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When positive integer N is divided by positive integer P, the quotient

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Bunuel
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When positive integer N is divided by positive integer P, the quotient [#permalink] New post   27 Feb 2015, 05:59
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When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N?

A. 151
B. 331
C. 511
D. 691
E. 871

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ynaikavde
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Re: When positive integer N is divided by positive integer P, the quotient [#permalink] New post   27 Feb 2015, 07:30
N/P=18 7/P= 18P+7

N/(P+2)=15 1/(P+2)=15P+30+1

solving these two equations
we get P=8 N= 151 answer is A.
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Re: When positive integer N is divided by positive integer P, the quotient [#permalink] New post   27 Feb 2015, 21:44
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Bunuel wrote:
When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N?

A. 151
B. 331
C. 511
D. 691
E. 871

Kudos for a correct solution.


Just remember a simple formula: Dividend = Quotient * Divisor + Remainder
i.e. Div. = QD + R

Given that,
N = 18P + 7 ----- (i)
N = 15(P + 2) + 1 ----- (ii)
Equate (i) and (ii),
So, 18P + 7 = 15(P + 2) + 1
So, P = 8
Put P = 8 in (i)
Hence N = 151.
Hence option A.

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Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
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Re: When positive integer N is divided by positive integer P, the quotient [#permalink] New post   28 Feb 2015, 00:30
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Here we go:


Dividend = Divisor * quotient + remainder.

Put in the values -> Solve the two equations.


option A is correct.
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Re: When positive integer N is divided by positive integer P, the quotient [#permalink] New post   02 Mar 2015, 05:52
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Bunuel wrote:
When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 1. What is the value of N?

A. 151
B. 331
C. 511
D. 691
E. 871

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

Use the rule dividend = (integer quotient)*(divisor) + remainder to translate each sentence.

The first sentence becomes N = 18P + 7. The second equation becomes N = (P + 2)*15 + 1, which simplifies to N = 15P + 31. These are ordinary simultaneous equations (https://magoosh.com/gmat/2012/gmat-quant ... variables/). Since they both equal N already, let’s set them equal and solve for P.
18P + 7 = 15P + 31
3P + 7 = 31
3P = 24
P = 8

Now that we know P = 8, we can just plug in. The product 15*8 is particularly easy to do, without a calculator, by using the “doubling and halving” trick. Double 15 to get 30, and take half of 8 to get 4 —- 15*8 = 30*4 = 120. So
N = 15(8) + 31 = 120 + 31 = 151
N = 151, answer = A.
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Re: When positive integer N is divided by positive integer P, the quotient [#permalink] New post   07 Feb 2022, 10:03
Hello,

The formula Says: Dividend=Divisor*Quotient + remainder, how we can flip this formula to get the answer.
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Re: When positive integer N is divided by positive integer P, the quotient [#permalink]
07 Feb 2022, 10:03
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