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Which of the following is tantamount to (265)(247)?<#permalink>
04 Mar 2019, 14:57
Another way to deal with it:Cyclicity:2 < 2,4,8,6 >3 < 3,9,7,1 >Test in the options:A. 2^8 − 3^2 --- Discard, is as well small.B. 2^8 − 3^4 -- last digit subtraction (6 - 1) ... 5 Hold.C. 2^12 − 3^2 --- last digit (6-9) -3 ... DiscardD. 2^16 − 3^4 --- critical digit subtraction (6 - 1) ... 5 Hold.E. 2^64 − 3^4 --- Discard, this one is also big.By approximation in between B&D.B. 2^8 − 3^4 (256)(81) the answer have to be (265)(247), therefore is smaller. --- DiscardD. 2^16 − 3^4 --- ideal possibilities to be correct.D

Which that the adhering to is indistinguishable to (265)(247)?A. 2^8 − 3^2B. 2^8 − 3^4C. 2^12 − 3^2D. 2^16 − 3^4 E. 2^64 − 3^4
If difference of squares doesn"t strike, just use approximation. 265 * 247 is close come 300 * 200 = 60,0002^8 is 256 i beg your pardon is means too tiny and therefore is 2^12 i beg your pardon is 4096.Now, due to the fact that 2^12 is around 4000, you need to multiply that by 16 (= 2^4) to carry it to 64000 i m sorry is close come 60,000. Hence, the correct choice is the one through 2^16. Note that what is gaining subtracted (3^4 = 81) is lot smaller 보다 2^16 for this reason it will not have actually much impact. 2^64 is lot much greater. Answer (D)_________________
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Which the the complying with is tantamount to (265)(247)?A. 2^8 − 3^2B. 2^8 − 3^4C. 2^12 − 3^2D. 2^16 − 3^4 E. 2^64 − 3^4
An alternate approach is to check THE ANSWERS.Every test-taker should know the strength of 2 through \(2^10\).B: \(2^8 − 3^4 = 256 - 81 =\) as well smallD: \(2^16 − 3^4 = (2^8 + 3^2)(2^8 - 3^2) = (256+9)(256-9) = (265)(247)\)Success!

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We can additionally BALLPARK.\(2^8 ≈ 250\)\(2^9 ≈ 500\)\(2^10 ≈ 1000\)Since (200)(200) = 40,000 and (300)(300) = 90,000, we get:(265)(247) = an integer between 40,000 and also 90,000A. \(2^8 − 3^2 ≈ 250\)B. \(2^8 − 3^4 ≈ 250\)C. \(2^12 − 3^2 ≈ (2^10)(2^2) = 4000\)D. \(2^16 − 3^4 ≈ (2^10)(2^6) ≈ (1000)(64) = 64,000\)E. \(2^64 − 3^4 = \) method too bigOnly D is viable.