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Wrong answer explanation?

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by gander123 » Sun Oct 14, 2012 6:27 am
Hi there I'm back with the following question:

GMAT Prep. Question Pack, Question "QDS09833":

If m and n are positive integers and r is the remainder when 5(10^n) + m is devided by 3, what is the value of r?

(1) n=10

(2) m=1


Official Answer explanation for statement (1):"If n = 10, then 5(10^10) + m has 5 as its leftmost digit, exatly 10 zeors, and m as its units digit. The sum of the digits is 5+m. If m=4, then the sum of the digits is 9, which is divisible by 3, and hence the remainder when 5(10^10) +4 is devided by 3 is 0. On the other hand, if m=2, then the sum of the digits is 7, which is not divisible by 3, and hence the remainder when 5(10^10) +4 is devided by 3 not 0; NOT SUFFICIENT"


My question:

1. Criticism: 5(10^10)+m does not necessarily have 5 as its leftmost digit!Why? Because we dont know anything about m. So m could be an integer that is even greater than 5(10^10). Adding this integer to the expression 5(10^10) would clearly change the leftmost digit!

2. Criticism: Following criticism 1. there would not necessarily be 10 zeros in the sum of 5(10^10) +m so that the sum rule for the following argumentation would not apply any longer?!

I thought we dont make assumptions on the GMAT (such as m is a unit integer)?!

Who can help ?! What did I miss? Or is there indeed anything wrong with the explanation?!

Kind regards,

Tobi
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Oct 14, 2012 7:21 am
gander123 wrote: 1. Criticism: 5(10^10)+m does not necessarily have 5 as its leftmost digit!Why? Because we dont know anything about m. So m could be an integer that is even greater than 5(10^10). Adding this integer to the expression 5(10^10) would clearly change the leftmost digit!
You're absolutely correct. The left-most digit need not be 5.
Having said that, the answer is still B

We know this because of the following rule.
If . . .
- The remainder, when A is divided by D, is p
- The remainder, when B is divided by D, is q
Then the remainder, when A+B is divided by D, is equal to the remainder when p+q is divided by D.

Target question: What is the remainder when 5(10^n) + m is divided by 3?
To answer this question, if would be sufficient to know the remainder when 5(10^n) is divided by 3 and the remainder when m is divided by 3

Statement 1: n=10
From this, we know that the remainder is 2 when 5(10^n) is divided by 3.
However, we don't know the remainder when m is divided by 3
As such, we cannot answer the target question with certainty.
INSUFFICIENT

Statement 2: m=1
Since 5(10^n) will always equal 5 followed by n zeros, we know that the remainder will always be 2, when 5(10^n) is divided by 3
Since m=1, we now know that the remainder will be 1, when m is divided by 3
So, when 5(10^n) + m is divided by 3, the remainder will equal the remainder when 2+1 is divided by 3 (i.e., the remainder is 0)
That is, the remainder will always be zero when 5(10^n) + m is divided by 3
SUFFICIENT

Answer = B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sun Oct 14, 2012 7:48 am, edited 1 time in total.
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by Brent@GMATPrepNow » Sun Oct 14, 2012 7:43 am
gander123 wrote: 2. Criticism: Following criticism 1. there would not necessarily be 10 zeros in the sum of 5(10^10) +m so that the sum rule for the following argumentation would not apply any longer?!
You're correct again, Tobi.
It's quite possible that 5(10^10) + m has no zeros.
For example, if m = 1,123,456,789 then 5(10^10) + m = 51,123,456,789
gander123 wrote: I thought we dont make assumptions on the GMAT (such as m is a unit integer)?!
Exactly. we cannot make that assumption.

It's a great question, but the solution needs some work.

Cheers,
Brent
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by gander123 » Sun Oct 14, 2012 10:12 am
Hey Brent,

So you give the GMAC guys a call to change the explanation ;) ?

Joking apart ...

[/quote]Then the remainder, when A+B is divided by D, is equal to the remainder when p+q is divided by D.

How do you know that ? I tried it for D=6 and A=10 and B = 13 which gives p = 4/6 and q = 1/6 and A+B/6 = 3 + 5/6 but your statement did not work on this one...

??

Cheers,

Tobi
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by Brent@GMATPrepNow » Sun Oct 14, 2012 10:32 am
gander123 wrote: How do you know that ? I tried it for D=6 and A=10 and B = 13 which gives p = 4/6 and q = 1/6 and A+B/6 = 3 + 5/6 but your statement did not work on this one...
The rule holds for those values.

10 divided by 6 gives us a remainder of 4.
13 divided by 6 gives us a remainder of 1.

When (10+13) is divided by 6, the remainder is the same as when 4+1 is divided by 6.

23 divided by 6 leaves a remainder of 5
5 divided by 6 also leaves a remainder of 5

Cheers,
Brent
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