barcodelib rdlc The larger rectangle has an area of 24, so the non-shaded rectangle must have an area of in Software

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The larger rectangle has an area of 24, so the non-shaded rectangle must have an area of
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12 Starting with the answer choices for the length of the shorter side, we can divide them into 12 until we find a valid length for the longer side A would give us 16 for the longer side, which wouldn t work because that wouldn t fit inside another rectangle with 6 as the longest side B would give us 12 for the longer side, which is still too big C gives us 8, which is also too big D gives us 5, which is possible and therefore is the correct answer
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7 E
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Since 4r and 5r form a straight line, which is 180 degrees, 4r + 5r = 180 When we simplify that
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to 9r = 180, we can solve to get r = 20 Therefore 5r = 100, and s 20 = 100 So we can tell that s = 120 Using those numbers, the equation 2s r becomes 2(120) 20, which equals 220
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8 C
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Statement (1) alone lets us find the radius, which can tell us the area of the whole circle, but
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we still don t know what portion of the circle is made up by the shaded region, so we have to eliminate A and D Statement (2) alone tells us what proportion of the circle is encompassed by the shaded region, but doesn t tell us the area of the whole circle, so we can eliminate B Putting the statements together, we have both pieces of information, which we can use to find the area of the shaded region, so statements (1) and (2) are sufficient together, and our answer is C
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Statement (1) is tempting, because the figure appears to be a parallelogram, but we don t
really know that it is without some indication that there are two sets of parallel lines So statement (1) is actually not sufficient, and we can eliminate A and D Remembering that we have to take statement (2) alone, it is not sufficient by itself to solve for the value of x, so we eliminate B Putting both statements together, we have the information we need: If the figure is a parallelogram, then the angles add to 360 If 2y = 100, then 2x = 260 and x = 130 So our answer is C
10 E
Statement (1) is not sufficient on its own, since you can never solve for one side of a triangle
given only one other side Let s eliminate A and D Statement (2) is not sufficient for the same reason, so we can eliminate B Putting the statements together, it appears that we have enough information to solve for the diagonal of the rectangle (also known as hypotenuse of a right triangle) except that we don t have any indication that the figure is actually a rectangle So the statements are still not sufficient and the answer is E
THE QUANTITATIVE SECTION
Boolean Problems and Combinatorics
INTRODUCTION
The GMAT contains a variety of logic problems designed to test your ability to think clearly and quickly about classes of objects and the relationships between them This ability is very valuable for any business analyst, as it is important to generating defensible answers about complex business questions It is particularly useful in the design of complicated spreadsheets, which are an important tool for financial and operations analysis However, since the authors of the GMAT have been instructed not to favor those with business analysis experience too greatly, they rely on a number of other types of problems for testing this aptitude These include basic logic problems in set theory, number theory, the binary mathematics of Boolean algebra, and combinatorics
BOOLEAN PROBLEMS ON THE GMAT
Boolean problems are those in which you are asked to determine whether a mathematical expression corresponds to one of two states These questions could ask whether an expression is $ True or false $ Even or odd $ Positive or negative $ Integer or noninteger These either/or groupings are called binary categories, in which an expression must fit in one category or the other, but not both simultaneously For example, an expression can be positive for certain values of x and negative for other values, but it cannot be both positive and negative at the same time Boolean tools, such as truth tables, can allow you to answer this type of question quickly and accurately Let s consider some examples
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