(2^12 - 2^6) / (2^6 - 2^3)

(2^6(2^6 - 1)) / 2^3 (2^3 - 1)

(2^3(2^6 - 1)) / (2^3 - 1)

(2^3 (63)) / 7

(2^3 * 9 * 7) / 7

2^3 * 9 = 72

imane81 wrote:Please help solve this one

(2^12 - 2^6) / (2^6 - 2^3) =

This is a perfect example of why you should always post answer choices.

2^12 is much much bigger than 2^6; similarly, 2^6 is much bigger than 2^3.

So, the expression you posted is very close to:

2^12/2^6 = 2^6 = 64

Now, depending on the choices, we could probably find the right answer just off of that estimation; but because we don't have them, we'll never know!

Stuart Kovinsky wrote:

imane81 wrote:Please help solve this one

(2^12 - 2^6) / (2^6 - 2^3) =

This is a perfect example of why you should always post answer choices.

2^12 is much much bigger than 2^6; similarly, 2^6 is much bigger than 2^3.

So, the expression you posted is very close to:

2^12/2^6 = 2^6 = 64

Now, depending on the choices, we could probably find the right answer just off of that estimation; but because we don't have them, we'll never know!

Stuart I think the dmateer25 solved the problem with right approach. i.e.
(2^12 - 2^6) / (2^6 - 2^3)
we should take out the power of 2 which is common and try to solve out the vlaues
= [2^6(2^6-1)]/[2^3(2^3-1)] = 2^3 (2^6 -1 )/(2^3 - 1) = 8(64-1)/(8-1) = 72 Ans


Well Stuart I think ur approach was very good but not correct for this problem
as you say 2^12 is much much bigger than 2^6 i.e. 4096 is much much bigger than 64 which is not true

similarly 2^6 is much bigger than 2^3 i.e. 64 is much bigger than 8 which is also not true

So you can't take this approach in this question otherwise you will end with the answer as 64 instead of 72 ....(a great difference.)


I hope stuart you will have a look on this ...
But alltogether I got a good approach of r which could be applied if no. is very big..in comparison to 2.

for eg (8796^12 - 8976^6) / (8976^6 - 8976^3)
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Shashank,

Stuart is actually not trying to solve the problem here. He's conveying that we could solve this problem just by looking at the answer choices. So, the 64 that he came up with, is an approximate estimation and not an actual answer. If the answer choices come closer to 64, then that is the right one.

Another each approch would be using a^2-B^2 =(a+b)(a-b)

2^12 -2^6 can be written as 2^6^2 - 2^3^2 which would give us (2^6 +2^3)(2^6 - 2^3)

so simplied form would be (2^6 +2^3)(2^6 - 2^3)/(2^6 - 2^3) =(2^6 +2^3) = 2^3(2^3+1) = 8*9 =72

papgust wrote:Shashank,

Stuart is actually not trying to solve the problem here. He's conveying that we could solve this problem just by looking at the answer choices. So, the 64 that he came up with, is an approximate estimation and not an actual answer. If the answer choices come closer to 64, then that is the right one.

100% correct!

For example, if the answers had been 32, 72, 256, 512, 1024, then we would know that 72 is correct without need for further work.

On the other hand, if the answers had been 60, 64, 68, 72, 76, then we'd have to be more precise and couldn't estimate as I did in my approach.

I'm not at all denying that dmateer's approach is 100% correct algebraically; I'm demonstrating that we don't always need to do such complicated and time-consuming algebra.

Remember this fundamental principle of the GMAT:

No matter how you end up clicking the right answer, you get full points for the question if you do so.

Accordingly, we should look for non-traditional approaches every time we do a practice question, because if we don't look for them in practice, we're never going to see them on Test Day.

Stuart Kovinsky wrote:

papgust wrote:Shashank,

Stuart is actually not trying to solve the problem here. He's conveying that we could solve this problem just by looking at the answer choices. So, the 64 that he came up with, is an approximate estimation and not an actual answer. If the answer choices come closer to 64, then that is the right one.

100% correct!

For example, if the answers had been 32, 72, 256, 512, 1024, then we would know that 72 is correct without need for further work.

On the other hand, if the answers had been 60, 64, 68, 72, 76, then we'd have to be more precise and couldn't estimate as I did in my approach.

I'm not at all denying that dmateer's approach is 100% correct algebraically; I'm demonstrating that we don't always need to do such complicated and time-consuming algebra.

Remember this fundamental principle of the GMAT:

No matter how you end up clicking the right answer, you get full points for the question if you do so.

Accordingly, we should look for non-traditional approaches every time we do a practice question, because if we don't look for them in practice, we're never going to see them on Test Day.

Hey Stuart,
Thanks for the above bold-faced post.I had one query in mind:-Calculators are not allowed in the exam so GMAT doesn't test ur calculating ability with decimals but as you had pointed out that if the option choices are given,we can easily approximate and find the answer.
Can GMAT test on such concepts??
For ex:-There was a question the answer of which was (0.9)^10.
Now,calculating the 10th power as such is difficult but if we use squares and cubes of the no. we can reach to the nearest option choice.Also,we can further approximate.
Can such questions not be asked on the GMAT only on the grounds that it requires tough calculations??
Can they also test as to how we approximate the different values??[After all,as managers we have to deal with lots of approximations]

harsh.champ wrote:Hey Stuart,
Thanks for the above bold-faced post.I had one query in mind:-Calculators are not allowed in the exam so GMAT doesn't test ur calculating ability with decimals but as you had pointed out that if the option choices are given,we can easily approximate and find the answer.
Can GMAT test on such concepts??
For ex:-There was a question the answer of which was (0.9)^10.
Now,calculating the 10th power as such is difficult but if we use squares and cubes of the no. we can reach to the nearest option choice.Also,we can further approximate.
Can such questions not be asked on the GMAT only on the grounds that it requires tough calculations??
Can they also test as to how we approximate the different values??[After all,as managers we have to deal with lots of approximations]

You will never be tested on your ability to do advanced calculations, i.e. the kind of things you'd normally just plug into your calculator (or send to your accounting department!).

It's quite possible that the choices for the question in this thread wouldn't be in simple number form, i.e. the correct answer may have been 9(2^3) rather than 72 - that's why posting answer choices is so important, since they often dictate the way we attack the question.

If (0.9)^10 is the correct answer, then it would appear in exactly that format among the choices. It's common to see such expressions among the choices on difficult exponent questions.

It's rare to be directly tested on approximating, but it's a skill that can pay off on questions with weird numbers; you don't have to be a great approximator to get the right answer, but being one can save you a lot of valuable time.

papgust wrote:Shashank,

Stuart is actually not trying to solve the problem here. He's conveying that we could solve this problem just by looking at the answer choices. So, the 64 that he came up with, is an approximate estimation and not an actual answer. If the answer choices come closer to 64, then that is the right one.

yeah papgust i actually misjudged the thing..actually stuart was helping us with right approach. though the ans was not exact. so I thought to solve it fully and solve out the exact answer...