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When the positive integer x is divided by 9, the remainder
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Updated on: 20 May 2014, 01:00
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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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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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Re: MGMT  Remainder
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22 Nov 2007, 18:11
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
I could use the plug in no. approach but it's too time consuming. Please help. 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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Re: MGMT  Remainder
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22 Nov 2007, 18:32
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
I could use the plug in no. approach but it's too time consuming. Please help. 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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Re: MGMT  Remainder
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22 Nov 2007, 20:50
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
I could use the plug in no. approach but it's too time consuming. Please help. thanks
Answer is 6
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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Re: MGMT  Remainder
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02 Dec 2007, 03:40
[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 159 = 6



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Re: When the positive integer x is divided by 9, the remainder is 5. What
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29 Apr 2011, 22:47
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
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29 Apr 2011, 23:32
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 Answer  E
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Re: When the positive integer x is divided by 9, the remainder is 5. What
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29 Apr 2011, 23:35
x = 9 * q + 5 3x = 27 *q + 15
159 = 6. Hence the remainder is 6. Which is less than 9.
If suppose x = 9 *q + 7 3x = 27 * q + 21
Remainder will be 219*2 = 3. Hope this will help you.
E.



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Re: When the positive integer x is divided by 9, the remainder is 5. What
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30 Apr 2011, 15:07
i tried plugging in numbers
x = 9q+5
x = 14
3x = 42 = 36 + 6 = 9*4+6
remainder is 6.
Answer is E.



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Re: MGMT  Remainder
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19 May 2014, 20:56
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: 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 159 = 6



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Re: MGMT  Remainder
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20 May 2014, 01:16
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. 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. Answer: E. Hope this helps.
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Re: When the positive integer x is divided by 9, the remainder
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20 May 2014, 03:50
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
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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).



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Re: When the positive integer x is divided by 9, the remainder is 5. What
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16 Oct 2016, 12:37
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
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16 Oct 2016, 13:03
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
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Re: When the positive integer x is divided by 9, the remainder
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16 Oct 2016, 13:44
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 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
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10 Jul 2017, 23:28
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 *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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Re: When the positive integer x is divided by 9, the remainder
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14 Mar 2019, 17:12
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 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. Answer: E
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Re: When the positive integer x is divided by 9, the remainder
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