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# (44^4 − 44)/44 =

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Math Expert
Joined: 02 Sep 2009
Posts: 64114

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28 Aug 2018, 04:28
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Difficulty:

15% (low)

Question Stats:

77% (00:53) correct 23% (00:56) wrong based on 144 sessions

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$$\frac{44^4 − 44}{44} =$$

A. 16,432
B. 70,321
C. 83,244
D. 85,183
E. 93,155

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Director
Joined: 20 Feb 2015
Posts: 722
Concentration: Strategy, General Management
Re: (44^4 − 44)/44 =  [#permalink]

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28 Aug 2018, 04:32
Bunuel wrote:
$$\frac{44^4 − 44}{44} =$$

A. 16,432
B. 70,321
C. 83,244
D. 85,183
E. 93,155

44(44^3 -1)/44 = last digit should be 4-1 = 3
D
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 950
WE: Supply Chain Management (Energy and Utilities)
Re: (44^4 − 44)/44 =  [#permalink]

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28 Aug 2018, 04:35
Bunuel wrote:
$$\frac{44^4 − 44}{44} =$$

A. 16,432
B. 70,321
C. 83,244
D. 85,183
E. 93,155

$$\frac{44^4 − 44}{44} =\frac{44(44^3-1)}{44}$$=$$44^3-1$$

unit digit of 44^3 is 4.

hence $$44^3-1$$ has unit digit, 4-1=3

Ans. (D)
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Rise above the storm, you will find the sunshine
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1120
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: (44^4 − 44)/44 =  [#permalink]

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28 Aug 2018, 04:39
=$$\frac{44^4−44}{44}$$

=$$\frac{44^344-44}{44}$$

=$$\frac{44(44^3-1)}{44}$$

=$$44^3-1$$

=Since 4 has a cyclicity of 2. Then $$44^3$$ will end in 4. Hence the unit digit should be 3.

VP
Joined: 31 Oct 2013
Posts: 1489
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: (44^4 − 44)/44 =  [#permalink]

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28 Aug 2018, 04:39
Bunuel wrote:
$$\frac{44^4 − 44}{44} =$$

A. 16,432
B. 70,321
C. 83,244
D. 85,183
E. 93,155

$$\frac{44^4 − 44}{44} =$$

= $$\frac{44(44^3 -1)}{44}$$

= $$44^3 - 1$$

Unit digits of 44^3 is the same as 4^3 .

$$4^3 = 64.$$

Now deduct 1 from 4.

4-1 = 3.

The only option is D .
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: (44^4 − 44)/44 =  [#permalink]

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30 Aug 2018, 17:09
Bunuel wrote:
$$\frac{44^4 − 44}{44} =$$

A. 16,432
B. 70,321
C. 83,244
D. 85,183
E. 93,155

Re-expressing the single fraction as two separate fractions, we have:

44^4/44 - 44/44

44^3 - 1

Instead of calculating the actual difference, let’s only calculate the units digit of the difference.

Recall that the pattern of units digits of 4 raised to positive integer exponents is 4, 6, 4, 6, … , so odd powers of 44 will end in 4, and even powers of 44 will end in 6.

Thus, we see that 44^3 ends in a 4, so 44^3 - 1 must have a units digit of 3. The only answer choice that is a number with a units digit of 3 is choice D.

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Re: (44^4 − 44)/44 =   [#permalink] 30 Aug 2018, 17:09