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6^4− 4^4 = ?

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Math Expert
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Posts: 52294
6^4− 4^4 = ?  [#permalink]

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New post 05 Oct 2016, 02:13
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:25) correct 12% (01:37) wrong based on 183 sessions

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CEO
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Re: 6^4− 4^4 = ?  [#permalink]

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

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


Since the answer choices are quite spread apart, we can approximate.

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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Re: 6^4− 4^4 = ?  [#permalink]

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New post 05 Oct 2016, 03:04
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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6^4− 4^4 = ?  [#permalink]

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New post 05 Oct 2016, 03:10
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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New post 03 Mar 2018, 11:52
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 = ? &nbs [#permalink] 03 Mar 2018, 11:52
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