Is |a| = |ab|? (1) a b (2) a^10 b^10 = 0

Question

Is  |a| = |ab|  ?

(1)  a ≠ b

(2)  a^{10} – b^{10} = 0

Kurtosis · Answer

St1: If a = 1/2; b = 1 --> Is |a| = |ab| ? --> Yes
If a = 2; b = 3 --> Is |a| = |ab| ? --> No

St2:  a^{10} – b^{10} = 0  -->  a^{10} = b^{10}  --> |a| = |b|
If a = 1; b = -1 then a = ab
If a = 2; b = 2 then  a 
eq {ab} 
Not Sufficient

Combining St1 and St2:  a 
eq {b}  and |a| = |b| --> a and b are similar in magnitude but opposite in sign
If a = 1; b = -1 then a = ab
If a = 2; b = -2 then  a 
eq {ab} 
Not Sufficient

Answer: E

Celestial09 · Answer

Dear experts!
I came across this question, since its from absolute value and i personally find this particular topic among the most tyrant once.
kindly help me with this question
along with some useful links for understanding
inequalities
absolute values
probability
permutation and combination
functions

there are numerous threads and some times i am lost.. so will focus on threads suggested by you all
 bunuel chetan4u veritas (need your quant wisdom links) magoosh egmat and math revolution

thanks
celestial

Bunuel · Answer

Is |a|=|ab|?

Is |a| = |ab|?
Is |a| - |ab| = 0
Is |a|(1 - |b|) = 0

Is |a| = 0 or |b| = 1
Is a = 0 or b = 1 or b = -1

(1) a ≠ b. Not sufficient.

(2) a^10 – b^10 = 0 --> a^10 = b^10 --> |a| = |b|. Not sufficient.

(1)+(2) From above since a ≠ b, then from |a| = |b| it follows that a = -b. Now, if a = -b = 0, then the answer is YES but if a = -b = 2, then the answer is NO. Not sufficient.

Answer: E.

Bunuel · Answer

For useful links please check ALL YOU NEED FOR QUANT ! ! ! . For absolute values check below links: Theory on Absolute Values: math-absolute-value-modulus-86462.html The E-GMAT Question Series on ABSOLUTE VALUE: the-e-gmat-question-series-on-absolute-value-198503.html Properties of Absolute Values on the GMAT: properties-of-absolute-values-on-the-gmat-191317.html Absolute Value: Tips and hints: absolute-value-tips-and-hints-175002.html DS Absolute Values Questions to practice: search.php?search_id=tag&tag_id=37 PS Absolute Values Questions to practice: search.php?search_id=tag&tag_id=58 Hard set on Absolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. The question |a|=|ab| is equivalent to a=0, b=1 or b=-1 for the following reason |a|=|ab| ⇔ |a|=|a||b| ⇔ |a||b|-|a|=0 ⇔ |a|(|b|-1)=0 ⇔ |a|=0 or |b|=1 ⇔ a=0, b=1 or b=-1 . Since we have 2 variables ( a and b ) and 0 equations, C is most likely 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) Condition 2) a^{10}-b^{10}=0 or a^{10}=b^{10} is equivalent to a = b or a = -b . If a = 1, b = -1 , then we have |a|=1, |ab|=1 and the answer is 'yes'. If a = 2, b = -2 , then we have |a|=2, |ab|=4 and the answer is 'no'. Since both conditions together do not yield a unique solution, 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.

bumpbot · Answer

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Is |a| = |ab|? (1) a b (2) a^10 b^10 = 0

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