Basic GMAT Strategies

Question 1

Picking numbers is a good strategy when:

Answer 1

Picking numbers is a good strategy when:

1. Variables, fractions or percentages in the question stem, no real numbers.
2. Variables, fractions, or percents in the answer choices
3. Must Be/Could Be/Cannot Be Questions
4. 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!!!

Question 2

How to pick numbers in Problem Solving:

Answer 2

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.

Question 3

Backsolving in Problem Solving:

Answer 3

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.

Question 4

Picking Numbers in Data Sufficiency:

Answer 4

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.

Question 5

BASIC PRINCIPLES of NUMBER PICKING IN DS:

Answer 5

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.

Question 6

Combining Statements in DS:

Answer 6

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.

Question 7

BASIC PRINCIPLES of COMBINING STATEMENTS in DS:

Answer 7

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.

Question 8

Getting to Answer After Combining statements in DS:

Answer 8

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

Question 9

Strategic Guessing in DS:

Answer 9

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.

Question 10

Strategic Guessing in Problem Solving:

Answer 10

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.

Question 11

Techniques to good Guessing in Problem Solving:

Answer 11

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.

Question 12

“Which of the following” questions:

Answer 12

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.

Question 13

Positives and Negatives when Picking Numbers:

Answer 13

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.

Question 14

Picking Numbers Between -1 and 1:

Answer 14

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.

Question 15

Solving DS questions in Number Properties:

Answer 15

• 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

Question 16

Solving Questions About Factors and Multiples:

Answer 16

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.

Question 17

Solving “Which of the Following Questions”:

Answer 17

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.

Question 18

Picking numbers:

Answer 18

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.

Question 19

Questions with Variables and Roman numeral answer choices:

Answer 19

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).

Question 20

Picking Numbers for DS Questions With Variables:

Answer 20

If you have a complicated DS question with variables check if you can pick a number for one of the variables to find out something about the value of the other one, e.g. what range of numbers ( certain numbers) that variable must lie in.

Question 21

Advanced Quant: Questions to Ask as You’re Solving Complex Quant Questions:

Answer 21

Ask yourself these questions as you read and solve complex quant questions. Try to do that each time to get a systematic process down that you can apply each time:

1. What exactly is the problem asking for?
2. What are the quantities I care about? (often the unknowns)
3. What do I know? (certain quantities, relationships etc.)
4. What don’t I know? (results, intermediate unknown that you need to get to solution. BUT: sometimes there are unknown that are not important for solving the question so don’t need to know all unknowns)
5. What is the problem testing? (i.e. what aspects of math are they testing? Learning how to see that right away will help you learn how to tackle these problems)

REMEMBER: Jot down any given numbers or formulas you remember as you read the question!!!

Question 22

Advanced Quant: What to do when you get stuck on complex quant questions:

Answer 22

Ask yourself the core questions for solving complex quant questions again:

1. What exactly is the problem asking for?
2. What are the quantities I care about?
3. What do I know?
4. What don’t I know?
5. What is the problem testing?

Now do this:

• reinterpret the given information
• write down any intermediate results you already know from the other strategy you used to solve the problem
• move away from the approach that didn’t work and instead find a new approach!

Question 23

Advanced Quant: Strategy: Draw Out the Solution:

Answer 23

In some questions it’s beneficial to do a quick drawing to visualize the problem, relationships etc. Especially in geometry, rate/distance, and word problems it is a good strategy to draw it out.

Question 24

Advanced Quant: Strategy: Solve an Easier Problem

Answer 24

If a problem contains larger numbers or complicated expression, you can simplify part of the problem, e.g. a given equation (while of course still keeping all the relationships etc.) and solve that first to understand how the math works and what the relationships are once. Once you know that you can return to the more complicated problem and apply the same solution path.

E.g. if x and y are positive integers and 1620x/y^2 is the square of an odd integer, what is the smallest possible value for xy?

1620 is a large number. In order to understand how the math and relationships works here you could look at a smaller number first. e.g. 20x/y^2.

If 20x/y^2 yields the square of an odd integer we have to somehow get rid of the even number in the numerator. 20x will be an even number but for the solution of the expression 20x/y^2 to be odd we have to get rid of the even number because even divided by odd would always be even. That shows us that y^2 has to get rid of the even number in the numerator. Since 20 = 4 x 5 we know that y^2 has to be 4 and y = 2. Then we have left: 5x = square of an odd integer. In order to get a square x has to be 5 as well and the solution would be 25 and xy would be 2 x 5 = 10.

Now apply this to the larger number in the question:

In order for y^2 to get rid of 1620 and make it an odd number we have to find out what odd number multiplied by an even number would result in 1620. 1620 divided by 2 would yield 810 which is still an even number. But divided by 4 it would yield: 405 which is odd. So we know y^2 = 4 and y = 2. Now we have 405x at the top We have to find the smallest possible number for 4 so that 405x = square of an odd number. We already know 405 x 4 is even, but 405 x 5 = 2025 which is the square of 45, an odd integer.

That means: y = 2, x = 5 and xy = 5x2 = 10

Question 25

Advanced Quant: Strategy: Be Organized

Answer 25

Part of solving complex quant questions within a limited amount of time is being well organized. So organize your work well, job down given numbers and relationship as you read the question, note down intermediate results, keep your notes on your scrap paper separate.

Question 26

Advanced Quant: PS Strategy: Choose Smart Numbers

Answer 26

One of the most productive strategies on GMAT. Good strategy for: - When concepts in a problem are especially complex. - Almost all questions with variables in answer choices. - Often for fraction of percent problems - If question puts specific conditions on input without giving exact numbers. (e.g. if problem specifies that a number is a positive even integer simply pick 2 to make calculations quick and easy)

Question 27

Advanced Quant: PS Strategy: How to Choose Smart Numbers

Answer 27

- In questions where you are given multiple relationships, part of picking smart numbers is to decide where to start, i.e. which variable to give the value of 100 for instance. Take a moment to make a smart decision here because depending on where you make that start the rest of the calculation will be easy or messy. - As you are going through answer choices to test which one yields the amount you got through the calculation after picking your numbers, you can stop the moment you realize that the number won't be the same even if the calculation is not completed (e.g. if you need the units digit to be 0 and while you are testing an answer realize quickly the units digit will not be 0) - Practice picking smart numbers a lot and you will see how proficient this strategy is on the GMAT!!!

Question 28

Advanced Quant: PS Strategy: Work Backwards!

Answer 28

Great Strategy especially when the problem asks for a single variable and the answer choices offer nice and easy integers. REMEMBER: Start with B or D because that allows you to eliminate certain other answers without having to test them, e.g. by recognizing whether numbers need to be larger or smaller. If you pay attention to the math you can often get by by just testing two or three answers. REMEMBER: You can stop when you find an answer that works.

Question 29

Advanced Quant: PS Strategy: Test Cases!

Answer 29

In some questions you have to test multiple numbers to eliminate answers until you get to the right answer. On PS problems often a good strategy in must be true or could be true problems. REMEMBER: When testing cases start with the simplest number that fits the problem's parameters. E.g. If n is a positive integer, what must be true of n^3 - n? A) It is divisible by 4 B) It is odd C) It is a multiple of 6 D) It is a prime number E) It has, at most, two distinct prime factors. Any positive integer for n will help you get to the answer. Since choosing the simplest numbers makes calculations easier and faster, choose 1 first. Then chose other numbers to continue eliminating until you get to the right answer, here C. Another way of solving the problem is to notice that: n^3 - n = n (n^2 - 1) = n (n - 1) (n + 1) = (n -1) n (n+ 1) That means the expression is the product of three consecutive integers. Any product of three consecutive integers is divisible by 2 (because there is one even number in the group) and by 3 (in group 0, 1, 2, 0 is divisible by any number and therefore also by 3). So a product of three consecutive integers is always divisible by 6. Also: Notice that since there is no upper limit, n could be a large number, making the value of the expression large so that the number can contain more than 2 distinct prime numbers, so you can eliminate that answer choice as well. In DS when you test cases your goal is to prove the statement insufficient. So if you test with one value, for the next value think about what number you could test that would give you a different outcome and make the statement insufficient. If you cannot prove a statement insufficient within a reasonable amount of time you have to assume it's sufficient and move on. Ideally you want to understand why you get the same outcome each time but if you can't figure it out within a reasonable amount of time and have tested different cases, assume it's sufficient and move on!

Question 30

Advanced Quant: PS Strategy: Avoid Needless Computation

Answer 30

Most GMAT questions, even the more complex ones need only easy computation to arrive at the right answer once the difficult concept or trick int he problem has been correctly identified. I.e. if you need to do a lot of complicated computation you are likely not using the right approach. In that case you can almost always be sure: A SHORTCUT must exist. Try to find the shortcut to save time!!! How to avoid needless computation: 1. Estimate! Whenever a question says things like "approximately" "closest to" "most nearly equal to" do not try to find the exact value but estimate! E.g. The percent change from 29 to 43 is approximately what percent of the percent change from 43 to 57? break the expression up into pieces and simplify complex numbers: 43-29/29 = 14/29 = approx. 1/2 57-43/43 = 14/43 = approx. 1/3 1/2 is what percent of 1/3? 1/2/1/3 = 1/2 x 3 = 3/2 which is 150/100 which is 150% Another way of calculating: ``` 1/2 = x/100 (1/3) 1/2/1/3 = x/100 (1/2) 3 = x/100 3/2 = x/100 3/2% = x 150% = x ``` NOTE: You can also usually estimate when the answer choices are far apart. 2. Heavy Long Division: When there are long complex divisions you can almost always approximate, or take common factors out. e.g. in fractions with decimals get rid of the decimal points so you are only dealing with integers. Look closely at complex fractions because most of the time you can factor out and simplify extensively. E.g. 3.507/10.02 = 3507/10020 = 7 (501)/10 (1002) = 7 (501)/10 x 2 (501) = 7/20 = 35/100 = 0.35 3. Quadratic Expressions in Word Problems: Some word problems make you create quadratic equations. Sometimes the computation can get messy. When you see that happening and the answer choices are simple numbers try working backwards by trying the answer choices after you have created the equations based on the info in the stem. E.g. A shoe cobbler charges n dollars to repair a single pari of loafers. Tomorrow, he intends to earn 240 dollars repairing loafers. If he were to reduce his fee per pair by 20 dollars, he would have to repair an additional pair of the loafers to earn the same mount of revenue. How many pairs of loafers does he intend to repair tomorrow? A) 1 B) 2 C) 3 D) 4 E) 5 from stem we can create these two equations: ``` x = number of loafer pairs he will repair n = dollars charged for repairing one pair of loafers ``` 1. xn = 240 2. (x + 1) (n - 20) = 240 You could now separate for n in first equation and substitute that into the second equation to find the value of x but the calculation might get messy and take longer than if you switched to backsolving now. Go to answer choices plug in B first. 1. 2n = 240 n = 120 2. 3 x 100 = 300 300 is larger than 240 so that can't be the right value of x. You can also see that x has to be larger because that would make n smaller and that would make the whole second equation smaller which is what you want. So try D next: 1. 4n = 240 n = 60 2. 5 x 40 = 200 200 is too small so x has to be smaller than 4 there is only one answer that could be correct: C) 3.

Question 31

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 31

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)! 2. Apply Cutoffs Sometimes you can eliminate answer choices that are below or above a certain threshold. sometimes you can find the threshold by imagining a slightly different scenario for the question in your head, e.g. if half of a group had a certain feature, then the ratio would change a certain way etc. In previous example you can easily see that since 1/3 of seniors and 1/4 of juniors study Japanese, between 1/3 and 1/4 of all students study Japanese. Normally 1/3 + 1/4 of a number would be more than 1/2 of that number (e.g. if total is 100 1/3 + 1/4 would be 33 + 25 = 58 which is more than 1/2 of 100) but in this case because a lot more students, twice as many, are juniors and only 1/4 of juniors study Japanese, you know that the fraction of total students who study Japanese has to be less than 1/2. This is actually a weighted average problem. You can calculate this as: 1/3 of total students are seniors, 2/3 are juniors. 1/3 of 1/3 study Japanese and 1/4 of 2/3 study Japanese. So the weighted average of all students who study Japanese is: 1/3 x 1/3 + 2/3 x 1/4 = 1/9 + 2/12 = 4/36 + 6/36 = 10/36 10/36 of all students study Japanese. That's less than half. That also means that the fraction of students who do not study Japanese must be more than half. So you can already eliminate Answer choices A, B, and C from above as they are all less than 1/2. If you continue the weighted average calculation, 10/36 study Japanese, 26/36 don't. That's 13/18 who don't study Japanese!!! 3. Look for Positive-Negative When some of answer choices are positive and some negative and you are in a situation where you have to guess try to figure out if the answer has to be positive or negative. 4. Draw to scale In geometry questions you can draw on your scrap paper to scale or look at the picture given and often estimate. REMEMBER: If a PS question does not say that the picture is not drawn to scale, then it is drawn to scale. Drawing to scale works often enough so you should think about using that if you can't come up with an approach to solve the problem.

Question 32

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 32

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 33

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 33

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 34

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 34

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 35

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 35

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 36

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 36

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 37

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 37

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 38

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 38

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs:

Question 39

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 39

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 40

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 40

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 41

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 41

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 42

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 42

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 43

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 43

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 44

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 44

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 45

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 45

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 46

Advanced Quant: PS Strategy: Advanced Guessing Tactics:

Answer 46

Try to solve with the strategies explained above but if nothing else helps you should guess and move on. But instead of guessing randomly, use one of these tactics: 1. Look for Answer Pairs: GMAT likes to build in one last obstacle by pairing answer choices in mathematically relevant ways so that you may have done the math right but solved for the wrong unknown or forgot to subtract from 1 in the end etc. Answer pairs may: 1. Add up to one on probability or fraction questions 2. add up to 100% in questions with percents 3. Add of to 0, i.e. be opposite to each other 4. multiply to 1, i.e. be reciprocals of each other. That Means: You can often ELIMINATE unpaired answer choices!!! Also: the way the answer choices are paired might provide clues as to how to solve the problem. E.g. At a high school the junior class is twice the size of the senior class. 1/3 of seniors and 1/4 of juniors study Japanese. What fraction of students of both classes don't study Japanese? A0 1/6 B) 5/18 C) 5/12 D) 7/12 E) 13/18 A look at answer choices shows that you have paired answer choices that add up to 1 each, 5/12 + 7/12 = 1 and 5/18 + 13/18 = 1. You can be sure that 1/6 is not the correct answer so eliminate. You can set up double-set matrix and solve. But picking numbers is easier. look at fractions in stem and pick smart numbers. Let's say there are 12 in junior class and 6 in senior class, altogether 18 students. 1/3 or 2 of seniors study Japanese and 4 do not. 1/4 or 3 of juniors study Japanese and 9 do not. So of the 18 students 4 + 9 = 13 don't study Japanese. So the answer is 13/18, E)!

Question 47

Manhattan GMAT Rules for Picking SMART NUMBERS:

Answer 47

Follow these: - Do not pick 0 or 1 - Do not pick numbers that appear elsewhere in the problem. - If you have to choose different numbers, choose different numbers, ideally with different properties (odd, even etc.)

Question 48

Rounding Up and Down When Estimating:

Answer 48

When you estimate numbers try to round some up and some down in a problem in order to minimize rounding errors and over or under estimating.