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when the integer n is divided by 17, the quotient is x and t
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03 Jun 2018, 07:47
03 Jun 2018, 07:47
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when the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and remainder is 14, which of the following is true?
A. 23x + 17y = 19
B. 17x - 23y = 9
C. 17x + 23y = 19
D. 14x + 5y = 6
E. 5x - 14y = -6
src: Orbit Test prep
A. 23x + 17y = 19
B. 17x - 23y = 9
C. 17x + 23y = 19
D. 14x + 5y = 6
E. 5x - 14y = -6
src: Orbit Test prep
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
when the integer n is divided by 17, the quotient is x and t
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04 Jun 2018, 10:01
04 Jun 2018, 10:01
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amorphous wrote:
when the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and remainder is 14, which of the following is true?
A. 23x + 17y = 19
B. 17x - 23y = 9
C. 17x + 23y = 19
D. 14x + 5y = 6
E. 5x - 14y = -6
A. 23x + 17y = 19
B. 17x - 23y = 9
C. 17x + 23y = 19
D. 14x + 5y = 6
E. 5x - 14y = -6
Here's a useful rule:
If A divided by B equals C with remainder D, then it's also true that BC + D = A (this is an important GRE concept)
Example: Since 32 divided by 5 equals 6 with remainder 2, then it's also true that (5)(6) + 2 = 32
Now onto the question:
We're told that "when n is divided by 17, the quotient is x and the remainder is 5," which means 17x + 5 = n
We're also told that "when n is divided by 23, the quotient is y and the remainder is 14," which means that 23y + 14 = n
Now, if 17x + 5 equals n AND 23y + 14 also equals n, it must be true that 17x + 5 = 23y + 14
If we rearrange the terms of this equation, we get 17x - 23y = 9
Answer: B
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Status:GRE Quant Tutor
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Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
Re: when the integer n is divided by 17, the quotient is x and t
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25 Sep 2022, 04:00
25 Sep 2022, 04:00
1
When the integer n is divided by 17, the quotient is x and the remainder is 5
Theory: Dividend = Divisor*Quotient + Remainder
n -> Dividend
17 -> Divisor
x -> Quotient
5 -> Remainder
=> n = 17*x + 5 = 17x + 5 ..(1)
When n is divided by 23, the quotient is y and remainder is 14
=> n = 23y + 14 ..(2)
From (1) and (2) we get
n = 17x + 5 = 23y + 14
=> 17x - 23y = 14 - 5 = 9
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
n -> Dividend
17 -> Divisor
x -> Quotient
5 -> Remainder
=> n = 17*x + 5 = 17x + 5 ..(1)
When n is divided by 23, the quotient is y and remainder is 14
=> n = 23y + 14 ..(2)
From (1) and (2) we get
n = 17x + 5 = 23y + 14
=> 17x - 23y = 14 - 5 = 9
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
