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When positive integer x is divided by positive integer y, the quotient
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11 May 2022, 01:58
11 May 2022, 01:58
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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
A. 169
B. 173
C. 180
D. 204
E. 211
Part of the project: GRE Quantitative Comparison & Problem Solving Challenge
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: When positive integer x is divided by positive integer y, the quotient
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11 May 2022, 06:13
11 May 2022, 06:13
1
Carcass 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
A. 169
B. 173
C. 180
D. 204
E. 211
There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3
So, we can write x = 17y + 3
When x is divided by (y-3), the quotient is 24 and the remainder is 5.
So, we can write x = 24(y - 3) + 5
What is the value of x?
Since we now have two equations that equal to x, we can write: 17y + 3 = 24(y - 3) + 5
Expand and simplify the right side: 17y + 3 = 24y - 67
Add 67 to both sides of the equation: 17y + 70 = 24y
Subtract 17y from both sides of the equation: 70 = 7y
Solve: y = 10
Find the corresponding value of x, just plug y = 10 into one of our two equations.
We get: 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
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08 Sep 2022, 20:25
08 Sep 2022, 20:25
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3
Theory: Dividend = Divisor*Quotient + Remainder
x -> Dividend
y -> Divisor
17 -> Quotient
3 -> Remainders
=> x = y*17 + 3 = 17y + 3
When x is divided by (y−3), the quotient is 24 and the remainder is 5
=> x = 24*(y-3) + 5 = 24y - 72 + 5 = 24y - 67
=> x = 17y + 3 = 24y - 67
=> 24y - 17y = 3 + 67 = 70
=> 7y = 70
=> y = \(\frac{70}{7}\) = 10
=> x = 17y + 3 = 17*10 + 3 = 170 + 3 = 173
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
x -> Dividend
y -> Divisor
17 -> Quotient
3 -> Remainders
=> x = y*17 + 3 = 17y + 3
When x is divided by (y−3), the quotient is 24 and the remainder is 5
=> x = 24*(y-3) + 5 = 24y - 72 + 5 = 24y - 67
=> x = 17y + 3 = 24y - 67
=> 24y - 17y = 3 + 67 = 70
=> 7y = 70
=> y = \(\frac{70}{7}\) = 10
=> x = 17y + 3 = 17*10 + 3 = 170 + 3 = 173
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
