Large exponents on GMAT

[Lamcc83]

I took my GMAT today and bombed pretty heavily. I had several questions that included adding and dividing very large exponents where neither the bases nor the exponents were identical. For example, what is 7^2013 minus 3^2019 all over 21^-2113?

How in the world do any of our study guides prepare us for such problems? This wasn't a data sufficiency question either.

Thanks in advance!

[velchal_rao]

As far as i understood the problem...

Is this somehow related to units digit patterns ...?

can it be solved based on that logic ...?


OR

what is 7^2013 minus 3^2019 all over 21^-2113?

21 can be written as ( 3 * 7)^ -2113

{(7 ^ 2013) (3^2113 ) (7^2113)} - {(3^2019)(3^2113)(7^2113)}

3^2113 { (7^2113)^2 - (3^2066)^2 }

3^2113 { (7^2113 + 3^2066) (7 ^2113 - 3^2066)}

............?

Anyone please help

[Lamcc83]

Thanks for the initial reply. Recognizing which concepts are being tested are a weakness of mine, and I appreciate you suggesting something that I previously didn't notice.

I also noticed large exponent problems on my official GMAT practice exam (the ones that are provided when you register for your GMAT).

[RonPurewal]

Some things:

* Division by a negative power is the same as multiplication by the corresponding positive power. So, division by blah^-2110 is the same as multiplication by blah^2110.

* 21 is the product of 7 and 3, so you can write 21^n as (3^n)(7^n), for whatever n is.
You'll be able to multiply the resulting expression by powers of 3 and/or 7.

* If you end up with a product of different powers of 3 and 7, you can "take out" as many 21's as possible, if that's the format of the answer choices.
e.g., if you have (3^10)(7^12), then you can take out (3^10)(7^10) = 21^10, and you'll be left with (21^10)(7^2).

[RonPurewal]

Last but not least, if you have exponents of moderate size -- 3^10, 7^8, etc. -- don't forget that you can always just multiply out the expressions and do good old-fashioned arithmetic.

Obviously this isn't going to work for exponents that are greater than two thousand, but it certainly could work next time.

[Lamcc83]

Thanks, Ron. It sounds like the key takeaway for me to is to break up large exponents into smaller, palatable exponents.

Maybe I just need to keep practicing (though I've been at studying for 6 months now), but I'm having a hard time solving the following problem in a timely manner (<2.5 minutes).

If 2x-2x-2=3(213), what is the value of X?

(Sorry, consider the tiny font/subscripts exponents).

I tackled this by breaking up 213 into 26 x 26 x 21. If I take the time to do the arithmetic for that, it still takes me about 120 seconds to get the total of the right side of the equation, 24576. But then I hit a wall with how I should apply this to the left side of the equation in a quick manner. Am I doing too much manual arithmetic on the right side of the equation?

Any advice is appreciated!

[velchal_rao]

Thank you Ron.

I am making lot of calculation mistakes .Can you please advise something ?

Thanks again.

[velchal_rao]

To
Lamcc83,

I have been struggling with GMAT too .Its very challenging .

I have come across different materials . The best ones were :
Type them on Manhattan site , you can find them.

1.Rephrasing Data Sufficiency Questions
by Stacey Koprince

2.Disguising - and Decoding - Quant Problems
Stacey Koprince

3. The Second Level of Learning to Take the GMAT
Stacey Koprince

4.How to Analyze a Practice Problem
By: Stacey Koprince

Very important :
Understand what's being said in the above articles and apply when you do problems.


Thank you everyone at Manhattan for these resources .
Thank you Ron and Stacy.
I only wish they has "Boot Camp" at all locations .I really wanted to join it .


I hope this helps .Just Don't give up.

For more resources:
Gmatclub.com
BeattheGmat.com

[Lamcc83]

That's very generous of you, velchal. I greatly appreciate these references!

[RonPurewal]

Thanks, Ron. It sounds like the key takeaway for me to is to break up large exponents into smaller, palatable exponents.

Maybe I just need to keep practicing (though I've been at studying for 6 months now), but I'm having a hard time solving the following problem in a timely manner (<2.5 minutes).

If 2x-2x-2=3(213), what is the value of X?

(Sorry, consider the tiny font/subscripts exponents).

I tackled this by breaking up 213 into 26 x 26 x 21. If I take the time to do the arithmetic for that, it still takes me about 120 seconds to get the total of the right side of the equation, 24576. But then I hit a wall with how I should apply this to the left side of the equation in a quick manner. Am I doing too much manual arithmetic on the right side of the equation?

Any advice is appreciated!

There are many existing forum threads about this problem. Here's one:
post16795.html#p16795

Also, if you're going to do calculations, you may as well just estimate. E.g., 2^10 = 1024, so you can just say 2^10 = approximately 1000. So, 2^13 is approximately 8000, and so on. (The answer choices to this problem are really, really, really far apart, so these estimates are more than good enough.)
If you can do that, then you can get an answer in substantially less time.

[RonPurewal]

At this point, I'm going to lock this thread, because it no longer contains anything that belongs in this folder.

* The problem with powers of 2 is a GMAT Prep problem with existing threads (see link above). If you have questions about that problem, please post them on the existing thread.

* As for problems with calculation -- If that refers to problems with standard arithmetic (adding/subtracting/multiplying/dividing), then the key there is just practice. Lots of people these days have gotten "rusty" at arithmetic as a result of using calculators/Excel/other automated calculation engines; you just have to get back into the habit.

* Questions about general strategy (e.g., preparation for the math section) belong in the General GMAT Strategy folder, not here.