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Are we not supposed to reduce the fraction in such questions? I'm getting 2 as a remainder to this problem. I reduced 42/9 to 14/3 leaving 2 as the remainder. Please point out my error.

Thanks

yezz wrote:

alimad wrote:

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9? 0

1

3

4

6

x= 9k+5 ie: 3x = 27k+15, 27k+15 / 9 = a reminder of 15-9 = 6

Are we not supposed to reduce the fraction in such questions? I'm getting 2 as a remainder to this problem. I reduced 42/9 to 14/3 leaving 2 as the remainder. Please point out my error.

Thanks

42 divided by 9 gives the reminder of 6. If you reduce 42/9 by 3 to 14/3, then the remainder you get dividing 14 by 3 is 2. The remainders are not the same which means that this approach is not correct. Actually the remainder will be 3 times as great (by the factor you reduced), so 6.

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0 B. 1 C. 3 D. 4 E. 6

Approach 1:

When the positive integer x is divided by 9, the remainder is 5: \(x=9q+5\).

\(3x=27q+15\). Now, 27 is divisible by 9, so the remainder is obtained only by division 15 by 9. 15 gives the remainder of 6 upon dividing by 9.

Answer: E.

Approach 2:

When the positive integer x is divided by 9, the remainder is 5 --> let x=5. Then 3x=15. 15 divided by 9 gives the remainder of 6.

Re: When the positive integer x is divided by 9, the remainder [#permalink]

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26 May 2014, 08:41

alimad wrote:

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0 B. 1 C. 3 D. 4 E. 6

dividend = quotient * divisior + R so, x = q * 9 + 5 so, q * 9 = x - 5

also, 3x = 9 * q + R so, q * 9 = 3x - R

Thus, 3x - R = x - 5 so, R = 2x + 5

Now x cannot be 0 or a negative number (as its given that it is positive). Thus, whatever the answer is, its greater than 5. As per the answer choices, only 6 is greater than 5. Thus we have answer as 6 (choice E).

Re: When the positive integer x is divided by 9, the remainder [#permalink]

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25 Mar 2016, 03:43

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When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0 B. 1 C. 3 D. 4 E. 6

*Test like approach:* choose a number that satisfies the given constraint I'm. Remainder 5 when divided by 9. Such number, x = 5, 14, 23 etc.

Choose smallest and find 3x I.e. 3x= 15 Divide by 9 and check remainder = 6

*Point to learn* A number when divided by 9 leaves remainder 5 will be of the form = 9a+5

I.e. x= 9a+5

Now 3x = 3(9a+5)= 27a+15

When 3x is divided by 9 then 27a is always divisible hence remainder will be obtained by getting the remainder when 15 is divided by 9

Answer : Remainder =6

Answer option E
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