HashimB

Geniee, I think this is an great solution. Note that this question combines averages with ratios. The average part gives us the equation to find the relationship and from that relationship we can find the ratio. Remember that often on the GMAT each of the methods (fraction, semi-colon or "to") are used interchangeably.

You can use a modified version of the probability method I laid out previously. Example: A group of 8 friends want to play a trivia game. How many different ways can the friends be divided into 4 teams of 2 people? Solution: We want four teams of two people: Set up the basic problem for selecting two cards: __ __(Team 1: P1 - P2) __ __(Team 2: P1 - P2) __ __(Team 3: P1 - P2) __ __(Team 4: P1 - P2) Enter information for the scenario described: Put in the number of choices as we attempt to fill each seat. 8 7 (Team 1: P1 - P2) 6 5 (Team 2: P1 - P2) 4 3 (Team 3: P1 - P2) 2 1 (Team 4: P1 - P2) We will be taking the product of all of these numbers to count the options. BUT, before we finish we need to consider whether there are any "teams" we have counted more than once. Consider that a team with Vikas and Mitzi would be counted as a different team than Mitzi and Vikas in out layout above. Actually that would be the same team so we need to reduce our count. We reduce our count by dividing by the potentially interchangeable places on each team. So for each team we must divide by 2! (1, 2 spaces), as to not count duplicates. 2! = 2. Consider also that if V and M are on team one we can get the same group of teams were they both on three. We will also need to reduce out options to account for this. So we must divide by 4! (1, 2, 3, 4 teams). 4! = 24. Answer: [(8)(7)/2 * (6)(5)/2 * (4)(3)/2 * (2)(1)/2]/24= (28*15*6*1)/24= 7*15 = 105 As always, I hope this helps.

Whether Correct that whether is used where there are two options. You will find there where the GMAT is testing that rule, you are given the choice between "whether" and "if." Also, you should recognize that the two options are not always stated. For example: Whether I cut my hair ... The meaning of the sentence could be to suggest that I am deciding whether to cut my hair OR NOT. This is the most likely case. OR The meaning of the sentence could be to suggest that I am deciding if to cut my hair, go for a walk, eat dinner, play cards or just do GMAT. If leaves open the entire world of alternative actions, whereas whether narrows the scope of the discussion to only the one choice and its "opposite." Like Like creates a similarity between the two items joined by the like. So since the choice would say that the 3 items lists are like "the rarer something becomes." If the choice/sentence instead were to state the rarer something, like ..., That would be better, but still a problem. Because we are talking about something ... general ... and the examples are just illustrations of what the something might be. General Comment I was going to comment earlier on other things about the sentence that made it unlike the real test, but instead just opted to provide whatever learning could be taken from this sentence. Where there are "bad"/questionable answers in examples provided, I try to point out the most glaring problems to the extent that those problems affect the best response. Sometimes I attribute the errors to the typist and assume the example was properly constructed.

Pronouns SPOT: Look for Pronouns in the underlined part of the sentence. RULE: A pronoun must clearly and correctly refer to one thing. The pronouns to be concerned about on the test are She, He, It, They (and their possessive forms), which/that, and who/whom. "Which" appears on the GMAT in two ways, as the introduction of a modifier, or as part of the introduction of a modifiers. Here, the introduction to the modifier "for which" clearly ties the modifier back to whatever came immediately before it, so it is fine. The Ing Thing SPOT: Look for –ing form of verbs. RULE: Use the –ing form of verbs for an action in progress –OR– to begin a modifier. Here the "making" is beginning a modifying, but when we consider the meaning (MEANING IS THE DRIVING FORCE BEHIND ALL GMAT TESTED RULES), are the SERVICES making the beneficiaries pay? The services are not making the beneficiaries do anything and therefore making cannot work. Answer E Note that I always focus my explanations on the rules and not the examples. The RULES are constant and you can reuse them. The examples are almost meaningless once you know the rules well. As always, I hope this helps.

Idioms SPOT: Look for your Idiom triggers. RULE: Each idiom has a rule (word and/or structure). Memorize the rules. Before choosing answers that use "like" you should consider your idioms/idiomatic usages. Like vs. Such as: "Like" is used to point out similarities and "Such as" is used to illustrate examples. The meaning of the sentence would be nonsense if the intended though was that the three examples were all similar to something rare (that is unknown/unmentioned). Lists SPOT: Look for lists of two or three things. RULE: A list must be logically and structurally consistent. Some lists are about usage and meaning more than about balancing words or part of a "list." Some things that are often called idioms also have a particular parallelism/structure that their use must follow. The ___-er I am, the more I eat french fries. OR The more I eat french fries, the ___-er I am. Comments: The construction of the list in the non-underlined part, "a baseball card or a musical recording or a postage stamp", is unlike the GMAT. The GMAT would probably not use a word as ambiguous as rarer in the underlined part without some strong indicator in the sentence of which meaning applies. See OG 10th ed SC #104. Note that the word could mean less cooked or less common. As always, I hope this helps.

I thought I would point out somethings for you guys to think about. Remember that while many explanations rely on strange rules that might be hard to remember, the GMAT is a standardized test. Which means the rules that it can and will cover are both finite and predictable. The Ing Thing SPOT: Look for –ing form of verbs. RULE: Use the –ing form of verbs for an action in progress –OR– to begin a modifier. Since there is no action that is currently being done. None of the answer choices that change to an -ing form of a verb should be appealing to us. Prepositions SPOT: Look for words that indicate placement. RULE: Prepositions must be used literally (e.g., over means spatially above, around means spatially encircling et cetera). "At" means a location. The choice that changes to to at is incorrect. Advanced Verbs SPOT: Look for actions in two time frames or have + verb combinations. RULE: When two actions occur are in the same frame (past present or future) and not happening at the same time, we must use the have been + verb form with one of those verb to distinguish. We do have actions in two time frames, therefore the has + verb form is appropriate. BUT, note that we are already given that form outside of the underlined part and so we do not need it again (remember that it distinguishes one verb/timeframe from another). The choices that use the have + verb forms in the underlined parts are incorrect. I hope this helps.

4. If x and y are integers between 10 and 99, inclusive, is (x-y)/9 an integer? (1) x and y have the same two digits, but in reverse order. (2) The tens’ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit. Rephrase the Information Given x and y are integers between 10 and 99. This means that × and y are two digit numbers. No matter how simple, you should be in the habit of rephrasing information and questions in DS. The entire game in DS is to hide information. Rephrase the Question (x – y)/9 = i? We can rewrite/manipulate this to be: (x – y) = 9i? OR x = 9i – y? et cetera DS Second Guess: We are again changing from a question answered with values to one that is answered with information. Here it seems that we are concerned with divisibility and the rules that relate to divisibility. In order for the difference of × and y to be a multiple of 9 either each numbers is a multiple of 9 or neither number is a multiple of 9. AD | BCE Translate the Statements Statement 1. x and y have the same digits. Translation: Using our rules for the divisibility by nine, we see that this would not change the divisibility. So either both are divisible by nine or neither is divisible by nine. We know that the first case would answer the question, let's check the second case. 62 – 26 = 36 (neither digit a mult of nine) 91 – 19 = 72 (one digit a mult of 9 one not) Note the focus on the concept being tested (div by 9). In either case we know the difference will be a multiple of 9. Sufficient. Eliminate BCE. Statement 2. The tens’ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit. When Statements give you a finite number of options one strategy is to list and check those options. x = 31, 42, 53, 64, 75, 86, or 97 y = 13, 24, 35, 46, 57, 68 or 79 Remembering our work (NOT THE INFORMATION) in Statement 1, we already know that where the digits are each reversed we will get a multiple of 9 for the difference, so we need to see what happens when we are not using numbers with reversed digits. 31 – 24 = 7 This defies the previous case and so we get conflicting answers for Statement 2. Insufficient. Eliminate D. Answer A. COMMENTS: Many question such as this one that ask the test-taker to manipulate numbers, are actually divisibility questions. Again, I hope this helps. Sorry for the long posts.

3. If x and y are positive integers and x is a multiple of y, is y = 2? (1) y ≠ 1 (2) x + 2 is a multiple of y. Rephrase the Information Given x and y are a positive integers. This means that × and y are each greater than zero and each whole numbers. No matter how simple, you should be in the habit of rephrasing information and questions in DS. The entire game in DS is to hide information. x is a multiple of y means that: x = y × i, where i is any integer. Rephrase the Question y = 2? If y is two, that would make x an even integer. Let's rewrite our question as: x an even number? DS Second Guess: We are again changing from a question answered with values to one that is answered with information. AD | BCE Translate the Statements Statement 1. y not equal to 1. Translation: This does not tell us whether x is even or not. [Nor does it bring us any closer to knowing what y might be.] Insufficient. Eliminate AD. Statement 2. x + 2 is a multiple of y Translation: × + 2 = y × i. Since we also already know that x = yi, y must be 1 or 2. We know this because we know that adding two yields another multiple of y. This means that 2 is some multiple of y. Because 2 is only a multiple of 1 and itself, we still do not know what y is or whether x is even. This statement does not answer our question. Eliminate B. Statement 3. Together: Statement 1 tells us that y is not 1. Statement 2 tells us that y is 1 or 2. Therefore, we know that y must be 2, and that x must be even. Answer C. COMMENTS: Many number properties style DS questions can be treated as Algebra type questions with expressions that can be manipulated. I hope this helps.

2. Is the positive integer n equal to the square of an integer? (1) For every prime number p, if p is a divisor of n, then so is p2. (2) sqrt n is an integer. Rephrase the Information Given N is a positive integer. This means that n is greater than zero. No matter how simple, you should be in the habit of rephrasing information and questions in DS. The entire game in DS is to hide information. Rephrase the Question N = i^2 Since we know that n is positive, the only question left is whether it is an integer squared. Let's rewrite our question as is n a non-square integer. DS Second Guess: We are again changing from a question answered with values to one that is answered with information. AD | BCE Translate the Statements Statement 1. For every prime number divisor (code for factor), p^2 is also a factor. Translation: So if × is a prime factor, then ×^2 is a factor. This seems to implicate prime factorization. Which leads us to ask HOW MANY xs are there, the information tells us at least 2, but what about 3? Example: If 2 is a factor, then 4 is also a factor, but this does not stop 8 from being a factor. So the original number, n, could be 4 or 8. So n could be (but does not have to be) a non-square integer. Eliminate AD. AD | BCE Statement 2. sqrt n = i Translation: Which we can rephrase as n = i^2. This statement answers our question. Eliminate CE. Answer B. COMMENTS: Strong test-takers pick up hints from the question. Since, statement 2 seems to be an obvious manipulation of the original question, double check (but do not second guess) your work. Be confident, but careful.

1. If a bottle is to be selected at random from a certain collection of bottles, what is the probability that the bottle will be defective? (1) The ratio of the number of bottles in the collection that are defective to the number that are not defective is 3:500. (2) The collection contains 3,521 bottles. Rephrase the Information Given To find the probability of an event we take the number of desired events over the total number of possible events. We are given that we want to choose a defective bottle, of an unknown number of bottles. We should recognize that since defective is a "either or type concept", if we are told the number of non-defective bottles that would suffice as well. Rephrase the Question The real question here is: How many defective bottles there are and how many bottles there are total? NOTE: Data sufficiency questions RARELY are actually concerned about values, you should rethink this question to pose it a different way. DS Second Guess: Since what we actually want is the relationship between defective and total, we should consider that we would be able to answer the question with the information DEF/TOTAL. Translate the Statements Statement 1. Defective to non-defective is 3:500 Translation: We can extend to tell us that Def : Non-def : Total = 3 : 500: 503 We understand that this cannot tell us actual values because the ratio does not allow us to know the actual number of options. But our DS second guess, allows us to see that statement one gives us the relationship we were looking for and therefore can answer the question. Eliminate BCE. Statement 2. Total = 3,521 This statement tells us the total which is insufficient by itself. Eliminate D. Answer A. COMMENTS: Strong test-takers will understand how the test/question writer intended to trick the test-taker on each question. The offered mistake here is to take both pieces of information as being necessary, when in fact the relationship alone would suffice. Test-takers of average ability will treat this like a basic PS type ratio question and pick C as the answer in their desire to solve. Strong test-takers understand that solving the problem presented is not the goal of DS.

Curly, I will do a modified version of a recent question posted. An un-GMAT-ish issue comes up in the question as presented. The selection criteria allows for overlap in the alternate conditions. My modification removes that possibility. Example: What is the probability of drawing two playing cards from a normal 52-card deck and selecting two face cards or two cards with prime numbers on them? Solution: If there are 2 face cards chosen: Set up the basic problem for selecting two cards: __(C1 - FC) __(C2 - FC) Enter information for the scenario described: 12/52 (C1) 11/51 (C2) = (12)(11)/(52)(51) Note: It is usually best to wait on calculating values as long as possible. If there are 2 prime numbered cards chosen: __(C1 - PN) __(C2 - PN) 16/52 (C1 - B) 15/51 (C2 - B) = (16)(15)/(52)(51) When asked for the probability of one event OR another, find the probability of each event then add those probabilities. 12)(11) = 132 (16)(15) = 240 132 + 240 = 372 372/(52)(51) = 186/(26)(51) = 93/(13)(51) = 31/(13)(17) = 31/(some number that ends in 1) Since there are no combination questions on this page, I will suggest instead that you go to GMAT-SAT-LSAT-ACT Test Prep | Bell Curves where you can find pages that explain this topic with examples (after login go to: prepare -> strategy pages). The signup and access to the pages is free. Sorry to send you elsewhere, but the topic is just too much to explain in a post. Also note, that you will not have more than 2 questions on the topic "advanced statitics," consider whether you using your study time in a way that reflects that reality. If you have more specific questions, I would be glad to help. As always, I hope this helps. Success, Hashim GMAT Test Prep | Bell Curves - Business School Home

Which type? Combination-Permutations? or Probability?

Curly, I am not sure whether there is a one question per post limit on this forum, but there is on many forums, you are also more likely to get meaningful answers if you describe what you want when posting the questions. Are you unclear on a general method to solve? Or perhaps, these questions just presented you with some particular difficulty? You might also sort questions better so that you can focus on asking about and learning the patterns in solving each TYPE of question and not on just learning the particular examples. For instance: Questions 1,2 and 4 are not probability at all. Question 5(b), 6, 7 9 and 10 all share a common variation on the basic probability question. Once you become aware of patterns like these, you can narrow down the problems you are having in your studies and adjust your learning to maximize your results. As always I hope this helps.

Hey guys, This question has some ambiguity issues. Unlike questions on the real GMAT, this question requires us to make an assumption about the proportion in which the two men invested. We actually do not know that Bob invested ANY money. This could as readily be a sweat equity arrangement whereby Bob invests nothing. We do not know whether there were other transactions that would cause money to be invested in or spent by the business. If there is a profit, then there had to be some other transactions. We do not know how they were affected by the withdrawals. In short, this is just a poorly written example. You should probably not worry too much about it. While the intent of the question is probably not that, the writers of the GMAT are not going to leave that sort of uncertainty in the questions.

Note: This question is anbiguous as it does nto describe properly the drawing of the balls. We actually want to know whether the selection simultaneous. I will just assume that the balls are chosen one at a time. Probability questions can be solved by laying out the information carefully and asking the key questions for this question type. For the second part: we want RRBB (ignoring order) so we can lay out the question __(R1) __(R2) __(B1) __(B2) Then we place the probability of getting the result we want for each slot in that slot. 6/10 (R1) 5/9 (R2) 4/8 (B1) 3/7 (B2) So, to find the probability of getting RRBB, we multiply these numbers. Note: You should wait to do operations until the end of the question or as long as possible. Now we need to consider order, as long as the balls selected have two red and two black we have met the conditions of the question. Therefore, we want to make sure to count all possible rearragements of the selction order that would give this result. The forumla to find rearragements is (total things rearranged)!/(# thing 1)!(number of thig 2)! ... In this case, that would give us: 4!/(2!)(2!) = 6 so our answer should be: 6/10 (R1) 5/9 (R2) 4/8 (B1) 3/7 (B2) * 6 = 3/7 I hope this helps.

Hardee, You might also want to check out gmat.bellcurves.com. There are lots of practice problems that you can get there for free. DS adaptive quizzes with topic specific question or just mixed. You might also rethink your DS approach. Normally, when a student has high problem solving success and significantly lower DS success, it means that the person is not recognizing the differences between the two question types clearly. DS is about hiding (the test hides) and finding (you are to find) information. The tougher the DS problem the less likely the question posed is the question relevant to solving the problem. If you alter your mind set slightly to attack DS as more like a word scramble puzzle (e.g., what is the word pzzlue) and less like a crossword puzzle (in which you need to basically know the information yourself), you will be MUCH stronger. Consider DS using the following steps: 1. Write down the information given. 2. Write down the question posed. 3. Rewrite/decode/rephrase the information given. 4. Rewrite/decode/rephrase the question posed. 5. Consider the statements (rewrite/decode these also if necessary). You may also want to check out the DS Process download (a powerpoint presentation that demonstrates this in more detail) at gmat.bellcurves.com. Access and the DL are free. As always, I hope this helps.

At a quick glance, these questions seem to be fair approximations of the types of questions you will see on the GMAT (other than than the things I already commented on). You can probably practice with the material and be fine. I am not sure what post you are asking about. I do not see anything about real versus actual. Free free to repost here or PM me.

ss1, The approximate percentages I described at the top of the explanation are true for any normal distribution. 2% of the group is more than 2 SDs away from the mean (to either side), 14% of the group is between 1 and 2 SDs away from the mean (to either side), and 34% of the group falls between 1 SD and the mean (again to either side). Perhaps this diagram would be more clear: ----2SD----1SD---MEAN---1SD---2SD ||||2%-> There was a period where the GMAT asked SD questions which required that information much more than the current test seems to, but SD questions are not uncommon. Recent questions seem to emphasize the spacing aspect rather than the percentage and calculation aspect. As always, I hope this helps.

The important thing to remember is that each question type on the GMAT has a particular "hook." The hook is something (a) to remember to do or not do and (b) that is the central idea of that question type. For standard deviation (SD) questions, the hook is (a) remember that SD often represents ranges and (b) you must apply the SD from the average and know its corresponding percentage as shown below. --2SD - 1SD - Mean - 1SD - 2SD 2% 14% 34% ----- 34% 14% 2% This means that between 2sd and 1 sd there is approximately 14% of the group. For the first question: Within one SD means +/-8. 1SD - Mean - 1SD 23 31 39 So the question asks for ages within the range 23 to 39. 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39. 17 numbers. This question is slightly unlike an actual question because of the ambiguity of the term "within." which could mean that the manager did not want the 23 and the 39. Luckily, the answer that would correspond to that, 15, is not in the choices. For the second question: Group A: mean of 460 and SD of 20 means that our SD chart looks like: 420 - 440 - 460 - 480 - 500 Group B: mean of 520 and SD of 40 means that our SD chart looks like: 440 - 480 - 520 - 560 - 600 2% of group b scored below 440 16% of group a scored below 440 Since the groups are the same size this means 18% of the combined scored below 440 2% divided 18% is the fraction 1/9. I have to say that I have taught the GMAT for a long time and cannot recall seeing a question that asks about SD fractions. What was the source of this question? I also know that it is not an actual questions because of the answer choices. Numerical GMAT answers (or the answers of well written GMAT type questions) will always be in ascending or descending order. Remember to learn patterns in questions and not the questions themselves. I hope this helps.

The important thing to remember is that each question type on the GMAT has a particular "hook." The hook is something (a) to remember to do or not do and (b) that is the central idea of that question type. For ratio questions, the hook is (a) remember that ratios are relationships and not numbers and (b) you must find a multiplier to convert the ratios to numbers. Before Change Flowering(FP) to Non Flowering (NFP) 3 to 2 Let's call the multiplier here 'm' (note that in many ratio questions you will be given a real number that corresponds to a ratio which will allow you to calculate a multiplier) So we know that the REAL number of FP initially was 3m, that the real number of NFP was 2m, and the total number of plants is 5m. Then 140 nonflowering plants were removed: Therefore, the number of nonflowering plants, 2m, is reduced by 140 leaving us with 2m-140 nonflowering plants and 3m flowering plants. After Change: The ratio of FP to NFP is: 4 to 1 We can set up a relationship: 4/1 = 3m/(2m-140) Solving this tell us that m = 112 Answering the question for the original number of plants, 5m, gives us a result of 560. I hope this helps. Remember to learn patterns in questions and not the questions themselves.