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Which is the first non-zero digit from the right in the product

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Which is the first non-zero digit from the right in the product [#permalink]

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New post 15 Jan 2018, 08:28
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Which is the first non-zero digit from the right in the product of \((2^4)(3^7)(4^3)(5^{11})(7^2)(9^3)(10^4)\)?
A) 3
B) 5
C) 6
D) 8
E) 9
[Reveal] Spoiler: OA

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Which is the first non-zero digit from the right in the product [#permalink]

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New post 15 Jan 2018, 08:52
souvonik2k wrote:
Which is the first non-zero digit from the right in the product of \((2^4)(3^7)(4^3)(5^{11})(7^2)(9^3)(10^4)\)?
A) 3
B) 5
C) 6
D) 8
E) 9


\((2^4)(3^7)(4^3)(5^{11})(7^2)(9^3)(10^4)=(2^4)(3^7)(2^3*2)(5^{11})(7^2)(9^3)(2*5)^4)\)

so we have \(2^{14}\) and \(5^{15}\).

Hence when these two are multiplied we will have \((2*5)^{14}*5\)

\(5\) multiplied with any Odd number will have units digit as \(5\).

\(3^7 =>\)unit's digit \(7\)

\(7^2=>\) unit's digit \(9\)

\(9^3=>\) unit's digit \(9\)

so product of the above number will result in an Odd number which when multiplied by \(5\) will have \(5\) as non-zero digit

Option B
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Which is the first non-zero digit from the right in the product [#permalink]

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New post 15 Jan 2018, 09:50
souvonik2k wrote:
Which is the first non-zero digit from the right in the product of \((2^4)(3^7)(4^3)(5^{11})(7^2)(9^3)(10^4)\)?
A) 3
B) 5
C) 6
D) 8
E) 9

\((2^4)(3^7)(4^3)(5^{11})(7^2)(9^3)(10^4)\)

= \(2^4*3^7*2^6*5^{11}*7^2*3^6*10^4\)

= \(2^{10}*3^{13}*5^{11}*7^2*10^4\)

= \(3^{13}*5*7^2*10^{14}\)

\(3^{13}\) will have last digit as 3
\(7^2\) will have last digit as 9

This the last non zero digit will be 3*9*5 = xxx5, last non zero digit will be 5, answer will be (B)
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Which is the first non-zero digit from the right in the product   [#permalink] 15 Jan 2018, 09:50
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