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Re: If t is a positive integer and r is the remainder when t^2+5t+6 is div [#permalink]

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11 Jul 2009, 19:06

Just wanted to add that I didn't know any way how stmt 2 could give an answer, but just in case there could be a possibility, and since i had no logic to check, i took random numbers satisfying stmt 2, in this case 6 and 8, and substituted in the polynomial expression, both gave different remainders, so i was sure that stmt 2 has to be insufficient.

Re: If t is a positive integer and r is the remainder when t^2+5t+6 is div [#permalink]

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13 Jul 2009, 08:13

Guys, this is a very interesting question , I have seen this type for the first time. I have couple of questions

1) if remainder for t/7 is known we can know the remainder for \(t^2/7\) , and vice verca is not possible ? ie if the the remainder for \(t^2/7\) is known t/7 is not known ?

2) where can I get additional information on these types of questions ?

Re: If t is a positive integer and r is the remainder when t^2+5t+6 is div [#permalink]

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13 Jul 2009, 08:53

1

This post received KUDOS

skpMatcha wrote:

Guys, this is a very interesting question , I have seen this type for the first time. I have couple of questions

1) if remainder for t/7 is known we can know the remainder for \(t^2/7\) , and vice verca is not possible ? ie if the the remainder for \(t^2/7\) is known t/7 is not known ?

2) where can I get additional information on these types of questions ?

Help !

Actually there is a remainder rule, that works only for additions, subtractions and multiplications, but not for divisions.

Ill illustrate this rule with an example.

25/7 - R= 4 41/7 - R= 6 addition (25+41)/7 should give remainder of 4+6, but 10 is greater than 7, so the final remainder will be that of 10/7, ie 3 checking this rule - 25+41 = 66..... 66/7 - R = 3

subtraction (41-25)/7 should give remainder 6-4 = 2...... check: 41-25 = 16. .....16/7 - R= 2

multiplication 41*25/7 should give remainder of (6*4)/7, ie 24/7 -> R= 3 check: 41*25 = 1025....1025/7 -> R= 3

Now square is nothing but (t/7) * (t/7), so applying multiplication rule, we get that remainder should be R*R

Square root is division, and therefore the rule doesnt apply to square roots.

Re: If t is a positive integer and r is the remainder when t^2+5t+6 is div [#permalink]

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04 Apr 2015, 22:09

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If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

First of all factor \(t^2+5t+6\) --> \(t^2+5t+6=(t+2)(t+3)\).

(1) When t is divided by 7, the remainder is 6 --> \(t=7q+6\) --> \((t+2)(t+3)=(7q+8)(7q+9)\). Now, no need to expand and multiply all the terms, just notice that when we expand all terms but the last one, which will be 8*9=72, will have 7 as a factor and 72 yields the remainder of 2 upon division by 7. Sufficient.

(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in \((t+2)(t+3)\) will give different remainder upon division by 7. Not sufficient.