Question

Show that only one of the number of n, n+2 and n +4 is divisble by 3.
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Answer 1

USING EUCLIDS DIVISION LEMMA,

a=bq+r

given,b=3

⇒a=3q+r

(r=0,1,2)

now,

When r=0,

n⇒a=3q+0——————————divisible

n+2⇒a=3q+2—————————not divisible

n+4⇒a=3q+4—————————not divisible

when r=1,

n⇒3q+1—————————not divisible

n+2⇒3q+3—————————divisible

n+4⇒3q+5—————————not divisible

when r=2,

n⇒3q+2—————————not divisible

n+2⇒3q+4—————————not divisible

n+4⇒3q+6—————————divisible

∴FROM 1,2,3 WE CAN SHOW THAT only one of the number of n, n+2 and n +4 is divisble by 3.

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Answer 2

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