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GRE 29- Quantity A Quantity

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Quantity A                                                    Quantity B
35,043 × 25,430                                     35,430 × 25,043


A)The quantity in Quantity A is greater.
B)The quantity in Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
A-   (In short, bigger small number *small large number is greater that small amount of small number * larger amount of larger number)

Before you start multiplying these huge numbers, realize that no GRE question requires a great deal of arithmetic. Notice that the three digits after the thousands place have merely been swapped to form quantity B from Quantity A. So, represent quantity A as (35K + 43)(25K + 430) and quantity B as (35K + 430)(25K + 43) (note: K is short for 1,000). In Foiling these, you’ll see that the result from multiplying the First expressions together is (35K)(25K) in both quantities. Similarly, the result from multiplying the Last
expressions is (43)(430) in both quantities. So these expressions can be ignored in comparing the two quantities. All that remains is  the Outer terms added to the Inner terms. In Quantity A, this is (35K)(430) + (43)(25K), and in Quantity B, this is (35K)(43) + (25K)(430). If you factor out 43 from each Quantity, you obtain 43(350K + 25K) and 43(35K + 250K), or 43(375K) and 43(285K) for Quantities A and B, respectively. Quantity A is larger. If you were pressed for time, you might also note that the bigger number
(35,000) is multiplied by 430 in Quantity A but only by 43 in Quantity B.

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