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How can I solve this within 1 min?

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by GMATGuruNY » Fri Sep 04, 2015 5:17 am
The problem should read as follows:
If 27^(4x + 2) * 162^(-2x) * 36^x * 9^(6-2x) = 1, then what is the value of x?


-9

-6

3

6

9
PRIME-FACTORIZE the bases:
(3³)^(4x + 2) * (2*3�)^(-2x) * (2²3²)^x * (3²)^(6-2x) = 1

MULTIPLY the exponents:
3^(12x + 6) * 2^(-2x) * 3^(-8x) * 2^(2x) * 3^(2x) * 3^(12 - 4x) = 1

Combine like terms by ADDING the exponents:
3^(12x + 6 - 8x + 2x + 12 - 4x) * 2^(-2x + 2x) = 1

Simplify:
3^(2x + 18) * 2� = 1
3^(2x + 18) = 1.

Since the exponent on the left side must be equal to 0, we get:
2x + 18 = 0
2x = -18
x = -9.

The correct answer is A.

This problem is more tedious and time-consuming that a typical GMAT problem.
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by [email protected] » Fri Sep 04, 2015 8:39 am
Hi oquiella,

Mitch's solution is spot-on, so I won't rehash any of that math here. Instead, I'd like to know more about the 'title' you gave this post. While overall pacing in each section is a significant factor in how you'll score on Test Day, your goal shouldn't really be 'speed', it should be 'efficiency.' While certain questions on the GMAT can be answered relatively quickly (in under a minute), others are designed to take longer to solve (upwards of 3 minutes, and that's if you know all of the patterns and 'shortcuts').

Are you dealing with a pacing problem in the Quant section? If so, then how significant is it? How many questions do you have to rush through just to finish?

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by oquiella » Fri Sep 04, 2015 8:53 am
[email protected] wrote:Hi oquiella,

Mitch's solution is spot-on, so I won't rehash any of that math here. Instead, I'd like to know more about the 'title' you gave this post. While overall pacing in each section is a significant factor in how you'll score on Test Day, your goal shouldn't really be 'speed', it should be 'efficiency.' While certain questions on the GMAT can be answered relatively quickly (in under a minute), others are designed to take longer to solve (upwards of 3 minutes, and that's if you know all of the patterns and 'shortcuts').

Are you dealing with a pacing problem in the Quant section? If so, then how significant is it? How many questions do you have to rush through just to finish?

GMAT assassins aren't born, they're made,
Rich

I thought each problem should take 1 min to 1.5 mins to finish. I can solve problems fairly quickly if it is not caught up in words but this one I lacked the factoring aspects and completely forgot how to work with exponents caught off guard by the extra long equation and inability to root big numbers quickly. Was hoping there was a faster way. Thank you
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by Matt@VeritasPrep » Fri Sep 04, 2015 5:49 pm
Here's the algebra in a few visuals:

Image

Image

Image

which leaves us with (12x + 6 - 8x + 2x + 12 - 4x) = 0, or 2x + 18 = 0, or x = -9
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by [email protected] » Sat Sep 05, 2015 9:35 am
Hi oquiella,

How is your pacing in the Quant section overall? When you take your CATs, do you find that you have to rush on a bunch of questions at the end of the section (just to finish them all on time)?

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by oquiella » Sat Sep 05, 2015 9:59 am
[email protected] wrote:Hi oquiella,

How is your pacing in the Quant section overall? When you take your CATs, do you find that you have to rush on a bunch of questions at the end of the section (just to finish them all on time)?

GMAT assassins aren't born, they're made,
Rich
It takes me a while on problem solving to figure what approach i should use like magic numbers or variables. im getting alot wrong and finishing with 10 problems left. i need help. ive taken 2 cats so far. should i continue to take them and just go over missed problems? I take Cat once a week.
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by [email protected] » Sat Sep 05, 2015 1:59 pm
Hi oquiella,

Before you make any big changes to your study plan, I'd like to know a bit more about how you've been studying:

1) How long have you been studying?
2) What resources have you been using?
3) How have you scored on your 2 CATs (including the Quant and Verbal Scaled Scores)?

4) What is your goal score?
5) When are you planning to take the GMAT?

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by Brent@GMATPrepNow » Sat Sep 05, 2015 3:16 pm
oquiella wrote: I thought each problem should take 1 min to 1.5 mins to finish. I can solve problems fairly quickly if it is not caught up in words but this one I lacked the factoring aspects and completely forgot how to work with exponents caught off guard by the extra long equation and inability to root big numbers quickly. Was hoping there was a faster way. Thank you
Early in your prep, there's a danger in focusing too much on your timing. In my view, this focus has the potential to actually hinder your preparation. I feel so strongly about the whole timing issue that I wrote two articles about it:
- Making Friends with Time on the GMAT - Part I (https://www.gmatprepnow.com/articles/mak ... %93-part-i)
- Making Friends with Time on the GMAT - Part II (https://www.gmatprepnow.com/articles/mak ... 93-part-ii)
Executive Summary: Use a timer, but only to get an idea of what 2 minutes feels like. Later on (once you've covered all of the content), you can start working on your speed.

Executive Summary of the Executive Summary: Content First - Speed Second

I hope that helps.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by oquiella » Sun Sep 06, 2015 8:58 am
[email protected] wrote:Hi oquiella,

Before you make any big changes to your study plan, I'd like to know a bit more about how you've been studying:

1) How long have you been studying?......2 MONTS
2) What resources have you been using? MANATTAN, VERITAS, (WILL USE POWERSCORE CR AND ARISTOTLE SC SOON.)
3) How have you scored on your 2 CATs (including the Quant and Verbal Scaled Scores)? VERY BAD GOT A 380. POOR QUANT AND POOR VERBAL BUT FOCUS IS A BIG ISSUE FOR ME (REREADING TE QUESTION 3-5 TIMES)

4) What is your goal score? 780
5) When are you planning to take the GMAT? MID NOVEMMBER

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by [email protected] » Sun Sep 06, 2015 12:53 pm
Hi oquiella,

The information that you've provided in your last post is important - it defines a couple of 'issues' with your studies, timeline and overall goals:

1) Many Test Takers spend 3 months (or more) on their studies, so it's likely that you just have not put in enough time and effort yet.
2) You were not very specific with the exact resources you've used, but it sounds like you've taken a 'book heavy' study approach. Many Test Takers who use this type of approach get 'stuck' at a particular scoring level.
3) With a 380 CAT score, you have a variety of things that you have to work on BEFORE pacing can even be discussed.
4) If you're planning to take the GMAT in November, then a 780 score goal is NOT realistic. So you will either have to push back your Test Date or change your score goal (or both).

When are you planning to take your next CAT?

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Rich
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by oquiella » Tue Sep 08, 2015 10:23 am
[email protected] wrote:Hi oquiella,

The information that you've provided in your last post is important - it defines a couple of 'issues' with your studies, timeline and overall goals:

1) Many Test Takers spend 3 months (or more) on their studies, so it's likely that you just have not put in enough time and effort yet.
2) You were not very specific with the exact resources you've used, but it sounds like you've taken a 'book heavy' study approach. Many Test Takers who use this type of approach get 'stuck' at a particular scoring level.
3) With a 380 CAT score, you have a variety of things that you have to work on BEFORE pacing can even be discussed.
4) If you're planning to take the GMAT in November, then a 780 score goal is NOT realistic. So you will either have to push back your Test Date or change your score goal (or both).

When are you planning to take your next CAT?

GMAT assassins aren't born, they're made,
Rich

I plan on taking it in 2 weeks once ive gone through some OG questions and reviewed why I am getting them wrong.
What are your suggestions? I dont mind pushing the day back. Realistically what day should I be shooting for with a goal of 780?
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by [email protected] » Tue Sep 08, 2015 3:20 pm
Hi oquiella,

That next CAT result will help to define how your studies are going (and what you'll still need to work on). As far as setting realistic score goals, it's important to remember that the GMAT is not the same as a College Test (the scoring isn't linear and getting more questions correct doesn't necessarily mean that you get a higher score), so you can't trail for it in the same way. Keeping all of those differences in mind, a 780 is an UN-realistic score goal. Thankfully, nobody *needs* a score that high to get into Business School.

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by Max@Math Revolution » Wed Sep 09, 2015 7:11 am
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.



If 27^(4x + 2)*162^(-2x)*36^x*9^(6-2x)=1, x=?

A. -9

B. -6

C. 3

D. 6

E. 9

27^(4x + 2)*162^(-2x)*36^x*9^(6-2x)=(3)^3(4x + 2) * (2*3^4)^(-2x) * (2*3)^2x * (3)^2(6-2x)=1

3^(12x + 6) * 2^(-2x) * 3^(-8x) * 2^(2x) * 3^(2x) * 3^(12 - 4x) = 1

==> "‹3^(12x + 6 - 8x + 2x + 12 - 4x) * 2^(-2x + 2x) = 1 ==> 3^(2x+18)*2^0=1 ==> 3^(2x+18)=1, 2x+18=0, x=-9. therefore the answer is A



If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
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by oquiella » Fri Sep 11, 2015 9:47 am
[email protected] wrote:Hi oquiella,

That next CAT result will help to define how your studies are going (and what you'll still need to work on). As far as setting realistic score goals, it's important to remember that the GMAT is not the same as a College Test (the scoring isn't linear and getting more questions correct doesn't necessarily mean that you get a higher score), so you can't trail for it in the same way. Keeping all of those differences in mind, a 780 is an UN-realistic score goal. Thankfully, nobody *needs* a score that high to get into Business School.

GMAT assassins aren't born, they're made,
Rich
What score should i be shooting for for a scholarship to HBS?
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