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(1/2)^3 is the probability that he won't be able to buy iced tea. 1-(1/2)^3=7/8 is the probability that he will be able to buy iced tea at one of 3 stores.

It is better to do as chanojmarian Combining x^2+2xy+y^2>6 xy=2 x^2+4+y^2>6 x^2+y^2>2

Xn+1 = 2Xn – 1 X20= 2X19– 1 2X19 – 1-X19=X19 -1 It is better to solve the problem as kluheve did.

When one of th statements says that x, y are integers that means there is a possibility that x and y are not integers. I missed that.

You are right guys

IMO B (x-y)(x+y)=23 23 is the prime number that is divisible only by 23 and 1 a. x-y=1 and x+y=23, y=11, x=12 b. -(x-y)=1 and -(x+y)=23, y=-11, x=-12 1. Insuff. Statement does not say whether x and y are positive or negative 2. x>0, x=12 Suff.

IMO C 1. 6 students could buy 6 books each, 1 student could by 4 books. The range 1 to 4. The median is 2.5. 5 students could buy 1 book each, 1 student 2 books and the 7th student 3 books. the range 1 to 3. The median 1.5 . Insuff. 2.Some students did not buy books, others bought 2 books each. the range 0 to 2. The median is 1. Some students bought 1 book each, some students bought 2 books each. the range 1-2. the median 1.5. Insuff. Combining, The range is 1 to 2. The median 1.5 Suff.

Consider x=y=sqrt2 1. (sqrt2+sqrt2)^2>6 true 2. sqrt2*sqrt2=2 true ((sqrt2)^2+(sqrt2)2 >6 wrong. C is insuff.

You are right.

2^20-2^19=2^19*2-2^19=2^19(2-1)= 2^19 Exponents are the product of the base (in this case base=2) n times (n in this case=20). 2*2*2*..... So 2^20 we can express as 2^19*2.

12 students - A movie. 12(A) 9 students - B. 9(B) 6 students -C. 6 © 2 students watched 3 movies. Total students 20. Students watched 2 movies - x. The formula is n(A U B U C) = n(A) + n(B) + n© - n(A intersect B) - n(B intersect C) - n(A intersect C)- 2*n(A intersect B intersect C) Where n(A intersect B) - n(B intersect C) - n(A intersect C) is x or number of students watched 2 movies. 2*2(A intersect B intersect C)= 4, this means 2 students watched 3 movies. We need to multiply the number of these students by 2, because they are included in 3 groups, we need to exlude them from 2 groups. 12(A)+9(B)+6©-4-x=20 x=3 Answer 3 students watched 2 movies.

Is ½x½ 1. The statement says that x has two values x=3 and x=1/3. In 1st case x is integer, in another one x is a fraction. Insuff. 2. The statement says that x is not equal to 3, but can be any other number. Insuff. Combining, x is not equal to 3, x is a fraction 1/3. Suff.

It is better to scetch the graph. The general rule is: x coordinate of the vertex -b/2a, y coordinate (4ac-b^2)/4a. Another form of quadratic equation is y=a(x-k)^2+h where k is value by which the graph is shifted to the right or to the left from y-axis, h is y coordinate of the vertex, a is the slope of the graph. In this case the graph is shifted to the right by 1 unit, the equation takes the form (x-1)^2. The slope is -1 because the graph is downwards. To find h, we can plug y-intercept point (0,3) in the above equation. 3=-1(0-1)^2+h, h=4 Actually, i did not do any calculations like this because it is time consuming. I just simply sketched the graph, found x-coordinate of the vertex, took a look how the graph is increasing from the point (-3,0) to the point (0,3). It is easy to find that from x=-3 to x=0, y increases by one point from y=0 to y=3. In this case the quadratic equation is as follows: y=-x+2x+3 or -(x-1)^2+3 Another link: Quadratic Functions(General Form)

E If denominator has other prime numbers at the base than 2 or 5, then deciaml is not terminated. A. 189=3^3*7 eliminated because prime numbers are 3 and 7 B. 196=2^2*7^2 eliminated because denominator has 7 C. 225=3^2*5^2 eliminated, 3 is in the denominator D. 144=2^4*3^2 eliminated, 3 is in the denominator E. 128=2^7 OK. No other prime numbers except of 2

Ranjeet, how you figure out that i am Sir? Sorry, i have to disappoint you, this is wrong answer.:) parabola has a quadratic equation like ax^2-bx+c=0. That calls quadratic because x has power of 2. Here is a link Quadratic Functions Unfortunately, i can't answer your question regarding whether quadratic graphs might be tested in GMAT exam. Probably, Bob 800 would answer it. Richita, by increasing x for one point on the graph, y also increases by one point. The graph crosses y axis at x=0 and y=3. So, adding 1 to x, we need to add 1 to y.

KilGmat, you are right. I have no idea why I subtracted 3, it should be 2. 10+6+5-2-x=15 x=4

Sorry, nazar. My bad. That should be 60. BE=EG=BG. This is equilateral an equilateral triangle. 3 sides are equal, so we need 180 divide by 3 and get 60.

I am a really a bad explainer. In this case it is better to scatch a graph with given points. Points (-3,0) and (5,0) are x-intercepts, they are the points where the graph crosses x axis. Point (0,3) is y intercept, where the graph crosses y-axis. You can see that graph is downwards that means a is negative. In this case we need to find the vertex to figure out at what range tha graph is increasing and decreasing. To find x-coordinate of that point we need to add x-coordinate of 2 x intercepts -3 and 5 and divide by 2 (-3+5)/2=1. y-coordinate is 4. The graph is increasing when x (-infinity, 1) and decreasing (1, +infinity)

E. 90 Angle FEG is 90. Triangle FEG is an isolesces triangle, where angle FEG is 45. the angle BEF is also 45. The angle BEG 45+45=90

It happens. Be careful at the exam.:) Bad scrabbing might effect on your score.

IMO C How many 5s are in 200! 200/5=40 40/5=8 8/5=1 40+8+1=49

IMO A 1. n=10q, where q is a quotent. 2n=2*10q=20q. 20q/10=2q. The remainder is 0. Suff. 2. n=4p, where p is quotent. 2n=2*4p=8p. 8p/10. The remainder depends on the value of p. Insuff.

IMO D This is a downward parabola with vertex at point (1,4) The parabola is increasing (-infinity, 1) and decreasing (1, +infinity) I. y is greater when x=-1 than when x=-2. That is true because the graph is increasing until x=1. When x=-2, y=1. When x=-1, y=2. f(-1)>f(-2) II. This is also true because the graph is increasing at the range (-infinity,1) x=0, y=3. x=1, y=4. III. False, the graph is decreasing at the range (1, +infinity) At this range greater is x, less is y.

Flex manny, how did you get -11? 1. x=11 and x=-17. x+3=14, x=11. -x-3=14, x=-17 2. x=11 and x=-15 (x+2)^2=13^2 x+2=13, x=11. x+2=-13, x=-15 Combining, x=11

Answer is C. http://www.www.urch.com/forums/gmat-problem-solving/91683-set-4-q-8-geometry.html