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Math Expert V
Joined: 02 Sep 2009
Posts: 59712
When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Question Stats: 90% (00:40) correct 10% (01:32) wrong based on 187 sessions

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When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

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Posts: 978
Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

since x is positive and 20 is multiple of 5 ,
we can divide 8 by 5 to get 3 remainder

Ans B
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4145
Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Top Contributor
1
Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

In this case, we aren't told how many times 20 divides into x, but this isn't a problem.
Let's just say that 20 divides into x k times.
In other words, x divided by 20 equals k with remainder 8
Applying the above rule, we can then say: x = 20k + 8 for some positive integer k

What is the remainder when x is divided by 5?
We know that: x = 20k + 8
Rewrite as: x = 20k + 5 + 3
And the factor to get: x = 5(4k + 1) + 3
So, we can see that x is 3 greater than some multiple of 5
This tells us that, if we divide x by 5, the remainder will be 3

Cheers,
Brent
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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

Quote:
When positive integer x is divided by 20, the remainder is 8.

Lest possible value of x = 28.

Quote:
remainder when x is divided by 5

Is, 3

Hence, correct aswer must be (B) 3

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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Abhishek009 wrote:
Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

Quote:
When positive integer x is divided by 20, the remainder is 8.

Lest possible value of x = 28.

Quote:
remainder when x is divided by 5

Is, 3

Hence, correct aswer must be (B) 3

Isn't least possible value 8 when quotient is 0
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Joined: 12 Sep 2015
Posts: 4145
Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Top Contributor
Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

Another approach:

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

When positive integer x is divided by 20, the remainder is 8.
So, the possible values of x are: 8, 28, 48, 68, 88,...
Let's test a few values

8 divided by 5 equals 1 with remainder 3
28 divided by 5 equals 5 with remainder 3
48 divided by 5 equals 9 with remainder 3
68 divided by 5 equals 13 with remainder 3
88 divided by 5 equals 17 with remainder 3
.
.
.
It certainly LOOKS like the remainder will always be 3

Cheers,
Brent
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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Abhishek009 wrote:
Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

Quote:
When positive integer x is divided by 20, the remainder is 8.

Lest possible value of x = 28.

Quote:
remainder when x is divided by 5

Is, 3

Hence, correct aswer must be (B) 3

To add to this least possible value of x is 8 not 28.

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SVP  V
Joined: 26 Mar 2013
Posts: 2343
Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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warriorguy wrote:
Abhishek009 wrote:
Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

Quote:
When positive integer x is divided by 20, the remainder is 8.

Lest possible value of x = 28.

Quote:
remainder when x is divided by 5

Is, 3

Hence, correct aswer must be (B) 3

Isn't least possible value 8 when quotient is 0

You are correct.

x=20q +8

When q=0......x=8 when divided by 5 the reminder is 3.
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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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awdxzs wrote:
To add to this least possible value of x is 8 not 28.

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Thanks and Regards

Abhishek....

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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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When x is divided by 20, the remainder is 8.
therefore x is of the form 20k+8 where k is an integer.

so x=20k+8=20k+5+3=5(4k+1)+3

When x is divided by 5, the component 5(4k+1) is divisible by 5. Hence remainder when x is divided by 5 = remainder(3/5) = 3.

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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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check least possible value for which x results in remainder 8
28/20 results in remainder 8
then divide 28/5 the result is 3
choice B
**Experts Please respond as I am a beginner
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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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Bunuel wrote:
When positive integer x is divided by 20, the remainder is 8. What is the remainder when x is divided by 5?

A. 1
B. 3
C. 5
D. 8
E. Cannot be determined

We can create the equation:

x/20 = Q + 8/20

x = 20Q + 8

When 20Q + 8 is divided by 5 we have:

(20Q + 8)/5 = 4Q + 8/5

Since 8/5 = 1 3/5, the remainder is 3.

Alternate Solution:

Since we have a remainder of 8 when x is divided by 20, x could equal 28. When we divide 28 by 5, the quotient is 5 with a remainder of 3.

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Re: When positive integer x is divided by 20, the remainder is 8. What is  [#permalink]

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1
since x is positive and 20 is multiple of 5 ,
we can divide 8 by 5 to get 3 remainder

Ans B Re: When positive integer x is divided by 20, the remainder is 8. What is   [#permalink] 08 Apr 2018, 07:16
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