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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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15 Jan 2018, 09:28
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Difficulty:

35% (medium)

Question Stats:

61% (01:31) correct 39% (01:14) wrong based on 41 sessions

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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

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

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15 Jan 2018, 09:52
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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15 Jan 2018, 10:50
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, 10:50
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