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Intern  Joined: 02 Jan 2015
Posts: 31
GMAT Date: 02-08-2015
GPA: 3.7
WE: Management Consulting (Consulting)
If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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9 00:00

Difficulty:   5% (low)

Question Stats: 83% (00:41) correct 17% (00:47) wrong based on 253 sessions

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If x and y are positive integers and x = 10y + 5, what is the remainder when x is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4
Intern  Joined: 02 Jan 2015
Posts: 31
GMAT Date: 02-08-2015
GPA: 3.7
WE: Management Consulting (Consulting)
Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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I understand the conceptual approach to this question. But could someone explain what is wrong with the algebraic approach below:

x = 10 y + 5
x = 5(2y + 1)
x/5 = 2y + 1

Therefore, remainder = 1.

Where am I going wrong there?

Thanks
Senior Manager  Joined: 13 Jun 2013
Posts: 250
Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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1
1
ElCorazon wrote:
I understand the conceptual approach to this question. But could someone explain what is wrong with the algebraic approach below:

x = 10 y + 5
x = 5(2y + 1)
x/5 = 2y + 1

Therefore, remainder = 1.

Where am I going wrong there?

Thanks

hi, the highlighted portion is wrongly interpreted by you.

x=5(2y+1), means that x is a multiple of 5. so, remainder when x is divided by 5 will be zero.

i hope it helps.
EMPOWERgmat Instructor V
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Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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2
Hi All,

This question asks "what IS...(the answer)", so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.

We're told that X and Y are POSITIVE INTEGERS and X = 10Y + 5. We're asked for the REMAINDER when X is divided by 5.

IF....
Y = 1
X = 15

15/5 = 3 remainder 0

GMAT assassins aren't born, they're made,
Rich
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Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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Thank you both - very helpful..
Intern  Joined: 10 Jun 2011
Posts: 7
Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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I don't think we need to test value.

If x = 10y + 5

10y = multiple of 5 and therefore divisible by 5
5 = divisible by 5

so 10y+5 is divisible by 5.
This shouldn't take more than 15 seconds
EMPOWERgmat Instructor V
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Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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1
Hi miro,

You're correct - you don't need to TEST VALUES, but that approach can get you to the correct answer rather easily. It's worth noting that GMAT questions can almost always be solved with more than one approach. The best Test Takers know how to do "more than one thing", so that on Test Day they can use whatever they're given in the prompt to quickly assess how best to approach the question and then answer it in an easy, efficient way. For that reason, it's sometimes a good idea to redo practice problems with different approaches so that you can build up more than one skill.

GMAT assassins aren't born, they're made,
Rich
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If x and y are positive integers and x=10y +5, what is the remainder when x is divided by 5?

1) 0
2) 1
3) 2
4) 3
5) 4
Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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ha15 wrote:
If x and y are positive integers and x=10y +5, what is the remainder when x is divided by 5?

1) 0
2) 1
3) 2
4) 3
5) 4

Merging topics.

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Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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x= 10y+5
x= 5*2y+5
x= 5(2y+1)

This whole term on the right side is divisible by 5. Thus the remainder is zero.
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Joined: 07 Dec 2014
Posts: 1231
Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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ElCorazon wrote:
If x and y are positive integers and x = 10y + 5, what is the remainder when x is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

x/5=2y+1
x=5(2y+1)
x is a multiple of 5
0
A
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Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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ElCorazon wrote:
If x and y are positive integers and x = 10y + 5, what is the remainder when x is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Another way you can think of this problem so as to save time is by recognizing what the restriction" x and y are positive integers" means relative to the equation. Ignoring Y, any positive integer multiplied by 10 will of course be a multiple of 10 and every multiple of 10 has a remainder of 0 when divided by 5- so any number that is a multiple of 10 has a remainder of 0 when 5 is added because 5 divided by 5 has a remainder of 0.

Thus
"A"
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Joined: 11 Sep 2015
Posts: 4318
Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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2
Top Contributor
ElCorazon wrote:
If x and y are positive integers and x = 10y + 5, what is the remainder when x is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

GIVEN: x = 10y + 5
Factor out 5 to get: x = 5(2y + 1)
We can see that x is a multiple of 5, which also means x is divisible by 5, which means the remainder will by ZERO when x is divided by 5

Cheers,
Brent
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Re: If x and y are positive integers and x = 10y + 5, what is the remainde  [#permalink]

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ElCorazon wrote:
If x and y are positive integers and x = 10y + 5, what is the remainder when x is divided by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

x= 10y+5 and X and Y are both positive integers =
10Y could be + 10*1 = 10 divisible by 5
10Y coulde be 2 = 10*2 = 20 divisible by 5
10Y coulde be 3 = 10*3 = 30 divisible by 5
10Y coulde be 4 = 10*4 = 40 divisible by 5

hence all values of 10Y will be divsible by 5

Target question s 10Y +5 divisble by 5 ... Yes as we just learnt 10y is always divisible by 5 and 5 is anyways divisble by 5 so (10Y +5 ) /5 = 0 reaminder ans Choice A Re: If x and y are positive integers and x = 10y + 5, what is the remainde   [#permalink] 28 Oct 2019, 23:44
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