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 : \((x-y ) (x+y) = (x^2-y^2)\)

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

Answer A

Appreciation in the gmatclub format is always welcome..
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Yeah \((2^12+1)\) must be corrected to \((2^{12}+1)\), otherwise it creates confusion and takes extra time..
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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

Sent from my SM-G610F using GMAT Club Forum mobile app
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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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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

Answer: A
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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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