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When positive integer x is divided by positive integer y

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daina1323031
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When positive integer x is divided by positive integer y [#permalink] New post   10 Nov 2020, 05:43
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When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
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B
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sameerkataria2801
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Re: Divisibility [#permalink] New post   10 Nov 2020, 08:48
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\(x = y * q + r\)
where q is the quotient and r is the remainder

dividing by y on both sides

\(x/y = q + r/y\)
we know what \(x/y\) is and as q is always non negative and \(r/y \)is less than 1

so \(96.12 = 96 + 9/y\)
\(0.12 = 9/y\)
Hence\( y = 75\)
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Re: When positive integer x is divided by positive integer y [#permalink] New post   11 Nov 2020, 13:46
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daina1323031 wrote:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12


The first part of the question can be written as x/y = ANS + 9/y, where "ANS" is our unknown quotient. The second part can be written as x/y = 96 + 12/100. Thus we know that our unknown answer from the first part of the question is 96, so we are left with x/y = 96 + 9/y = 96 + 12/100. Set 9/y equal to 12/100 and solve for y: you are left with y = 75. Answer choice B is correct.
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daina1323031
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Re: When positive integer x is divided by positive integer y [#permalink] New post   06 Dec 2020, 18:49
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just think,
9/y = 0.12

then, y = 75
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Re: When positive integer x is divided by positive integer y [#permalink] New post   28 Dec 2023, 03:07
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When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

\(\frac{x}{y}\) = 96.12
=> x = 96.12y = (96 + 0.12)y = 96y + 0.12y

=> x when divided by y gives 96 as the quotient and 0.12y as the remainder
=> 0.12y = 9
=> y = \(\frac{9}{0.12}\) = 75

So, Answer will be B
Hope it helps!

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Re: When positive integer x is divided by positive integer y [#permalink]
28 Dec 2023, 03:07
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