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:
After just 3 months of studying with the TTP GMAT Focus course, Conner scored an incredible 755 (Q89/V90/DI83) on the GMAT Focus. In this live interview, he shares how he achieved his outstanding 755 (100%) GMAT Focus score on test day.
In this conversation with Ankit Mehra, IESE MBA and CEO & Co-Founder, of GyanDhan, we will discuss how prospective MBA students can finance their MBA education with education loans and scholarships.
Grab 20% off any Target Test Prep GMAT Focus plan during our Flash Sale. Just enter the coupon code FLASH20 at checkout to save up to $320. The offer ends on Tuesday, April 30.
What do András from Hungary, Pablo from Mexico, Conner from the United States, Giorgio from Italy, Leo from Germany, and Rishab from India have in common? They all earned top scores on the GMAT Focus Edition using the Target Test Prep course!
Ready to conquer GMAT's toughest Data Insights questions? Unlock the secrets of Graphical Interpretation & Two-Part Analysis with our expert-led webinar! Limited seats!
What do András from Hungary, Conner from the United States, Giorgio from Italy, Leo from Germany, and Saahil from India have in common? They all earned top scores on the GMAT Focus Edition using the Target Test Prep course!
If \(a\) , \(b\) , \(c\) , and \(d\) are non-zero numbers such that \(\frac{a}{b} = \frac{c}{d}\) and \(\frac{a}{d} = \frac{b}{c}\) , which of the following must be true?
Because \(\frac{a}{b} = \frac{c}{d}\) , it is true that \(ad = bc\) or \(c = a*\frac{d}{b}\) . Because \(\frac{a}{d} = \frac{b}{c}\) , it is true that \(ac = bd\) or \(c = b*\frac{d}{a}\) . Thus, \(c = a*\frac{d}{b} = b*\frac{d}{a}\) . Because \(d\) is not 0, \(\frac{a}{b} = \frac{b}{a}\) or \(a^2 = b^2\) or \(|a| = |b|\) . To see that the other choices are not necessarily true consider \(a = 1\) , \(b = -1\) , \(c = -2\) , \(d = 2\) . The correct answer is D.
Can someone please explain me how to solve this problem efficiently? I don't understand the approach used in the solution to manipulate the variables? I did some variable manipulations but figured that if you don't do that a certain way you end up with a different answer like Mod(c) = Mod(d) which is not one of the answer choices?
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
If \(a\) , \(b\) , \(c\) , and \(d\) are non-zero numbers such that \(\frac{a}{b} = \frac{c}{d}\) and \(\frac{a}{d} = \frac{b}{c}\) , which of the following must be true?
Because \(\frac{a}{b} = \frac{cb}{dc}\) , it is true that \(ad = bc\) or \(c = a*\frac{d}{b}\) . Because \(\frac{a}{d} = \frac{b}{c}\) , it is true that \(ac = bd\) or \(c = b*\frac{d}{a}\) . Thus, \(c = a*\frac{d}{b} = b*\frac{d}{a}\) . Because \(d\) is not 0, \(\frac{a}{b} = \frac{b}{a}\) or \(a^2 = b^2\) or \(|a| = |b|\) . To see that the other choices are not necessarily true consider \(a = 1\) , \(b = -1\) , \(c = -2\) , \(d = 2\) . The correct answer is D.
Can someone please explain me how to solve this problem efficiently? I don't understand the approach used in the solution to manipulate the variables? I did some variable manipulations but figured that if you don't do that a certain way you end up with a different answer like Mod(c) = Mod(d) which is not one of the answer choices?
The four numbers can be any non-zero real numbers. You can also use some basic algebra and manipulate the two proportions. For example:
Multiply side-by-side the two equalities. It is in fact just simple multiplication of two fractions. You get \(\frac{a^2}{bd}=\frac{cb}{dc}\), from which it follows that \(a^2=b^2\) (after reduction and cross-multiplication). Now, take the square root of both sides, and get \(|a|=|b|\).
You can do all the manipulation above as all the numbers are non-zero. And don't forget that \(\sqrt{x^2}=|x|\).
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.