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# (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) =

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Intern
Joined: 27 Sep 2017
Posts: 3
(2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 04:54
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Difficulty:

15% (low)

Question Stats:

80% (00:48) correct 20% (01:22) wrong based on 99 sessions

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$$(2^3-1)(2^3+1)(2^6+1)(2^{12}+1)=$$

A. $$(2^{24} -1)$$

B. $$(2^{24} +1)$$

C. $$(2^{48} -1)$$

D. $$(2^{96} +1)$$

E. $$2^6(2^{12} -1)$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Oct 2017, 05:33, edited 1 time in total.
Edited the question.
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 05:01
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VitalyCIB wrote:
Hi everyone!

I've come across this case in Kaplan and still cannot understand, how to solve it in 1.5-2 minutes. Can anybody help?

$$(2^3-1)(2^3+1)(2^6+1)(2^12+1)$$=

A. (2^24 -1)
B. (2^24 +1)
C. (2^48 -1)
D. (2^96 +1)
E. $$2^6$$(2^12 -1)

Hey VitalyCIB, This question can be solved in just 20 seconds. Since U wrote "how to solve it in 1.5-2 minutes", it gave me a presumption in my mind that the question is going to be tough and hence I took 23 seconds..

So, lets start solving this question.
Formula required : $$(x-y ) (x+y) = (x^2-y^2)$$

$$(2^3-1)(2^3+1)(2^6+1)(2^{12}+1)$$
$$= ((2^3-1)(2^3+1))(2^6+1)(2^{12}+1)$$
$$= (2^6-1)(2^6+1)(2^{12}+1)$$
$$= ((2^6-1))(2^6+1))(2^{12}+1)$$
$$= (2^{12}-1)(2^{12}+1)$$
$$= (2^{24}-1)$$

Appreciation in the gmatclub format is always welcome..
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Last edited by shashankism on 02 Oct 2017, 05:15, edited 1 time in total.
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 05:09
Please correct the last term of the qstn (2^12+1)

Posted from my mobile device
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 05:16
akshata19 wrote:
Please correct the last term of the qstn (2^12+1)

Posted from my mobile device

Yeah $$(2^12+1)$$ must be corrected to $$(2^{12}+1)$$, otherwise it creates confusion and takes extra time..
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 05:47
shashankism Thank you!
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 05:50
It applies the formula a^2 - b^2 = (a+b)(a-b);

(2^3−1)(2^3+1)(2^6+1)(2^12+1)
= (2^6−1)(2^6+1)(2^12+1)
=(2^12−1)(2^12+1)
=2^24 - 1;

Ans: A

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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 11:32
VitalyCIB wrote:
shashankism Thank you!

I hope now you will be able to solve such questions easily.. Also remember each and every question of QA GMAT level can be solved under 1.5 minutes maximum..
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 13:28
I think the trick here is that whenever you find such questions, it has to trigger something in your mind that this questions uses the formula
(x−y)(x+y)=(x2−y2)
Lot of such questions can be simplified if you know when to apply this.
I think the best way would be to practice questions that uses this formula. So that you get the hang of it.
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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02 Oct 2017, 23:41
This question is all about the formula : $$(a-b)(a+b) = a^2-b^2$$

=> $$(2^3−1)(2^3+1)(2^6+1)(2^{12}+1)$$
=$$((2^3)^2-1^2)(2^6+1)(2^{12}+1)$$
=$$(2^6-1)(2^6+1)(2^{12}+1)$$
=$$((2^6)^2-1^2)(2^{12}+1)$$
=$$(2^{12}-1)(2^{12}+1)$$
=$$((2^{12})^2-1^2)$$
=$$(2^{24}-1)$$

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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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05 Oct 2017, 09:15
VitalyCIB wrote:
$$(2^3-1)(2^3+1)(2^6+1)(2^{12}+1)=$$

A. $$(2^{24} -1)$$

B. $$(2^{24} +1)$$

C. $$(2^{48} -1)$$

D. $$(2^{96} +1)$$

E. $$2^6(2^{12} -1)$$

We can simplify the equation:

(2^3 - 1)(2^3 + 1)(2^6 +1)(2^12 + 1)

(2^6 - 1)(2^6 + 1)(2^12 + 1)

(2^12 - 1)(2^12 + 1)

2^24 - 1

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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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06 Oct 2017, 20:50
VitalyCIB wrote:
$$(2^3-1)(2^3+1)(2^6+1)(2^{12}+1)=$$

A. $$(2^{24} -1)$$

B. $$(2^{24} +1)$$

C. $$(2^{48} -1)$$

D. $$(2^{96} +1)$$

E. $$2^6(2^{12} -1)$$

(2^3-1)(2^3+1)(2^6+1)(2^{12}+1)=

(2^3-1)^2 (2^6+1)(2^{12}+1)=
[(2^6-1) (2^6+1)](2^{12}+1)=
(2^{12}-1)(2^{12}+1)=
(2^{24} -1)

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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) = [#permalink]

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14 Oct 2017, 05:43
cubs wrote:
I think the trick here is that whenever you find such questions, it has to trigger something in your mind that this questions uses the formula
(x−y)(x+y)=(x2−y2)
Lot of such questions can be simplified if you know when to apply this.
I think the best way would be to practice questions that uses this formula. So that you get the hang of it.

Yes a lots of question is asked using this formula $$(x−y)(x+y)=(x^2−y^2)$$ .. And if you just figure it out, you can solve the question in few seconds.. Since this type of problem will boost your score.. Just ensure to solve such questions for practice....
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Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) =   [#permalink] 14 Oct 2017, 05:43
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