If x and y are positive integers and x = 10y + 5, what is the remainde

Question

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

BrentGMATPrepNow · Accepted Answer

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

Answer: A

Cheers,
Brent

ElCorazon · Answer

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

manpreetsingh86 · Answer

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.

EMPOWERgmatRichC · Answer

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

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

ElCorazon · Answer

Thank you both - very helpful..

miro · Answer

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

EMPOWERgmatRichC · Answer

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

ha15 · Answer

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

Bunuel · Answer

Merging topics. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

Shiv2016 · Answer

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.

gracie · Answer

x/5=2y+1
x=5(2y+1)
x is a multiple of 5
0
A

Nunuboy1994 · Answer

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"

mimajit · Answer

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

Kinshook · Answer

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

x/5 = 2y + 1: x is completely divisible by 5.

IMO A

BrushMyQuant · Answer

Given that x and y are positive integers and x = 10y + 5 and we need to find what is the remainder when x is divided by 5

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

=> x when divided by 5 gives 2y + 1 as quotient and 0 as remainder

So,  Answer will be A 
Hope it helps!

Watch the following video to learn the Basics of Remainders

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x and y are positive integers and x = 10y + 5, what is the remainde

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If x and y are positive integers and x = 10y + 5, what is the remainde

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards