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.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
16 Sep 2014, 01:24
Kudos
Bookmarks
If \(x\) is a positive integer, which of the following is closest to \(\frac{22^{22x} - 22^{2x} }{11^{11x} - 11^x}\)?
A. \(2^{11x}\)
B. \(11^{11x}\)
C. \(22^{11x}\)
D. \(2^{22x}*11^{11x}\)
E. \(2^{22x}*11^{22x}\)
A. \(2^{11x}\)
B. \(11^{11x}\)
C. \(22^{11x}\)
D. \(2^{22x}*11^{11x}\)
E. \(2^{22x}*11^{22x}\)
10 Mar 2018, 14:06
Kudos
Bookmarks
Great question
It very easy to waste a lot of time trying to solve this question algebraically (because it looks a little like you need to use difference of squares) if you miss the hint "closet to" and don't realise you're being asked to approximate, thus can take out 22^2X and 11^2X as factors and discard the +1s they produce when factoring out.
However, even if you don't notice that, you should realise that once you break down 22 to prime factors (22^22=2^22*11^22) you have powers of 2 up on the numerator and nothing to cancel that or decrease it on the denominator. In contrast, you do have powers of 11 on the denominator - so look for an answer choice where the exponent of the 2s is unchanged but the exponent on the 11s is being decreased - there's only one option which has that, which is D. (not to mention 11^22/11^11 is 11^11 so D is in the right 'range' for what you'd expect the exponent on 11 to be, as well)
It very easy to waste a lot of time trying to solve this question algebraically (because it looks a little like you need to use difference of squares) if you miss the hint "closet to" and don't realise you're being asked to approximate, thus can take out 22^2X and 11^2X as factors and discard the +1s they produce when factoring out.
However, even if you don't notice that, you should realise that once you break down 22 to prime factors (22^22=2^22*11^22) you have powers of 2 up on the numerator and nothing to cancel that or decrease it on the denominator. In contrast, you do have powers of 11 on the denominator - so look for an answer choice where the exponent of the 2s is unchanged but the exponent on the 11s is being decreased - there's only one option which has that, which is D. (not to mention 11^22/11^11 is 11^11 so D is in the right 'range' for what you'd expect the exponent on 11 to be, as well)
16 Sep 2014, 01:24
Kudos
Bookmarks
Official Solution:
If \(x\) is a positive integer, which of the following is closest to \(\frac{22^{22x} - 22^{2x} }{11^{11x} - 11^x}\)?
A. \(2^{11x}\)
B. \(11^{11x}\)
C. \(22^{11x}\)
D. \(2^{22x}*11^{11x}\)
E. \(2^{22x}*11^{22x}\)
First of all, it's important to note that we are looking for an approximate value of the given expression.
Now, considering that \(22^{22x}\) is significantly larger than \(22^{2x}\), the value of \(22^{22x}-22^{2x}\) will be very close to just \(22^{22x}\). In this context, \(22^{2x}\) becomes negligible. Similarly, \(11^{11x}-11^x\) will be almost equivalent to \(11^{11x}\)
Therefore, \(\frac{22^{22x}-22^{2x} }{11^{11x}-11^x} \approx \frac{22^{22x} }{11^{11x} } = \frac{2^{22x}*11^{22x} }{11^{11x} } = 2^{22x}*11^{11x}\).
For further verification, one can also approach this algebraically: \(\frac{22^{22x}-22^{2x} }{11^{11x}-11^x} = \frac{22^{2x}(22^{20x}-1)}{11^x(11^{10x}-1)}\). Since the -1 in both the denominator and numerator is negligible, the expression simplifies to: \(\frac{22^{2x}(22^{20x}-1)}{11^x(11^{10x}-1)} \approx \frac{22^{2x}*22^{20x} }{11^x*11^{10x} } = \frac{22^{22x} }{11^{11x} } = 2^{22x}*11^{11x}\).
Answer: D
If \(x\) is a positive integer, which of the following is closest to \(\frac{22^{22x} - 22^{2x} }{11^{11x} - 11^x}\)?
A. \(2^{11x}\)
B. \(11^{11x}\)
C. \(22^{11x}\)
D. \(2^{22x}*11^{11x}\)
E. \(2^{22x}*11^{22x}\)
First of all, it's important to note that we are looking for an approximate value of the given expression.
Now, considering that \(22^{22x}\) is significantly larger than \(22^{2x}\), the value of \(22^{22x}-22^{2x}\) will be very close to just \(22^{22x}\). In this context, \(22^{2x}\) becomes negligible. Similarly, \(11^{11x}-11^x\) will be almost equivalent to \(11^{11x}\)
Therefore, \(\frac{22^{22x}-22^{2x} }{11^{11x}-11^x} \approx \frac{22^{22x} }{11^{11x} } = \frac{2^{22x}*11^{22x} }{11^{11x} } = 2^{22x}*11^{11x}\).
For further verification, one can also approach this algebraically: \(\frac{22^{22x}-22^{2x} }{11^{11x}-11^x} = \frac{22^{2x}(22^{20x}-1)}{11^x(11^{10x}-1)}\). Since the -1 in both the denominator and numerator is negligible, the expression simplifies to: \(\frac{22^{2x}(22^{20x}-1)}{11^x(11^{10x}-1)} \approx \frac{22^{2x}*22^{20x} }{11^x*11^{10x} } = \frac{22^{22x} }{11^{11x} } = 2^{22x}*11^{11x}\).
Answer: D
