Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes.
This is a good candidate for REPHRASING the target question. Take a² + b²= 2ab and subtract 2ab from both sides to get: a² - 2ab + b²= 0 Factor to get: (a - b)(a - b) = 0 Solve to get: a - b = 0 In other words, a = b
So, we get.... REPHRASED target question:Does a = b?
NOTE: Once we REPHRASE the target question, the statements should be easy to analyze.
Statement 1: a + b = 3 There are several values of a and b that satisfy statement 1. Here are two: Case a: a = 1 and b = 2. In this case, the answer to the REPHRASED target question is NO, a does NOT equal b Case b: a = 1.5 and b = 1.5. In this case, the answer to the REPHRASED target question is YES, a DOES equal b Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: ab > 0 There are several values of a and b that satisfy statement 2. Here are two: Case a: a = 1 and b = 2 (these values satisfy the condition that ab > 0). In this case, the answer to the REPHRASED target question is NO, a does NOT equal b Case b: a = 1.5 and b = 1.5. In this case, the answer to the REPHRASED target question is YES, a DOES equal b Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED. In other words, Case a: a = 1 and b = 2. In this case, the answer to the REPHRASED target question is NO, a does NOT equal b Case b: a = 1.5 and b = 1.5. In this case, the answer to the REPHRASED target question is YES, a DOES equal b Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.
Since we have 2 variables (x and y) 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) : \(a = 1.5\), \(b = 1.5\) : The answer is Yes \(a = 1\), \(b = 2\): The answer is No.
Since we don't have a unique solution, both conditions together are not sufficient.
Therefore, the answer is E.
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.
_________________
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________