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Divisor Quotient Remainder

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by nlpfollower » Mon Mar 15, 2010 9:33 pm
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 the 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

OA is B. Please elaborate how.
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by harsh.champ » Mon Mar 15, 2010 10:28 pm
nlpfollower 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 the 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

OA is B. Please elaborate how.
n/17 = (n-5)/17 + 5/17 = x + 5/17 or n=17x + 5

Likewise,
n=23y + 14
so,17x+5 =23y+14
Hence, C is the answer.
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by lkm » Mon Mar 15, 2010 10:30 pm
Integer to be find = n


Case 1:
Divisor = 17
Quotient = x
Remainder = 5

Form the equation:-

17x + 5 = n

Case 2:
Divisor = 23
Quotient = y
Remainder = 14

Form the equation:-

23y + 14 = n

compare the equation 1 and 2

17x + 5 = 23y + 14

=> 17x - 23y = 9

Answer is B
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by Phirozz » Mon Mar 15, 2010 10:33 pm
nlpfollower 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 the 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

OA is B. Please elaborate how.
n = 17x+5 = 23y+14
ie 17x-23y = 9
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by nlpfollower » Mon Mar 15, 2010 11:17 pm
Thanks.
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by Brent@GMATPrepNow » Fri May 20, 2011 9:52 am
nlpfollower 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 the 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

OA is B. Please elaborate how.
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 GMAT 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 choice B)

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by angry.birds » Mon Jul 11, 2011 2:23 am
Hi,

Can someone please answer this?

If the quotient of a/b is positive, which of the following must be true?

1. a>o
2. b>0
3. ab>0
4. a-b>0
5. a+b>0

I am stuck between 1,2 and 3. I know 3 will be true always but somehow cant seem to get why is 1 or 2 wrong?

If I assume my dividend = 6 (a), divisor = -3 (b), then also my quotient will be positive (2). I am not sure if the question is talking about the entire expression (a/b) being positive or the quotient being positive.

If the quotient has to be positive it will hold true when my b is negative and a is positive. Similarly, if i assume my dividend to be -6 and divisor to be 3. then also my quotient will be positive.

Am I missing something here?
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by GMATGuruNY » Mon Jul 11, 2011 3:08 am
angry.birds wrote:Hi,

Can someone please answer this?

If the quotient of a/b is positive, which of the following must be true?

1. a>o
2. b>0
3. ab>0
4. a-b>0
5. a+b>0

I am stuck between 1,2 and 3. I know 3 will be true always but somehow cant seem to get why is 1 or 2 wrong?

If I assume my dividend = 6 (a), divisor = -3 (b), then also my quotient will be positive (2). I am not sure if the question is talking about the entire expression (a/b) being positive or the quotient being positive.

If the quotient has to be positive it will hold true when my b is negative and a is positive. Similarly, if i assume my dividend to be -6 and divisor to be 3. then also my quotient will be positive.

Am I missing something here?
Try to show that the answers DON'T have to be true.
Let a = -2, b = -1.
a/b = (-2)/(-1) = 2, yielding a positive quotient.

Now plug a = -2 and b = -1 into the answers.
Eliminate any answer choices that are not true when a=-2 and b=-1.

A: -2>0. Not true. Eliminate A
B: -1>0. Not true. Eliminate B.
C: (-2)(-1) > 0. True. Hold onto C.
D: -2-(-1) > 0. Not true. Eliminate D.
E: -2+(-1) > 0. Not true. Eliminate E.

The correct answer is C.

Quotient = the result of division.
For the quotient of a and b to be positive, a and b must have the same sign.
Since (positive)*(positive)>0 and (negative)*(negative)>0, answer choice C must be true.
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by amit2k9 » Mon Jul 11, 2011 9:21 pm
n=17x+5=23y+14
gives B
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by MBA.Aspirant » Tue Jul 12, 2011 2:19 am
nlpfollower 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 the 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

OA is B. Please elaborate how.
n = 17x+5
n = 23y + 14

17x+5 = 23y +14

17x -23y = 9
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