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Which of the following is equivalent to (265)(247)?

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Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 10 Aug 2018, 03:41
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A
B
C
D
E

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  55% (hard)

Question Stats:

64% (02:07) correct 36% (02:08) wrong based on 85 sessions

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Re: Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 10 Aug 2018, 03:46
Bunuel wrote:
Which of the following is equivalent to (265)(247)?

A. 2^8 − 3^2
B. 2^8 − 3^4
C. 2^12 − 3^2
D. 2^16 − 3^4
E. 2^64 − 3^4



is it 256 or 265 ? Kindly review it.
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New post 10 Aug 2018, 04:02
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Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 10 Aug 2018, 04:12
1
Bunuel wrote:
Which of the following is equivalent to (265)(247)?

A. 2^8 − 3^2
B. 2^8 − 3^4
C. 2^12 − 3^2
D. 2^16 − 3^4
E. 2^64 − 3^4


\((265)(247)
=(256+9)(256-9)
=(16^2+3^2)(16^2-3^2)
=(16^2)^2-(3^2)^2
=16^4-3^4
=(2^4)^4-3^4
=2^{16}-3^4\)

Ans. (D)
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New post 10 Aug 2018, 04:15
Bunuel wrote:
Which of the following is equivalent to (265)(247)?

+1 for D.

= ( 265 ) * ( 247 )
= ( 256 + 9 ) * ( 256 - 9 )
= ( 2^8 + 3^2 ) * ( 2^8 - 3^2 )
= ( 2^16 - 3^4 )

Hence, D.
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Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 10 Aug 2018, 08:41
Bunuel wrote:
Which of the following is equivalent to (265)(247)?

A. 2^8 − 3^2
B. 2^8 − 3^4
C. 2^12 − 3^2
D. 2^16 − 3^4
E. 2^64 − 3^4


\((265)(247)\)

\(= (2^8 + 3^2)(2^8 - 3^2)\)

= \(2^{16} - 3^4\), Answer must be (D)
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Re: Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 10 Aug 2018, 15:10
How do you know that you are suppose to subtract and add 9?? Is there a faster way to approach this question?
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Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 10 Aug 2018, 15:31
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Sandy56 wrote:
How do you know that you are suppose to subtract and add 9?? Is there a faster way to approach this question?



Happy to respond . GMAT questions are designed based on pattern. Why 9 ? If u look at the answer choices u must see one thing that all the options have their base 2 and 3. That's giving u hint that u can some how break down the numbers and convert them into formula. 265 = 256 + 9 . see 256 can be expressed as \(2^8\) and 9 as \(3^2\) . This is how it works. Some times u need deduct to apply formula. U can back solve this question. it was also possible to guess . experts may need max 30 sec.

Hope it's clear.
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Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 13 Aug 2018, 07:48

Solution


To find:
    • Which of the given answer choices is equal to 265 * 247

Approach and Working:
    • 265 * 247 can be written as (256 + 9) * (256 – 9)
      o (256 + 9) * (256 – 9) = (28 + 32) * (28 – 32), since 28 = 256 and 32 = 9
      o Now, this is of the form, (a + b) * (a – b), which is equal to \(a^2 – b^2\)

Therefore, (28 + 32) * (28 – 32) = \((28)^2 – (32)^2\) = \(2^{16} - 3^4\)

Hence, the correct answer is option D

Answer: D

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Re: Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 18 Aug 2018, 19:31
Bunuel wrote:
Which of the following is equivalent to (265)(247)?

A. 2^8 − 3^2
B. 2^8 − 3^4
C. 2^12 − 3^2
D. 2^16 − 3^4
E. 2^64 − 3^4


Breaking each answer choice into the difference of squares, we have:

A) 2^8 − 3^2

(2^4 - 3^1)(2^4 + 3^1)

13 x 17

We see that A is not correct.

B) 2^8 − 3^4

Since the expression in B is close in value to the expression in A, we see that B is not correct.

C) 2^12 − 3^2

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

61 x 67

We see that C is not correct.

D) 2^16 − 3^4

(2^8 - 3^2)(2^8 + 3^2)

(247)(265)

We see that D is correct.

Answer: D
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Which of the following is equivalent to (265)(247)?  [#permalink]

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New post 04 Mar 2019, 15:57
Another way to solve it:

Cyclicity:

2 [ 2,4,8,6 ]
3 [ 3,9,7,1 ]

Test in the options:

A. 2^8 − 3^2 --- Discard, is too small.
B. 2^8 − 3^4 -- Last digit subtraction (6 - 1) ... 5 Hold.
C. 2^12 − 3^2 --- Last digit (6-9) -3 ... Discard
D. 2^16 − 3^4 --- Last digit subtraction (6 - 1) ... 5 Hold.
E. 2^64 − 3^4 --- Discard, this one is too big.

By approximation between B&D.

B. 2^8 − 3^4 (256)(81) the answer must be (265)(247), hence is smaller. --- Discard

D. 2^16 − 3^4 --- Best possibilities to be correct.

D
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Which of the following is equivalent to (265)(247)?   [#permalink] 04 Mar 2019, 15:57
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