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Intern  Joined: 09 Dec 2009
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What is the remainder when the positive integer n is divided  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:26) correct 32% (01:32) wrong based on 417 sessions

### HideShow timer Statistics What is the remainder when the positive integer n is divided by the positive integer k, where k>1

(1) n= (k+1)^3
(2) k=5

Originally posted by JoyLibs on 25 Jun 2010, 23:42.
Last edited by Bunuel on 12 Nov 2012, 03:26, edited 1 time in total.
Renamed the topic and edited the question.
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Re: GMAT prep DS- Remainder  [#permalink]

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What is the remainder when the positive integer n is divided by the positive integer k, where k>1

(1) $$n=(k+1)^3= k^3 + 3k^2 + 3k + 1=k(k^2+3k+3)+1$$ --> first term, $$k(k^2+3k+3)$$, is obviously divisible by $$k$$ and 1 divide by $$k$$ yields the remainder of 1 (as $$k>1$$). Sufficient.

(2) $$k=5$$. Know nothing about $$n$$, hence insufficient.

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Re: GMAT prep DS- Remainder  [#permalink]

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bunuel's solution is certainly the quickest way to solve. (Of course, it would be (k+1)^3 = k^3 + 3k^2 + 3k + 1, and since each of the "k" terms is divisible by k, the remainder is 1).

But if this deduction/concept didn't jump out at you, you could also solve fairly quickly by picking numbers. If we pick different integer values for k and always end up with the same remainder for n/k, then we can trust that (1) is sufficient. On the other hand, if ever we get different remainder values, we know at once (1) is insufficient:

(1): let k=2. Then, n = (2+1)^3 = 27. 27/2 leaves a remainder of 1.
----let k=3. Then, n = (3+1)^3 = 64. 63 is clearly divisible by 3. Thus, 64/3 leaves a remainder of 1 again.
----let k=4. Then, n = (4+1)^3 = 125. 124 is clearly divisible by 4. Thus, 125/4 leaves a remainder of 1 again.

We've convinced ourselves that (1) is sufficient!
##### General Discussion
Intern  Joined: 24 Nov 2008
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Re: GMAT prep DS- Remainder  [#permalink]

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Yep A. Nice explanation Bunuel.
Intern  Joined: 22 Jun 2010
Posts: 33

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Samarth0711 wrote:
What is the remainder when the positive integer n is divided by the positive integer k, where k > 1?
(1) n = (k+1)**3
(2) k = 5

Answer given is (A) - Need solution.

1 sufficient

n=3k + 3 ==> reminder is 3
Intern  Joined: 25 Apr 2010
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Its (k+1) cubed and not 3 multiplied by (K+1)
Intern  Joined: 22 Jun 2010
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Samarth0711 wrote:
Its (k+1) cubed and not 3 multiplied by (K+1)

it is likely the same

n=(k+1)^3 ==> n=k^3 + 3k²+3k+1 ==> n=k(K²+3k+3) +1 so the reminder is 1

DO you agree ?
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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JoyLibs wrote:
What is the remainder when the positive integer n is divided by the positive integer k, where k>1

(1) n= (k+1)^3
(2) k=5

(k+1)^3

Take any value of k(for eg 8)
K= 8 ; 9^3/8 = (1^3)/9 = 1(because each value of 9/8 gives remainder 1.Hence 1 X 1 X 1)
k = 2 ; 3^3/2 = (1^3)/2 = 1
etc.A sufficient

b) Insufficient
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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1
Testluv wrote:
bunuel's solution is certainly the quickest way to solve. (Of course, it would be (k+1)^3 = k^3 + 3k^2 + 3k + 1, and since each of the "k" terms is divisible by k, the remainder is 1).

But if this deduction/concept didn't jump out at you, you could also solve fairly quickly by picking numbers. If we pick different integer values for k and always end up with the same remainder for n/k, then we can trust that (1) is sufficient. On the other hand, if ever we get different remainder values, we know at once (1) is insufficient:

(1): let k=2. Then, n = (2+1)^3 = 27. 27/2 leaves a remainder of 1.
----let k=3. Then, n = (3+1)^3 = 64. 63 is clearly divisible by 3. Thus, 64/3 leaves a remainder of 1 again.
----let k=4. Then, n = (4+1)^3 = 125. 124 is clearly divisible by 4. Thus, 125/4 leaves a remainder of 1 again.

We've convinced ourselves that (1) is sufficient!

Plugging values was an easier way to understand and solve this problem.
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Re: What is the remainder when the positive integer n is divided  [#permalink]

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A is sufficient

n = (k + 1 )^3
Randomly put values k > 1 i.e. 2,3,4,5,6,7 ...........
n = (2+1)^3 = 27
n/k = 27/2 = remainder 1

same as for 3,4,5,6,7,8...........

so A is sufficient

B. no details available Re: What is the remainder when the positive integer n is divided   [#permalink] 15 Jun 2019, 20:39
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