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# Simplify (16^3-15^3)(16^2-15^2)

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Intern
Joined: 17 Jun 2014
Posts: 27
Location: India
WE: Information Technology (Computer Software)

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05 Sep 2014, 21:50
1
7
00:00

Difficulty:

5% (low)

Question Stats:

91% (01:00) correct 9% (02:34) wrong based on 106 sessions

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Simplify $$(16^3-15^3)(16^2-15^2)$$ =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon
Math Expert
Joined: 02 Sep 2009
Posts: 47006

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05 Sep 2014, 21:57
3
1
ankitaprsd wrote:
Simplify (16^3-15^3)(16^2-15^2) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon

(16^3 - 15^3)(16^2 - 15^2) =

= ({number with units digit of 6} - {smaller number with units digit of 5})*({number with units digit of 6} - {smaller number with units digit of 5}) =

= {number with units digit of 1}*{number with units digit of 1} = {number with units digit of 1}.

P.S. You must provide the OA if you have it.

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08 Sep 2014, 00:23
1
2
ankitaprsd wrote:
Simplify (16^3-15^3)(16^2-15^2) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon

$$(16^3 - 15^3)(16^2 - 15^2)$$

$$= (16-15)(16^2 + 16*15 + 15^2)(16+15)(16-15)$$

= (256+225+16*15) * 31

(256+225+16*15) >> This expression would give 1 at the units place

Multiplying it by 31 also gives 1 at the units place

Out of the 5 options, only 22351 qualifies

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Status: The Best Or Nothing
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Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

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08 Sep 2014, 01:05
ankitaprsd wrote:
Simplify (16^3-15^3)(16^2-15^2) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon

One More method

$$(16^3-15^3)(16^2-15^2)$$

$$= 16^5 - 16^3 * 15^2 - 15^3 * 16^2 + 15^5$$

Writing down the last digits (Units digits) of the above 4 terms

= 6 - 0 - 0 + 5

= 1

Last digit comes to 1, only 22351 fits in

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Manager
Joined: 10 Sep 2014
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01 Oct 2014, 08:42
Is there an alternate way to solve this problem? Or can someone explain how to know what the units digits will be please?
Math Expert
Joined: 02 Sep 2009
Posts: 47006

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01 Oct 2014, 09:23
1
DangerPenguin wrote:
Is there an alternate way to solve this problem? Or can someone explain how to know what the units digits will be please?

This might help: math-number-theory-88376.html
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15 Sep 2017, 10:08
1
1
ankitaprsd wrote:
Simplify $$(16^3-15^3)(16^2-15^2)$$ =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

We can focus on units digits to solve the question.

Since 6 raised to an exponent always produces a units digit of 6, and 5 raised to an exponent always produces a units digit of 5, we have the units digit of the expression as:

(6 - 5)(6 - 5) = 1 x 1 = 1

Thus, the correct answer must have a units digit of 1. Thus, the answer is 22,351.

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Re: Simplify (16^3-15^3)(16^2-15^2)   [#permalink] 15 Sep 2017, 10:08
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