lsr

When adding a number that is greater than the arithmetic mean; the new arithmetic mean will be bigger. (i.e: the new number is pulling the average up) When adding a number that is equal to the arithmetic mean; the new arithmetic mean will be the same. (i.e: the new number has no impact on the average) When adding a number that is less than the arithmetic mean; the new arithmetic mean will be smaller. (i.e: the new number is pulling the average down) Since x

Answer is B. The question asks which quadrants contain the LINE (not LINE SEGMENT). Since the two points have the same y-coordinate, we know that it will be a horizontal line which will either be above the x-axis (b is positive), below the x-axis (b is negative) or on the x-axis (b is zero). Therefore, we only need information on 'b'. (I am assuming that 'a' does not equal 'c' - without this assumption we would need the first statement as well). (as a rule of thumb, I would not make any assumptions on the GMAT, but Princeton Review is sometimes sloppy about this).

I think it is D. The biologist claims that the PACE of deforestation is the problem (too high), therefore if the pace is slowed and the koala survives, then it is consistent with the biologist's claim. On the other hand, the politician claims that deforestration has to STOP in order for the koala to survive, therefore deforestation at any rate that allows for the survival of the koala is inconsistent with the politician's claim.

Answer is B. First statement: f(x)-4 is a vertical shift downward by four units; therefore f(x) can have 0,1 or 2 points of intersection with the x-axis -- not sufficient. Second statement: f(x-4) is an horizontal shift to the right by four units; therefore f(x) must also have 2 points of intersection with the x-axis -- sufficient.

Another one for B.

The line y = Kx + B will be tangent to the circle x^2 + y^2 = 1 if and only if B^2 - K^2 = 1. (to see why, either substitue the equation of the line into the eqaution of the circle and set the quadratic formula such that there is only one solution, or use the distance formula from the center of the circle to the line and set it equal to the radius of the circle). First statement: Since K+B=1 satifies the above condition only for one set of values (B=1 and K=0), we do not have sufficient information (K and B can take other values that satisfy the conditions in the first statement, but do not satify the conditions in the question stem). Not sufficient. Second statement: Same as in the first statement. (But in this case, both B=1;K=0 and B=-1; K=0 will satisfy the conditions in both the second statement and the question stem). Not sufficient. Both statements: There are two sets of values that will satisfy the conditions in both statements: B=0 and K=1 or B=1 and K=0; The first set of values does not satisfy the conditions in the question stem, while the second set of values does. Not sufficient. Answer is E.

The answer will depend on the respective dimenstions of the cereal boxes and the cardboard carton; since both statements together only provide us with the respective volumes, the answer is E.

Great explanation.

Elton, If x>5 then it must be true that x>0 (since every number that is greater than 5 is also greater than zero), x>5 is a subset of x>0. But we cannot say that it must be that x>6 (since not every number that is greater than 5 is also greater than 6), x>5 is not a subset of x>6. Once you find the solution set for x/|x| Another example, if you live in Chicago, then it must be true that you live in the United States, but I cannot conclude that it must be true that you live in Lincoln Park.

Another one for E.

x/|x| For x>0; x>1 For x-1 Therefore x is always greater than -1. Answer is B.

Another one for B.

Even if one of the statements was b=d, it would not have affected the answer, since under either interpretations (the mathematical definition of point of intersection, or the english definition of crossing) you would still have sufficent information to answer the question (it just that the two interpretations would lead to contradicting answers). However, it was just a side note. On a different side note, how did you upload the diagram? I have been trying to upload diagrams in the past and was never able to do so.

To find the points of intersections, equate the two equations and solve for x. a*(x^2) + b = c*(x^2) + d For a=c, either the two equations are the same (when b=d) or there are no points of intersecions. For a not equal c: x^2 = (d-b)/(a-c) Since x^2 is never negative, therefore the two lines will intersect only when the RHS is zero or positive. This will happen only when b=d and ac, or d>b and a>c, or d First statement: Either a=c=0 (in which case we are not dealing with parabolas), or a is positive and c is negative (a>c), or a is negative and c is positive (a Insufficient. Second statement: We know that b>d, but we don't know anything about the relation between a and c. Insufficient. Both statements: We a can be greater, less than or equal to c. Insufficient. Answer is E. As a side note, I am not completely comfortable with the phrasing of the question; in mathematics we usually deal with points of intersections (which is not the same as crossing), if the two equations were the same (a=c and b=d), then there would be an infinite numbers of points of intersections, yet the two parabolas will never technically cross each other. Also if b=d and a does not equal c, there would be one point of intersection, but again technically we could not say that the two parabolas cross each other.

The phrase "previously unknown" must have a reference point in order to convey viable information. It can be argued that everything we now know, was unknown at some point earlier in time. Thus, to take "previously unknown" to mean "it was unknown at some earlier point in time" would strip that phrase from its logical connotation. "previously unknown" means it was unknown previous to the point the pharse refers to ("previously unknown crystalline structure" means that it was the first time this structure was encountered) "Although Fullerenes-spherical molecules made entirely of carbon-were first found in the laboratory,..." From the first line of the argument, we know that the structure of the laboratory synthesized fullerenes was known by the time they have discovered the naturally occuring fullerenes, so the only way the natrually occuring fullerenes had a previously unknown structure, is if that structure differ from the one of the laboratory synthesized fullerenes.

maverick312, The argument is based on one premise: there is an over-representation of vehicals that are equipped with radar detector among the ones ticketed for exceeding the speed limit. Note that the conclusion in the argument does not refer to the number of speeding tickets each individual recieved, but just to a general behaviour pattern. In order to conclude that a group is likely to posses or exhibit a certain characteristic or behaviour pattern solely based on the premise that the group is over-represented in some category, we must first assume that the specified characteristic or behaviour pattern is dominant in that category. For example, if I were to change the conclusion to: clearly people that equip their car with radar detectors are more likely to drive at night. The conclusion will hinge on the assumption that in general people who are ticketed for exceeding the speed limit are more likely to drive at night; absent this assumption, the argument would sound ridiculous. Option A still requires the assumption that people who are ticketed are in general the ones who exceed the speed limit on a regular basis. (in essence, option A exacerbates the perplexity arising from the premise, but does nothing to link the premsie to the conclusion). Think of the argument as consisting of two premises and a conclusion. First argument (using option A) Permise 1: There is an over-representation of vehicals that are equipped with radar detector among the ones ticketed for exceeding the speed limit. Premise 2: Drivers who equip their vehicles with radar detectors are less likely to be ticketed for exceeding the speed limit than are drivers who do not. Conclusion: Clearly, drivers who equip their vehicles with radar detectors are more likely to exceed the speed limit regularly than are drivers who do not. Second argument (using option B) Premise 1: There is an over-representation of vehicals that are equipped with radar detector among the ones ticketed for exceeding the speed limit. Premise 2: Drivers who are ticketed for exceeding the speed limit are more likely to exceed the speed limit regularly than are drivers who are not ticketed. Conclusion: Clearly, drivers who equip their vehicles with radar detectors are more likely to exceed the speed limit regularly than are drivers who do not.

Premise 1: Fullerencess are rarely found in nature and can also be synthesized in a laboratory. Premise 2: The laboratory synthesis of fullereness requires distinctive condiontions of tempurature and pressure. Assumption: Fullereness synthesis in a laboratory requires the same conditions as required for naturally occuring fullereness. Conclusion: Geolegist can use the data of tempurature and pressure needed for laboratory synthesis of fullereness as a reference to validate or dismiss hypothesis regarding temperature and pressure of the Earth's crust at the time that the naturally occuring fullereness were formed. To undermine the argument, we need to look for a statement that challanges the assumption (the link between the premises and the conclusion) Option D states that the structure of naturally occuring fullereness differ from that of laboratory synthesized fullereness, a difference in structure brigns into question the validity of assuming that the conditions for formation are the same, and hence undermines the argument.

vineetdixit, excellent observation! If and only if A then B, is equivalent to saying If A then B And If B then A. It is called biconditional. It is important to remember that it does not imply a causal relation, that is If A then B, does not imply that A causes B, it means that if A is true then B must also be true (without any reference to the causal relation). For example if you are human then you are mortal. This does not imply a causal relation (being human did not cause you to be mortal), however notice that in this case, being human implies that you are mortal, but being mortal does not imply being human. (however being immortal implies that you are not human, and not being human does not exclude one from being mortal). Another way to treat if A then B: A is sufficient but not necessary to imply B. (in the absent of A, B could still be true). If and only if a polygon has three sides then it is a triangle, again does not imply a causal relation, however it is a triangle implies that it is a polygon with three sides and it is a polygon with three sides implies that it is a triangle; it is not a polygon with three sides implies that it is not a triangle and it is not a triangle implies that it is not a polygon with three sides. So we can write the above as if it is a triangle then it is a polygon with three sides and if it is a polygon with three sides then it is a triangle. Another way to treat if and only if A then B: A is sufficient and necessary to imply B. (in the absent of A, B cannot be true) You are absolutely right in spotting a connection between circular reasoning and the biconditional, although the former is an example of an informal fallacy and the latter is not a fallacy at all. Bellow are two excerpts on circular reasoning: “Any form of argument in which the conclusion occurs as one of the premises, or a chain of arguments in which the final conclusion is a premise of one of the earlier arguments in the chain. More generally, an argument begs the question when it assumes any controversial point not conceded by the other side.” “Unlike most informal fallacies, Begging the Question is a validating form of argument. Moreover, if the premises of an instance of Begging the Question happen to be true, then the argument is sound. What is wrong, then, with Begging the Question? First of all, not all circular reasoning is fallacious. Suppose, for instance, that we argue that a number of propositions, p1, p2,…, pn are equivalent by arguing as follows (where "p => q" means that p implies q): p1 => p2 => … => pn => p1 Then we have clearly argued in a circle, but this is a standard form of argument in mathematics to show that a set of propositions are all equivalent to each other. So, when is it fallacious to argue in a circle? For an argument to have any epistemological or dialectical force, it must start from premises already known or believed by its audience, and proceed to a conclusion not known or believed. This, of course, rules out the worst cases of Begging the Question, when the conclusion is the very same proposition as the premise, since one cannot both believe and not believe the same thing. A viciously circular argument is one with a conclusion based ultimately upon that conclusion itself, and such arguments can never advance our knowledge.”

There are seven odd prime numbers between 1 and 20 inclusive. 3, 5, 7, 11, 13, 17, 19 To find the highest power of each: [20/3] + [20/9] = 8 [20/5] = 4 [20/7] = 2 [20/11] = 1 (13, 17, and 19 also have a highest power of 1) 9*5*3*(2^4) = 2160 Answer is C.

HTTHTH HTHTTH

sqrt(x^2) = |x| is the definition of absolute value and thus holds true for all x such that x is a real number. I cannot think of a reference of the top of my head, buy I am sure that you would be able to find it in the OG, any math book dealing with the absolute value function, or on the internet.

quiver, how come you doubt the reasoning? Those are the rules of formal logic. If A then B, means that if A then always B, therefore if not B then not A; but the reverse is not true, if not A then B might or might not happen, and if B then A might or might not have happened. (there could be other events beside A that cause B) If A then B implies 2 relations: if A then B and if not B then not A. If and only if A then B, means that if A then always B, and that it is the only way to get to B (this is a fully reciprocal relation - if A then B and if B then A; if not A then not B and if not B then not A) If and only if A then B implies 4 relations: if A then B, if B then A, if not A then not B and if not B then not A. For the above question, you can think of it as a chain reaction, if A then B, if B then C, and if C then D. Therefore if A then D so if not D then not A.

IMO B. ksgill, what is your reasoning for D? Do you have the OA? (and source of the question)

Actually, it is that straight forward :) For a circular arrangments of n items, we first need to "fix" one of the items as a "refrence point", thus we are left with (n-1) items to arrange in an (n-1)! ways.

sqrt(n) denotes only the positive root of n. (for all n>0) sqrt(4)=+2 only.