Is |a|a|b|?

Question

Is |a|>a|b|?
(1) a>0
(2) b<0

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 2 variables ( a and b ) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) If a = 1 , b=-\frac{1}{2} , then we have |a| = 1 , a|b| = \frac{1}{2} and the answer is 'yes'. If a = 1 , b=-2 , then we have |a| = 1 , a|b| = 2 and the answer is 'no'. Since both conditions together do not yield a unique answer, they are not sufficient. Therefore, E is the answer. Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.

Kinshook · Answer

Asked: Is |a|>a|b|? (1) a>0 |a| = a Q. a > a |b|? Q. 1 > |b|? Since there is no information about b NOT SUFFICIENT (2) b<0 |b| = -b Q. |a| > a |b|? Q. |a| > -ab? Since there is no information about a NOT SUFFICIENT (1) + (2) (1) a>0 (2) b<0 Q. |a| > a |b|? Q. a > -ab? Q. 1 > -b? Q. -1 < b? It is not given whether b>-1 or not NOT SUFFICIENT IMO E

ccooley · Answer

From the statements, this looks like a question about positives and negatives, not really an inequalities problem per se. Start by understanding the question, probably in terms of what you know about a and b being positive.

The only value in the question stem that isn't in an absolute value is the "a" on the right side of the inequality. If a is positive, then a = |a|, so we can divide both sides of the inequality by a, and get this:

Is |a| > a|b|?

Is 1 > |b|?

In other words, if a is positive, the question is really asking "is b between -1 and 1?"

What if a is negative? Then, divide both sides by |a|. a / |a| = -1, so we get this:

Is |a| > a|b|?

Is 1 > -|b|?

Is -1 < |b|?

Interesting - this is always true, since |b| is always at least 0! So, if a is negative, we already know the answer to the question: the answer is definitely "yes."

But if a is positive, we don't know the answer - it depends on whether b is between -1 and 1, or whether it's something different.

Statement 1 : a is positive, and we already figured out that in this situation, we don't know the answer. Insufficient.

Statement 2 : b is negative. If a was negative also, we'd know the answer was "yes." But if a was positive, the answer would depend on the exact value of b, and just knowing that b is negative isn't enough. So, this statement is insufficient as well.

Statements 1 and 2 together : a is positive, so the answer depends on whether b is between -1 and 1. We know that b is negative, but we don't know whether it's a big negative number, or a small negative number. So, we still don't have enough info. Insufficient, and the answer is  E .

Is |a|>a|b|?

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