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gander123
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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
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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