# The boxes remind you that x and y stand for digits a

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Unformatted text preview: to be the digits in A and B: x and y. Let A = x y (not the product of x and y: x is in the tens place, and y is in the units place). The boxes remind you that x and y stand for digits. A is therefore the sum of x tens and y ones. Using algebra, we write A = 10x + y. Since B ’s digits are reversed, B = y x . Algebraically, B can be expressed as 10y + x. The difference of A and B can be expressed as follows: A − B = 10x + y − (10y + x) = 9x − 9y = 9(x − y) Place value can help you solve tough problems about digits. Clearly, 9 must be a factor of A − B. The correct answer is (E). You can also make up digits for x and y and plug them in to create A and B. This will not necessarily yield the unique right answer, but it should help you eliminate wrong choices. In general, for unknown digits problems, be ready to create variables (such as x, y, and z) to represent the unknown digits. Recognize that each unknown is restricted to at most 10 possible values (0 through 9). Then apply any given constraints, which may involve number properties such as divisibility or odds &amp; evens. Rounding to the Nearest Place Value The GMAT occasionally requires you to round a number to a specific place value. What is 3.681 rounded to the nearest tenth? First, find the digit located in the specified place value. The digit 6 is in the tenths place. Second, look at the right-digit-neighbor (the digit immediately to the right) of the digit in question. In this case, 8 is the right-digit-neighbor of 6. If the right-digit-neighbor is 5 or greater, round the digit in question UP. Otherwise, leave the digit alone. In this case, since 8 is greater than five, the digit in question (6) must be rounded up to 7. Thus, 3.681 rounded to the nearest tenth equals 3.7. Note that all the digits to the right of the right-digit-neighbor are irrelevant when rounding. Rounding appears on the GMAT in the form of questions such as this: If x is the decimal 8.1d5, with d as an unknown digit, and x rounded to the nearest tenth is equal to 8.1,...
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