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# If x is a positive integer, what is the remainder when x is divided by

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If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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12 Oct 2017, 07:29
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67% (02:02) correct 33% (01:37) wrong based on 200 sessions

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If x is a positive integer, what is the remainder when x is divided by 7?

(1) The remainder when x is divided by 4 is 3
(2) The remainder when x is divided by 5 is 1
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Joined: 11 Sep 2015
Posts: 4889
GMAT 1: 770 Q49 V46
Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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12 Oct 2017, 07:54
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Top Contributor
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tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?

(1) The remainder when x is divided by 4 is 3
(2) The remainder when x is divided by 5 is 1

Target question: What is the remainder when x is divided by 7?

Statement 1: The remainder when x is divided by 4 is 3
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.

So, if the remainder when x is divided by 4 is 3, then some possible values of x are: 3, 7, 11, 15, 19, 23, etc
Let's examine some of these possible values of x
Case a: If x = 3, then the remainder when x is divided by 7 is 3
Case b: If x = 7, then the remainder when x is divided by 7 is 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The remainder when x is divided by 5 is 1
Some possible values of x are: 1, 6, 11, 16, 21, 26, 31, etc
Let's examine some of these possible values of x
Case a: If x = 1, then the remainder when x is divided by 7 is 1
Case b: If x = 6, then the remainder when x is divided by 7 is 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that some possible values of x are: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, etc
Statement 2 tells us that some possible values of x are: 1, 6, 11, 16, 21, 26, 31, etc
Since we already have 2 possible x-values that BOTH statements share, let's examine the following cases:

Case a: If x = 11, then the remainder when x is divided by 7 is 4
Case b: If x = 31, then the remainder when x is divided by 7 is 3
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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12 Oct 2017, 07:55
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tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?

(1) The remainder when x is divided by 4 is 3
(2) The remainder when x is divided by 5 is 1

Statement 1: x=4k+3, where k is any integer. Thus there could be multiple value of x and hence multiple remainders when divided by 7. Insufficient

Statement 2: x=5q+1, where q is any integer. Thus there could be multiple value of x and hence multiple remainders when divided by 7. Insufficient

Combining 1 and 2 we know x is of the form 4k+3 & 5q+1, so x can be 11 or 51, for k=q=2 and k=12 & q=10. so again multiple remainders possible. Hence Insufficient

Option E
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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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27 Nov 2017, 18:18
tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?

(1) The remainder when x is divided by 4 is 3
(2) The remainder when x is divided by 5 is 1

We need to determine the remainder of x/7.

Statement One Alone:

The remainder when x is divided by 4 is 3.

We see that x can be values such as 3, 7, 11, 15, 19, 23, 27, 31, etc.

However, using those values, we get various remainders when dividing by 7. For example, when 3 is divided by 7, the remainder is 3, but when 7 is divided by 7, the remainder is 0. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The remainder when x is divided by 5 is 1.

We see that x can be values such as 1, 6, 11, 16, 21, 26, 31, etc.

However, using those values, we get various remainders when dividing by 7. For example, when 1 is divided by 7, the remainder is 1, but when 6 is divided by 7, the remainder is 6. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the two statements together, we see that x could be 11 or 31. When x = 11, the remainder is 4 when 11 is divided by 7. However, when x = 31, the remainder is 3 when 31 is divided by 7.

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If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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04 May 2018, 06:01
niks18 gmatbusters Bunuel chetan2u VeritasPrepKarishma amanvermagmat

Is there any other approach than plugging numbers to solve this Q?
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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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04 May 2018, 06:09
Hi
The approach taken by GMATprepnow is a nice one.
Try to practice and be used to this approach, this will help in similar questions.

Is there any other approach than plugging numbers to solve this Q?

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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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04 May 2018, 08:03
gmatbusters

I could not understand approach by GMATPrepNow , esp this quote:

Quote:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

I understood niks18 approached this by using:

Dividend = (Integer Quotient) * Divisor + Remainder

Let me know if my understanding is correct or flawed.
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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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04 May 2018, 08:12
Hi
Both are same approach, it is the matter of presentation that differs.
"If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. "
Example to explain this: Here D is Divisor, R is Remainder
let N when divided by 2 gives remainder as 1.
then N can be 1, 2+1, 2*2+1, 3*2+1...
N can be 1, 3, 5, 7... so on...

Grasp the concept, terminology doesn't matter much.

gmatbusters

I could not understand approach by GMATPrepNow , esp this quote:

Quote:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

I understood niks18 approached this by using:

Dividend = (Integer Quotient) * Divisor + Remainder

Let me know if my understanding is correct or flawed.

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Joined: 11 Sep 2015
Posts: 4889
GMAT 1: 770 Q49 V46
If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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04 May 2018, 08:15
1
Top Contributor
gmatbusters

I could not understand approach by GMATPrepNow , esp this quote:

Quote:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

I understood niks18 approached this by using:

Dividend = (Integer Quotient) * Divisor + Remainder

Let me know if my understanding is correct or flawed.

Here are three important things you need to know about remainders:

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

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 N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0

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Re: If x is a positive integer, what is the remainder when x is divided by  [#permalink]

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04 May 2018, 21:34
tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?

(1) The remainder when x is divided by 4 is 3
(2) The remainder when x is divided by 5 is 1

Check out this post first:
https://www.veritasprep.com/blog/2011/0 ... unraveled/
http://www.veritasprep.com/blog/2011/05 ... emainders/
https://www.veritasprep.com/blog/2011/0 ... s-part-ii/

Here,
Stmnt 1: x = 4a + 3
So x = 3, 7, 11, 15...
Stmnt 2: x = 5b + 1
So x = 1, 6, 11, 16 ...

First number of both types is 11. Next such number will be 11 + 4*5 = 31.
11 divided by 7 will give remainder 4.
31 divided by 7 will give remainder 3 and so on...

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Veritas Prep GMAT Instructor

Re: If x is a positive integer, what is the remainder when x is divided by   [#permalink] 04 May 2018, 21:34