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If k is a positive integer, then k(k+1)(k+3) is

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If k is a positive integer, then k(k+1)(k+3) is  [#permalink]

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New post 20 Mar 2017, 22:49
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E

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Question Stats:

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If k is a positive integer, then k(k+1)(k+3) is

(A) even only when k is even
(B) even only when k is odd
(C) odd whenever k is odd
(D) divisible by 3 only when k is odd
(E) divisible by 4 whenever k is odd

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Re: If k is a positive integer, then k(k+1)(k+3) is  [#permalink]

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New post 20 Mar 2017, 23:21
If k is a positive integer, then k(k+1)(k+3) is

If K is an even positive integer and expressed as 2a, then the above expression becomes 2a (2a+1) (2a+3), which means whenever K is even the above expression is also even

If K is an odd positive integer and expressed as 2a+1, then the above expression becomes (2a+1) (2a+2) (2a+4), and can be simplified to 4(2a+1)(a+1)(a+2) which means whenever K is odd the above expression is also even and divisible by 4

Now Let's look at each of the options

(A) even only when k is even --> False as shown above
(B) even only when k is odd --> False as shown above
(C) odd whenever k is odd --> False as shown above
(D) divisible by 3 only when k is odd --> If K=2, then above expression becomes divisible by 3. Hence False.
(E) divisible by 4 whenever k is odd --> As shown above, this is true for whenever K is Odd. Hence True

Answer is E
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Re: If k is a positive integer, then k(k+1)(k+3) is  [#permalink]

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New post 21 Mar 2017, 01:12
saswata4s wrote:
If k is a positive integer, then k(k+1)(k+3) is

(A) even only when k is even
(B) even only when k is odd
(C) odd whenever k is odd
(D) divisible by 3 only when k is odd
(E) divisible by 4 whenever k is odd


when k is odd say 2a+1, the expression will be (2a+1)(2a+2)(2a+4) = 4(2a+1)(a+1)(a+2) . even and divisible by 4
when k is even sat 2a, the expression will be 2a(2a+1)(2a+3) even

A. rejected because for k=odd the expression is even
B. rejected as for k=even the expression is even
C. rejected as this is never the case
D. Cannot say as the divisibility depends on the value of a
E. for odd values, the expression is definitely divisible by 4. ANSWER
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Re: If k is a positive integer, then k(k+1)(k+3) is  [#permalink]

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New post 21 Mar 2017, 18:31
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Hi saswata4s,

This question can be solved rather easily by TESTing VALUES. From the answer choices, we can see the Number Property rules that we should focus on are ODDs and EVENS.

We're told that K is a POSITIVE INTEGER and we're asked about the product (K)(K+1)(K+3)

IF....
K = ODD = 1
then (1)(2)(4) = 8, so K is EVEN

K = EVEN = 2
then (2)(3)(5) = 30, so K is EVEN

With these two TESTs, we can eliminate 4 of the answers, leaving....

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Re: If k is a positive integer, then k(k+1)(k+3) is &nbs [#permalink] 21 Mar 2017, 18:31
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If k is a positive integer, then k(k+1)(k+3) is

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