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

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Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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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
[Reveal] Spoiler: OA

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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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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}.

Answer: B.

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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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New post 08 Sep 2014, 00:23
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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

Answer = B
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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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New post 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

Answer = B
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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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New post 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? :)

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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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Re: Simplify (16^3-15^3)(16^2-15^2) [#permalink]

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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.

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