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

Question

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

PKN · Accepted Answer

(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)

KSBGC · Answer

is it 256 or 265 ? Kindly review it.

Bunuel · Answer

__________________
It's correct as it is.

sudarshan22 · Answer

+1 for   D  .

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

Hence,   D  .

Abhishek009 · Answer

(265)(247)

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

=  2^{16} - 3^4 , Answer must be (D)

Sandy56 · Answer

How do you know that you are suppose to subtract and add 9?? Is there a faster way to approach this question?

KSBGC · Answer

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.

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-Algebra-e1533292089856.jpg

JeffTargetTestPrep · Answer

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

jfranciscocuencag · Answer

Another way to solve it:

Cyclicity:

2  
3

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

BlueRocketAsh · Answer

(265)(247)
(256+9)(256-9)
256^2 - 9^2
2^16 − 3^4

Answer is D

KarishmaB · Answer

If difference of squares doesn't strike, just use approximation.

265 * 247 is close to 300 * 200 = 60,000

2^8 is 256 which is way too small and so is 2^12 which is 4096.
Now, since 2^12 is about 4000, you need to multiply it by 16 (= 2^4) to bring it to 64000 which is close to 60,000.

Hence, the correct option is the one with 2^16. Note that what is getting subtracted (3^4 = 81) is much smaller than 2^16 so it will not have much impact.

2^64 is much much greater.

Answer (D)

GMATGuruNY · Answer

An alternate approach is to TEST THE ANSWERS.
Every test-taker should know the powers of 2 through  2^{10} .

B:  2^8 − 3^4 = 256 - 81 =  too small

D:  2^{16} − 3^4 = (2^8 + 3^2)(2^8 - 3^2) = (256+9)(256-9) = (265)(247) 
Success!

D

We can also 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 90,000

A.  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 =   way too big

Only D is viable.

D

epicstudent · Answer

Is there a way to find more questions like these?

Paras96 · Answer

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

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

Hence D

RitwikAgrawal · Answer

Well. It was pretty simple. the units digit should be 5.

XX5 * XX7 = XXXX5

2 powered up has units digit in pattern 2-4-8-6
3 powered up has units digit in pattern 3-9-7-1

only D and E could have units digit as 5.
E would be larger than 256*256 meaning 2^16 << 2^64
 
So (D)

Malar95 · Answer

Units digits - 5 x 7 = 35 so the unit digit is 5.
2^16, 4th unit digit = 6, 3^4 = 81, thus 1 ---> 6-1=5
Option E is too large.
Thus D.

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

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