When the positive integer x is divided by 9, the remainder

Question

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

Bunuel · Accepted Answer

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. 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.

Ravshonbek · Answer

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

gmatv11 · Answer

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

Amit0507 · Answer

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

rohit8865 · Answer

GMATinsight · Answer

*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

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

Let the number x be in the form 9q + 5

3x is 27q + 15 and this on dividing by 9 will give us a remainder same as the remainder when 15 is divided by 9 which is 6.

(option e)

Devmitra Sen
GMAT SME

BrushMyQuant · Answer

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

Lets solve the problem using two methods

Method 1: Substitution

When the positive integer x is divided by 9, the remainder is 5
Let x = 9 + 5 = 14
=> 3x = 14*3 = 42

3x divided by 9 = 42 divided by 9, will give 6 remainder (36 + 9)

Method 2: Algebra

When the positive integer x is divided by 9, the remainder is 5.

Dividend = Divisor * Quotient + Remainder

=> x = 9*a + 5 (where a is the quotient)
=> x = 9a + 5 ...(1)

What is the remainder when 3x is divided by 9?

=> 3x = 3*(9a + 5) = 27a + 15

Remainder of 3x by 9 = Remainder of 27a + 15 by 9 = Remainder of 27a by 9 + Remainder of 15 by 9 = 0 + 6 = 6

So,  Answer will be E 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

shivani1351 · Answer

Given: When the positive integer x is divided by 9, the remainder is 5.

Hence, x = 9k+5

Thus, 3x = 27k+15

Dividing 3x by 9:

Remainder when 27k is divided by 9 = 0, and remainder when 15 is divided by 9 is 6. Hence, the overall remainder is 6 (Option E)

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

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