve. That saves time that you need later in the section for more complicated questions.
- The two statements will never contradict each other but they might add information that gives you more clues about variables, e.g. one statement says x>-5 and the other says x=positive number.
- When combining statements and then starting to think about numbers to pick start with the more restrictive statement and find permissible numbers to pick that also satisfy the other statement.
- When combining statements often you can use the same numbers as before when you were looking at statements separately. You can usually pretty quickly see whether the two statements combined offer any new information that can make a statement sufficient or if it doesn’t add anything new besides what had already proven insufficient in the statements separately.
BASIC PRINCIPLES of COMBINING STATEMENTS in DS:
BASIC PRINCIPLES of COMBINING STATEMENTS:
- Each data statement is true. Therefore, when combining statements, look for values that are permitted by both statements.
- Treat combined statements as a long statement.
- Never combine statements unless each statement is insufficient on its own.
Getting to Answer After Combining statements in DS:
Getting to Answer After Combining statements:
- If statement 1 says x = -1 or 1, and statement 2 says, x = 1, or 2 then combined you know that x must be 1 to satisfy both statements. So x=1 and answer is C.
- If statement 1: x = -1, or 0 and statement 2: x
Strategic Guessing in DS:
Strategic Guessing in DS:
- Use sound DS guessing strategy for very complicated questions.
- Skip statement that looks more complicated and go straight to the easier one first. Even if you can only declare insufficiency or sufficiency on this one you have already increased your chance to find the right answer.
- On the GMAT, complicated or hard-to-evaluate statements are more likely to be sufficient than insufficient. ⇒Avoid E and lean toward A unless you have a logical reason to suspect that the statement is insufficient. Not a guarantee that the answer is right but if you are falling behind in time this strategy will help move forward more quickly.
- REMEMBER: No particular question will make or break your GMAT score but spending too much time on one question and losing valuable time for others where then maybe you have to guess because you’re running out of time or worse you can’t finish in time, will hurt your score.
- Be sure you know the rules for eliminating answer choices absolutely cold by test day.
- Be wary of guessing that a statement is insufficient unless you can see exactly why it is. If you don’t know how to deal with a statement, guessing that it’s sufficient is often the better strategy.
Strategic Guessing in Problem Solving:
Strategic Guessing:
- If you have lost time win it back by strategic guessing. You’ll get a high penalty if you don’t finish in time.
- BUT: GMAT builds in twists and writes problems in complicated ways so don’t rush. Testmakers base many wrong answers on common misperceptions. Make a strategic guess.
- Strategic guess is good if you just don’t know how to approach a problem.
- Some problems are even best solved using guessing techniques. Remember GMAT mainly tests your ability to find efficient solutions through critical thinking.
- Every so often they give you a set of choices with only one logically possible answer. ⇒Look at answers first before you decide approach.
- Hardest questions are the ones where you’re most likely to have to guess on and if you get them wrong they are also the ones to least affect your score. So Guess!!
- GMAT asks specific questions where they want you to guess. If Question stem says approximately, that’s a clear signal that you should guess.
- When guessing remember: if answer choices is number that’s also in question stem or easily related to numbers in question stem, i.e. just the sum of numbers, then it’s most likely wrong.
Techniques to good Guessing in Problem Solving:
Techniques to good Guessing in Problem Solving:
- eliminate likely wrong answers using knowledge of problem and of GMAT tendencies.
- Keep eye on big picture, don’t waste time on a question you can’t seem to figure out.
- Use critical thinking! Some answers are logically impossible.
- Estimate the answer
- Eliminate Numbers appearing in the Question stem
- Eliminate Oddball, that doesn’t mean the number that’s notably bigger or smaller because GMAT does build in such tricks so it could be the right answer. What this means is the only fraction in the answer choices, or the only negative number, or the only root of a number etc. Those are likely wrong so eliminate.
- Eliminate uncritical solutions. Because GMAT is a test of critical thinking, answers you’d get by simply mashing numbers together are usually wrong.
- On “which of the following” questions, favor D and E (60% probability). Reason: Testmakers hide correct in those question in the last answers so if you haven’t eliminated them for other reasons, there’s a good chance, one of the two is the right answer (only true for problem solving in quant section). If you want to solve rather then guess, then start with answer E in “which of the following” questions.
“Which of the following” questions:
In “Which of the following” questions where you have to go through the answer choices to see which one applies always start with answer choice E.
Positives and Negatives when Picking Numbers:
Sometimes on the GMAT it makes a huge difference whether the numbers you picked are negative or positive. the GMAT uses that tactic so make sure that if both are permissible to pick positive as well as negative numbers. The special properties of -1, 0 and 1 make them important numbers to consider when picking numbers for DS questions and for “could be/must be” kinds of Problem Solving questions.
Picking Numbers Between -1 and 1:
Because numbers between -1 and 1 can make things larger or smaller in different ways than do other numbers, they’re good numbers to pick when testing if one expression is always less than or greater than another.
Solving DS questions in Number Properties:
- Simplify equations and inequalities first.
- Pick numbers to show sufficiency or insufficiency
- In questions with equations with variables, if you have to consider statements combined because separately they are insufficient, solve for one variable in the equation in one statement to find out something about one of the variables. Once you know something about one variable, you can then go back to the equation and figure out something about the other variable.
E.g. Is x>y?
(1) 9x = 4y
Simplifying gives you x = 4/9y. Then pick numbers and you’ll see that depending on whether x and y are positive or negative you’ll get different results. I.e. insufficient.
(2) x > - y
Pick numbers and again you’ll see that depending on whether x and y are positive or negative the answers can be different. i.e. insufficient.
Now combined:
We found that x = 4/9 y. Put that in inequality in statement (2): 4/9y>-y I+y
4/9y + y > 0
13/9 y >0
Looking at 13/9 y > 0 we know that y can’t be 0 and has to be positive.
Now go up again and look at x = 4/9 y. If y can’t be 0 and is positive then x must be smaller than y because anything multiplied by a number between 0 and 1 (so a fraction smaller than 1) will become a smaller number.
I.e. x
Solving Questions About Factors and Multiples:
As with all number properties questions, picking numbers is a good strategy.
Keep these in mind when picking numbers:
- Every number is both a factor and a multiple of itself (because it can be divided by itself and when multiplied by 1 is a multiple of itself)
- 1 is a factor for every number.
- 0 is a multiple of every number.
Solving “Which of the Following Questions”:
Remember in which of the following questions you should always begin with answer choice E. So, most of the times you’ll pick numbers and then plug them in the equations, inequality, expression etc. in answer choice E first.
Picking numbers:
A good strategy for a lot of questions with variables. But remember: If after picking permissible numbers you see that more than one answer choice fulfill the requirement, i.e. are right, you have to pick a new set of numbers and then test them on just the numbers the worked out the first time.
Questions with Variables and Roman numeral answer choices:
In questions on the GMAT where you are provided with three statements in Roman numerals that contain variables and have to decide which ones are true, PICK NUMBERS. When deciding which of the three statements to begin with (I, III, or III) go with the one that appears the most in answer choices.
So you pick permissible numbers and create an original sequence which you base all other calculations on. For instance if Question says that an arithmetic sequence is a sequence where after the first one each term is the sum of the preceding term and a constant, just decide that the constant be 3 and create a sequence for instance like this:
6, 9, 12, 15 etc. adding a constant of 3 each time. Use this sequence as an original sequence on which you base your calculations on. Test the sequences in the 3 statements based on this original statement. If you are asked which of the three statements is also an arithmetic sequence, remember that an arithmetic sequence is a sequence where each next number is exactly the same distance away from the preceding (e.g. each number is 9 numbers higher than the previous).
