An argument is made up of premises (data) and a conclusion which was drawn on the basis of these premises. An argument is comprised of:
Premise(s) - factual data or a given;
Conclusion - statement, opinion, or judgment based on the premise(s). The conclusion may be logical (Example 1) or flaw...
GMAT Review Main - Questions and Answers An argument is made up of premises (data) and a conclusion which was drawn on the basis of these premises. ✅An argument is comprised of: Premise(s) - factual data or a given; Conclusion - statement, opinion, or judgment based on the premise(s). The conclusion may be logical (Example 1) or flawed (Example 2): 1. All cars have wheels. Therefore, John's car has wheels. Ballparking π ≅3+ will become extremely useful when solving geometry questions involving circles. ✅Replace π with ≅3+, or " a little more than 3" the only way to add or subtract powers is by extracting a common factor. ✅--> 2·3m·31 - 3m = 135 31 is essentially 3, so --> 2·3·3m - 3m = 135 --> 6·3m - 3m = 135 Now, extract 3m as a common factor. 3m needs to be multiplied by 6 to reach in 6∙3m, and by 1 to reach 3m: --> 3m·(6 -1) = 135 --> 3m∙5 = 135 Divide by 5, and: --> 3m = 135/5 = 27 Yes/No Data Sufficiency - Issue - Plug In - Plug Into Stem - DOZEN F ✅- Issue: Figure out the issue before diving deeper into the stmt. - Yes/No or must be: - Definite "yes" or "no" = Sufficient (S) - "maybe" = Insufficient (IS) -Plug in - Find #'s that don't contradict the stmts. - Regard the stmts as facts. - Once you find the # that completes the stmt, plug that into the ? stem. Test for Y/N. - "Is it true for any #?". DOZEN F DOZEN F ✅Different One Zero Equal #'s for different variables Negative Factors Anything raised to the power of 1 equals ✅itself. 423 raised to 1 = 423 1 raised to any power equals ✅= 1 1 raised to 3 = 1 Any number (except 0) raised to the power of 0 equals ✅= 1 423 raised to 0 = 1 0 raised to any power (except 0) equals ✅= 0 0 raised to 423 = 0 When dividing powers of the same base, ????? the exponents ✅subtract the exponents. a^5 / a ^3 = a^5 -3 = a^2 reverse 3^x - 2 = 3^x / 3^2 any number raised to a negative power = ✅the inverse. 2^-2 = 1 / (2^2) = 1/ 4 is (y) to the power of ( -x) negative? stmt: Y is positive ✅No. There is no power that can turn a positive base into a negative result. plug in 2 for y and -3 for x 2 to the power of -3 = 1 / (2 to the power of 3) = 1/8 = positive is y to the power of (x) negative? stmt: x is even. ✅No. An even power will always be non -negative. plug in -3 for y and 2 for x -3 to the power of 2 = ( -3)(-3) = 9 (non -negative) is (y) to the power of ( -x) positive? stmt: y is negative stmt: x is odd ✅No. An odd power will maintain the bases original sign. plug in -2 for y and 3 for x -2 to the power of -2 = 1/ -2 to the power of 3 = 1 / (-2)(-2)(-2) = 1/ -8 An even power will always be non -negative. (y) to the power of ( -x) If y=-3 and x=2, then y to -x = (-3) to -2 = 1/( -3) to 2 = 1/9, which is positive ✅An odd power will maintain the base's original sign. (y) to the power of ( -x) If y=-3 and x=1, then y to -x = (-3) to -1 = 1/( -3) to 1 = 1/ -3, which is negative Integer ✅an integer is simply a non -fraction or a non -decimal. Integers can be positive or negative. 0 is an integer. Real Number ✅A real number can be anything: positive, negative, integer, fraction. Power is made up of a base and an exponent. x to the power of 5. (x) is the base and 5 is the exponent. ✅which is the base? which is the exponent? (Y) to the power of ( -x) base ✅Power is made up of a base and an exponent. x to the power of 5. (x) is the base and 5 is the exponent. exponent ✅Power is made up of a base and an exponent. x to the power of 5. (x) is the base and 5 is the exponent. How do you divide powers of the SAME BASE? ✅Subtract the exponents. (a) to the power of 5 divided by a to the power of 3 (a to 5) / (a to 3) = a to (5 -3) = a to 2 reverse:
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