When the positive integer x is divided by 9, the remainder : GMAT Problem Solving (PS)
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# When the positive integer x is divided by 9, the remainder

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

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22 Nov 2007, 17:04
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 May 2014, 00:00, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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22 Nov 2007, 17:11
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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
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22 Nov 2007, 17:32
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
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22 Nov 2007, 19:50
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....
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02 Dec 2007, 02:40
[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
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Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

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29 Apr 2011, 21:47
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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29 Apr 2011, 22:32
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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29 Apr 2011, 22:35
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.
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Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

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30 Apr 2011, 14:07
i tried plugging in numbers

x = 9q+5

x = 14

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

remainder is 6.

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19 May 2014, 19:56
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
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20 May 2014, 00:16
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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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20 May 2014, 02:50
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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Re: When the positive integer x is divided by 9, the remainder [#permalink]

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26 May 2014, 07:41
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 [#permalink]

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

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16 Oct 2016, 11:37
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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16 Oct 2016, 12:03
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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16 Oct 2016, 12:44
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] 16 Oct 2016, 12:44
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