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# 6^4− 4^4 = ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58311

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05 Oct 2016, 03:13
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:23) correct 14% (01:36) wrong based on 225 sessions

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6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040

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Posts: 3990
Re: 6^4− 4^4 = ?  [#permalink]

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05 Oct 2016, 06:37
5
Top Contributor
2
Bunuel wrote:
6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040

NOTE: This technique relies on a nice trick that can come in handy in many cases. So, I urge that you learn it (it only takes 1 minute to learn). The technique is squaring numbers that end in 5 quickly in your head. You'll find the video at the bottom of this post.

6⁴ - 4⁴ = (6²)² - (4²)²
= (36)² - (16)²
≈ (35)² - (15)²
≈ 1225 - 225
≈ 1000

The only close answer choice is .....

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##### General Discussion
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Posts: 578
Re: 6^4− 4^4 = ?  [#permalink]

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05 Oct 2016, 04:04
Bunuel wrote:
6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040

We can write the above in terms of

(a+b) (a-b)

6^4−4^4= (6^2)2 - (4^2)2 = (6^2−4^2)*(6^2+4^2) =
(36−16)*(36+16) => 20*52 = 1040

IMO option E.
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05 Oct 2016, 04:10
Bunuel wrote:
6^4− 4^4 = ?

A. 20
B. 52
C. 104
D. 520
E. 1040

$$6^4 - 4^4$$

= $$(6^2)^2 - (4^2)^2$$

= $$(6^2 + 4^2) (6^2 - 4^2)$$

= $$(36+16) (6+4) (6-4)$$

= $$(52) * (10) * (2)$$

= 1040 $$(E)$$

$$OR$$

$$6^4 - 4^4$$

$$= (2 * 3)^4 - (2 * 2)^4$$

$$= 2^4 * 3^4 - 2^4 * 2^4$$

$$= 2^4 (3^4-2^4)$$

$$= 16 * (81-16)$$

$$= 16 * 65$$

$$= 1040 (E)$$

$$OR$$

$$(6*6*6*6) - (4*4*4*4)$$

$$= 1296 - 216$$

$$= 1040$$ $$(E)$$
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Re: 6^4− 4^4 = ?  [#permalink]

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03 Mar 2018, 12:52
6^4 -4^4

The options given makes this question easier to calculate.
The unit digits of 6^6 and 4^6 both ends in 6, so the difference between them end in 0. The only logical answer choice that ends in 0 is 1040.

Ans: E
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Re: 6^4− 4^4 = ?   [#permalink] 03 Mar 2018, 12:52
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