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If r is the remainder when each of 7654, 8506, and 9997 is divided by the greatest number d = (d > 1) then d - r is equal to = ?

114
218
324
428

Answer:- 1

Explanation:-

Solution:

d = HCF of (8506 - 7654), (9997 - 8506), (9997 - 7654)
= HCF of 857, 1491, 2343 = 213

\begin{aligned} 213 \bar{) 7654 (} 35 \\ \frac{639}{1264} \\ \frac{1065}{199} \\ Clearly r  =  199 \\ ∴ d - r = 213 - 199 \\ = 14 \end{aligned}

$\eqalign{ & {\text{213}}\overline {){\text{ 7654 (}}} 35 \cr & \,\,\,\,\,\,\,\,\,\,\frac{{639}}{{{\text{ }}1264}} \cr & \,\,\,\,\,\,\,\,\,\,\frac{{{\text{ }}1065}}{{{\text{ }}199}} \cr & {\text{Clearly r = 199}} \cr & \therefore d - r = 213 - 199 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 14 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

d = HCF of (8506 - 7654), (9997 - 8506), (9997 - 7654)
= HCF of 857, 1491, 2343 = 213

\begin{aligned} 213 \bar{) 7654 (} 35 \\ \frac{639}{1264} \\ \frac{1065}{199} \\ Clearly r  =  199 \\ ∴ d - r = 213 - 199 \\ = 14 \end{aligned}

$\eqalign{ & {\text{213}}\overline {){\text{ 7654 (}}} 35 \cr & \,\,\,\,\,\,\,\,\,\,\frac{{639}}{{{\text{ }}1264}} \cr & \,\,\,\,\,\,\,\,\,\,\frac{{{\text{ }}1065}}{{{\text{ }}199}} \cr & {\text{Clearly r = 199}} \cr & \therefore d - r = 213 - 199 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 14 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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