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Director  Joined: 10 Feb 2006
Posts: 611
When the positive integer x is divided by 9, the remainder  [#permalink]

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Difficulty:   5% (low)

Question Stats: 88% (01:10) correct 12% (01:26) wrong based on 249 sessions

### HideShow timer Statistics 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

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Originally posted by alimad on 22 Nov 2007, 18:04.
Last edited by Bunuel on 20 May 2014, 01:00, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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3
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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?
0

1

3

4

6

thanks

X=9K+5

3X=3(9K+5)

then

(27K+15)/9
3K+15/9
15/9 ends with remainder 6.

E
also plug any number into K to test
##### General Discussion
Director  Joined: 08 Jun 2007
Posts: 528

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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?
0

1

3

4

6

thanks

6
Plugging is simple here.

x = 9k + 5
for k =1 x = 14
3x = 42 . Divide by 9 , you get remainder 6.
Same with k=2 and other k's
Senior Manager  Joined: 06 Aug 2007
Posts: 297

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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?
0

1

3

4

6

thanks

lets say the quotient is y.

So from the first part 9y+ 5 = x

so 3x = 27y + 15(remainder)

since 15 when divided by 9 gives you 6....
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1657

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[quote="alimad"]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
Intern  Joined: 29 Apr 2011
Posts: 6
Re: When the positive integer x is divided by 9, the remainder is 5. What  [#permalink]

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plug in nos.

Let x = 14, 23, 32
x/9
Reminder is 5

Let 3x = 3*14, 3*23, 3*32
3x/9
Reminder is 6
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Re: When the positive integer x is divided by 9, the remainder is 5. What  [#permalink]

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x= 9k + 5

=> 3x = 27k + 15

=> 3x = 27k + 9 + 6

=> 3x/9 = 9(3k + 1)/9 + 6/9

So remainder is 6

Otherwise, just take 5 as an example :

So 5/9 = remainder 5

15/9 = remainder 6

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Re: When the positive integer x is divided by 9, the remainder is 5. What  [#permalink]

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x = 9 * q + 5
3x = 27 *q + 15

15-9 = 6. Hence the remainder is 6. Which is less than 9.

If suppose
x = 9 *q + 7
3x = 27 * q + 21

Remainder will be 21-9*2 = 3.

E.
Director  Joined: 01 Feb 2011
Posts: 629
Re: When the positive integer x is divided by 9, the remainder is 5. What  [#permalink]

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i tried plugging in numbers

x = 9q+5

x = 14

3x = 42 = 36 + 6 = 9*4+6

remainder is 6.

Manager  Joined: 26 May 2013
Posts: 52

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1
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:
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
Math Expert V
Joined: 02 Sep 2009
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3
Amit0507 wrote:
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.

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.

Theory on remainders problems: remainders-144665.html

Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

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

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Lets take the number as x

when x is divided by 9 the remainder is 5 hence x can be written as

x=9k +5

Multiplying by 3 will give

3x = 27k + 15

we can also write
3x = 27k + 9 + 6

Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
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Posts: 4
Re: When the positive integer x is divided by 9, the remainder  [#permalink]

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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

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).
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Re: When the positive integer x is divided by 9, the remainder is 5. What  [#permalink]

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E is correct. Here's why:

From the prompt we can create the following equation:

x=9y+5

Now, let's say y = 0 --> then x = 5 --> plug this into 3x --> 3x = 15

15/9 = 1 Remainder 6
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Re: When the positive integer x is divided by 9, the remainder  [#permalink]

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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

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

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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

Least possible number of x is 5

So, 3x = 15

$$\frac{15}{9}$$ = Remainder 6

Hence correct answer will be (E) 6

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

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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

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

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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

We can let x = 14 since the remainder when 14 is divided by 9 is 5. So 3x = 42 and 42/9 = 4 R 6. Therefore, the remainder is 6.

Alternate Solution:

Since the remainder from the division of x by 9 is 5, we can write x = 9s + 5 for some positive integer s.

Multiplying by 3, we get 3x = 27s + 15 = 27s + 9 + 6 = 9(3s + 1) + 6. Thus, the quotient is 3s + 1 and the remainder is 6.

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