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# When positive integer x is divided by positive integer y, the quotient

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Joined: 02 Sep 2009
Posts: 59020
When positive integer x is divided by positive integer y, the quotient  [#permalink]

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12 Jun 2017, 02:34
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Difficulty:

15% (low)

Question Stats:

84% (01:54) correct 16% (02:52) wrong based on 121 sessions

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When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211

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Re: When positive integer x is divided by positive integer y, the quotient  [#permalink]

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12 Jun 2017, 03:15
1
Bunuel wrote:
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211

Required number is in form
$$x = 17y + 3$$ ----------- (i)
$$x = 24(y-3) + 5$$ -------- (ii)

Equating (i) and (ii), we get;
$$17y + 3 = 24 (y - 3) + 5$$
$$17y + 3 = 24y - 72 + 5$$
$$24y - 17y = 72 + 3 - 5$$
$$7y = 70$$
$$y = 10$$

$$x = 17 (10) + 3 = 170+3 =173$$. Answer B...
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Re: When positive integer x is divided by positive integer y, the quotient  [#permalink]

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14 Jun 2017, 16:21
Bunuel wrote:
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211

We are given that when positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. Thus:

x/y = 17 + 3/y

x = 17y + 3

We are also given that when x is divided by (y−3), the quotient is 24 and the remainder is 5. Thus:

x/(y-3) = 24 + 5/(y-3)

x = 24(y-3) + 5

x = 24y - 72 + 5

x = 24y - 67

We can equate our two equations and we have:

17y + 3 = 24y - 67

70 = 7y

y = 10

Thus, x = 17(10) + 3 = 173.

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Re: When positive integer x is divided by positive integer y, the quotient  [#permalink]

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11 Oct 2018, 00:38
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Re: When positive integer x is divided by positive integer y, the quotient   [#permalink] 11 Oct 2018, 00:38
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