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Number theory

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by mgmt_gmat » Fri Feb 12, 2010 1:03 am
If n is a positive integer, what is the remainder when (74n + 3)(6n) is divided by 10 ?
A. 1
B. 2
C. 4
D. 6
E. 8

Explain the method.
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by ajith » Fri Feb 12, 2010 5:58 am
mgmt_gmat wrote:If n is a positive integer, what is the remainder when (74n + 3)(6n) is divided by 10 ?
A. 1
B. 2
C. 4
D. 6
E. 8

Explain the method.
444n^2+ 18n

When n = 1 it leaves a remainder of 2
when n= 2 it leaves a remainder of 2
when n = 3 it leaves a remainder of 0

I do not think it would leave a unique remainder for all the positive integers - please check the question
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by sanju09 » Fri Feb 12, 2010 6:02 am
mgmt_gmat wrote:If n is a positive integer, what is the remainder when (74n + 3)(6n) is divided by 10 ?
A. 1
B. 2
C. 4
D. 6
E. 8

Explain the method.
Simple, if this question really has a unique answer, then it would work for any positive integer, 1 is the best to try with. When n = 1, (74n + 3)(6n) = 77 × 6, which will have [spoiler]2[/spoiler] as its unit’s digit, and as remainder too, when 77 × 6 is divided by 10.

[spoiler]B[/spoiler]
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by sanju09 » Fri Feb 12, 2010 6:10 am
ajith wrote:
mgmt_gmat wrote:If n is a positive integer, what is the remainder when (74n + 3)(6n) is divided by 10 ?
A. 1
B. 2
C. 4
D. 6
E. 8

Explain the method.
444n^2+ 18n

When n = 1 it leaves a remainder of 2
when n= 2 it leaves a remainder of 2
when n = 3 it leaves a remainder of 0

I do not think it would leave a unique remainder for all the positive integers - please check the question
agreed
The mind is everything. What you think you become. –Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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