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mlane25269
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atlantic
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Hi mlane,
Everytime that you see inequalities, the best is to plug numbers.
(1) when x^2, x can be either positive or negative that x^2 is always positive, and that is the same that happens in mod(x), a negative number returns positive and a positive remains positive. Exactly what is said in this option. So SUFF.
(2) imagine the following negative numbers, x=-3 and y=-6. We can say that x is greater than y. Now try to compute these numbers on the inequality, you get 3>6, which is not true. Now picking x=6 and y=3, that satisfy x>y, the inequality give us 6>3. Two different results for the same proposition, so INSUFF.
Answer A.
Everytime that you see inequalities, the best is to plug numbers.
(1) when x^2, x can be either positive or negative that x^2 is always positive, and that is the same that happens in mod(x), a negative number returns positive and a positive remains positive. Exactly what is said in this option. So SUFF.
(2) imagine the following negative numbers, x=-3 and y=-6. We can say that x is greater than y. Now try to compute these numbers on the inequality, you get 3>6, which is not true. Now picking x=6 and y=3, that satisfy x>y, the inequality give us 6>3. Two different results for the same proposition, so INSUFF.
Answer A.
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mlane25269
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Stuart@KaplanGMAT
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Good solution!
Another way to attack this is to actually change the question.
Remember, we can do whatever we want to an inequality as long as we do the same thing to both sides. As long as we don't multiply or divide by a negative, inequalities follow the exact same rules as equations.
Is |x| > |y|?
Well, let's square both sides! We know that both sides are positive, so nothing weird will happen. We can actually change the question to:
Is x^2 > y^2?
If we ask the question in this form, then it's easy to see that (1) is sufficient alone, since it states exactly what we want to know.
Another way to attack this is to actually change the question.
Remember, we can do whatever we want to an inequality as long as we do the same thing to both sides. As long as we don't multiply or divide by a negative, inequalities follow the exact same rules as equations.
Is |x| > |y|?
Well, let's square both sides! We know that both sides are positive, so nothing weird will happen. We can actually change the question to:
Is x^2 > y^2?
If we ask the question in this form, then it's easy to see that (1) is sufficient alone, since it states exactly what we want to know.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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mlane25269
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Ian Stewart
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No, that is not true- inequalities certainly do not 'follow the exact same rules as equations' with the one exception of multiplying or dividing by negatives. You cannot take reciprocals on both sides of an inequality. You cannot square both sides of an inequality. You cannot multiply two inequalities together. You cannot take the absolute value of both sides of an inequality. You cannot multiply both sides of an inequality by zero. I could go on. In each case, you risk arriving at something that is incorrect, unless you use additional information about the quantities on either side of the inequality. You can safely do all of these things with equations (with the lone exception of taking reciprocals when each side is equal to zero).Stuart Kovinsky wrote: Remember, we can do whatever we want to an inequality as long as we do the same thing to both sides. As long as we don't multiply or divide by a negative, inequalities follow the exact same rules as equations.
With an inequality, it is always safe to do the following: you can add or subtract the same quantitiy from both sides. You can multiply or divide by the same positive quantitiy on both sides. You can multiply or divide by the same negative quantity on both sides if you reverse the inequality. In other situations, we need to be more careful.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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