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

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2
7 00:00

Difficulty:   15% (low)

Question Stats: 76% (01:05) correct 24% (02:17) wrong based on 153 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. $$2^6(2^{12} -1)$$

Originally posted by VitalyCIB on 02 Oct 2017, 05:54.
Last edited by Bunuel on 02 Oct 2017, 06:33, edited 1 time in total.
Edited the question.
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4
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 : $$(x-y ) (x+y) = (x^2-y^2)$$

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

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Originally posted by shashankism on 02 Oct 2017, 06:01.
Last edited by shashankism on 02 Oct 2017, 06:15, edited 1 time in total.
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Please correct the last term of the qstn (2^12+1)

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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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shashankism Thank you!
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GMAT 1: 730 Q49 V41 Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) =  [#permalink]

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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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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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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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GMAT 1: 730 Q50 V38 Re: (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) =  [#permalink]

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1
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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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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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)

A is the correct answer
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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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If I do this question wrong, I will undoubtely be considered as a nut =)))

(a^2-b^2) (2^3 - 1)(2^3 + 1)(2^6 + 1)(2^12 + 1) =   [#permalink] 18 Jan 2019, 01:24
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