Events & Promotions
|
|
GMAT Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 2008:00 AM PDT
-08:30 AM PDT
What’s in it for you- Live Profile Evaluation Chat Session with Jenifer Turtschanow, CEO, ARINGO. Come with your details prepared and ARINGO will share insights! Pre-MBA Role/Industry, YOE, Exam Score, C/GPA, ECs Post-MBA Role/ Industry & School List.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
Updated on: 06 May 2021, 04:16
Originally posted by MathRevolution on 06 Apr 2020, 03:51.
Last edited by MathRevolution on 06 May 2021, 04:16, edited 1 time in total.
Last edited by MathRevolution on 06 May 2021, 04:16, edited 1 time in total.
Kudos
Bookmarks
MathRevolution
=>
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.
Since we have many variables to determine the function f(x), E 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)
Since \(f(3) = 5\), we have:
\(f(5) = \frac{(f(3) - 1) }{ (f(3) + 1)}\)
\(f(5) = \frac{(5 - 1) }{ (5 + 1)}\)
\(f(5) = \frac{4}{6} = \frac{2}{3}.\)
Then we have:
\(f(7) = \frac{(f(5) - 1) }{ (f(5) + 1) }\)
\(f(7) = ((\frac{2}{3}) - 1) / ((\frac{2}{3}) + 1) \)
\(f(7) = -(\frac{1}{3}) / (\frac{5}{3}) = -(\frac{1}{5}).\)
We have:
\(f(9) = \frac{(f(7) - 1) }{ (f(7) + 1)} \)
\(f(9) = (-(\frac{1}{5}) - 1)/(-(\frac{1}{5}) + 1) \)
\(f(9) = -(\frac{6}{5}) / (\frac{4}{5}) = -(\frac{3}{2}).\)
We have:
\(f(11) = \frac{(f(9) - 1) }{ (f(9) + 1)} \)
\(f(11) = (-(\frac{3}{2}) - 1)) / (-(\frac{3}{2}) + 1)\)
\(f(11) = -(\frac{5}{2}) / -(\frac{1}{2}) = 5.\)
Since \(f(3) = f(11)\), we have \(f(8k - 5) = 5.\)
Then we have:
\(f(8k-3) = \frac{2}{3}\), \(f(8k-1) = -(\frac{1}{5})\) and \(f(8k+1) = -(\frac{3}{2}).\)
\(f(2007) = f(8*251-1) = -(\frac{1}{5}).\)
Since both conditions together yield a unique solution, they are sufficient.
Therefore, C is the answer.
Answer: C
Updated on: 04 Apr 2021, 03:42
Originally posted by MathRevolution on 06 Apr 2020, 03:52.
Last edited by MathRevolution on 04 Apr 2021, 03:42, edited 1 time in total.
Last edited by MathRevolution on 04 Apr 2021, 03:42, edited 1 time in total.
Kudos
Bookmarks
MathRevolution
=>
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.
Since we have 10 variables (x1, x2,…,x10) and 0 equations, E 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)
a10 = (x1 + x2 + … + x10) / 10 and a9 = (x1 + x2 + … + x9) / 9
x10 = 10a10 – 9a9
a10 = a1 + 9*2 = 5 + 18 = 23.
a9 = a1 + 8*2 = 5 + 16 = 21.
x10 = 10a10 – 9a9 = 10*23 – 9*21 = 230 – 189 = 41.
Since both conditions together yield a unique solution, they are sufficient.
Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
However, each condition alone does not provide enough information on its own, and therefore neither condition alone is sufficient.
Therefore, C is the answer.
Answer: C
In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
06 Apr 2020, 03:53
Kudos
Bookmarks
[GMAT math practice question]
(Number Properties) What is the solution of (\(x, y\))’s satisfying \(\sqrt{500} = \sqrt{x} +\sqrt{y}\) and \(x < y\)?
1) \(x\) and \(y\) are positive integers.
2) \(x = 5t^2\) with \(0 < t < 5.\)
(Number Properties) What is the solution of (\(x, y\))’s satisfying \(\sqrt{500} = \sqrt{x} +\sqrt{y}\) and \(x < y\)?
1) \(x\) and \(y\) are positive integers.
2) \(x = 5t^2\) with \(0 < t < 5.\)
