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20 Mar 2017, 23:49
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
78% (01:38) correct
22%
(01:40)
wrong
based on 185
sessions
History
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Time
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Not Attempted Yet
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
(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
21 Mar 2017, 00:21
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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
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
21 Mar 2017, 02:12
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saswata4s
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
