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06 May 2005, 19:30
1. Watch for |X|, GMAT likes questions involving modulus.
2. In general, X^^2 is greater than X. However, if X is a fraction between 0 and 1, any higher (n greater than or equal to 2) powers of X ie X^^N < X i.e. X is bounded with in 0 and 1. i.e. 0 < X < 1.
3. Note that 2 is a very special number. It is an even number and also a prime number. When plugging in numbers for a problem involving prime numbers, usually we think of odd numbers but not 2. Note that GMAT is setting up a trap for you.
4. Note that the inequality changes when multiplied by negative numbers.
eg: X < 2 implies -2X > -4
By multiplying by -2, the inequality has changed.
However, multiplying by a positive number, the inequlity does not change.
For example, if X < 2 then 3 X < 6.
5. If the problem involves 3 consecutive integers, you might want to try n-1,n,n+1. Note that the sum of 3 consecutive integers, in this case is 3n. So, you can see right away that irrespetive of what n is, a sum of three consecutive integers is always divisible by 3.
6. Translate information in the question into equations and vice versa.
i.e. As already posted by someone, if y is a factor of x, x/y = integer.
Write this down on the scratch paper so that you know you need to include this information to solve the problem.
Another example is, if the problem says, x and y are positive integers, write it down as x > 0, y > 0.
7. Note the following simple facts:
sum, product or difference of two even numbers yields an even number.
Sum and difference of two odd numbers is Even.
product of two odd numbers is Odd.
sum or difference of an odd and even number is odd.
Product of an odd and even number is Even.
8. Know the difference between a factor and a multiple. Do not get confused.
9. Note that for any real number x not equal to zero, x ^^ 2 is always positive.
10. Even though X^^2 = 16 has two solutions, X^^3 = 8 has only one real solution. i.e. X ^^3 = 8 does not mean x is either 2 or -2. NO. X is 2.
Eg:
1. statement 1 : X^^2 = 4, Statement 2: X^^3 > X Answer C.
2. Statement 1: X^^3 = 8, statement 2: X^^3 > X. Answer A.
11. As already posted earlier, test some critical conditions such as
x=0,1,-1.
x=even and odd
x=fraction between 0 and 1
12. Note that 2 independent equations are needed to solve for x and y. GMAT likes to set up a trap where Statement 1 and Statement 2 appear to provide two equations. So, it is natural to pick answer C thinking that two equations and two unknown. Write down the equations. In some cases, both statements 1 and 2 might give you the same equation. In other words, you will end up with only one equation to solve for x and y. So, in this case the answer should be E.
13. Do not assume any information that is not provided.
For example, GMAT tries to set you up by saying x,y,z are three consecutive integers. This does not mean
x<y<z or x>y>z unless otherwise stated.
-Srinivas.