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.