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GMAT Number Theory
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Author:  questioner [ Thu Feb 03, 2011 7:43 pm ]
Post subject:  GMAT Number Theory

When the integer n is divided by 8, the remainder is 5. Which of the following is NOT an even number?

A. n + 3
B. n/2 + 3.5
C. n – 3
D. 3n + 1
E. 5n + 2

(E) The most efficient way to solve this problem is to substitute a possible value of n into the answer choices and see which one is not an even number. n could be 5, 13, 21, etc. Let’s substitute these trial numbers.

Let’s choose 5:
(A) 5 + 3 = 8. This is EVEN.
(B) 5/2 + 3.5 = 6. This is EVEN.
(C) 5 – 3 = 2. This is EVEN.
(D) 3(5) + 1 = 16. This is EVEN.
(E) 5(5) + 2 = 27. This is ODD.

The correct answer is choice (E), since this is the only answer choice that produced an odd with n = 5.

Note: 5 divided by 8 is 0 with a remainder of 5. When you are looking for the remainder, you should stop dividing when continuing to do so would result in a decimal. For example, 13 divided by 8 has a remainder of 5. Dividing until you have 1.625 is not helpful here.
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As per the explantion 5 is taken as the example. However when 5 is divided by 8 the remainder is not 5 as it said in the question.

So I took an example as 50. When 50 is divided by 8 the remainder is 5 and thus 50 + 3 = 53 odd so answer is A.
Please explain.

Author:  Gennadiy [ Thu Feb 03, 2011 8:00 pm ]
Post subject:  Re: math (test 1, question 17): number theory

For positive integers n and b,
If n = m × b + k,
where k < b, m and k are non-negative integers,
then k is the remainder when n is divided by b.

Note, that any dividend which is less than the divisor is also a remainder, because n = 0 × b + n.

The practical way to find the remainder is to divide using log division method.

Let's consider the given question.
5 = 0 × 8 + 5
Therefore 5 is the remainder when 5 is divided by 8.

When 50 is divided by 8 the remainder is 2, since 50 = 6 × 8 + 2.

Author:  questioner [ Sun Aug 05, 2012 3:42 pm ]
Post subject:  Re: GMAT Number Theory

Which of the following is NOT an EVEN number is asking us which of the following is ODD.
The answer to this question is E - which is the only answer that yields an EVEN number.
The question asks us which of the following yields an ODD result and selects the equation that yields an EVEN as the answer.

Author:  Gennadiy [ Sun Aug 05, 2012 3:43 pm ]
Post subject:  Re: GMAT Number Theory

Quote:
… E - which is the only answer that yields an EVEN number.
The answer choice E is odd.
Plug in n = 5 to get
A. 8
B. 6
C. 2
D. 16
E. 27


In general, the proof is the following.
n = m × 8 + 5 is given by the question statement. Plug it in E.
E. 5n + 2 = 5(8m + 5) + 2 = 40m + 27 = even + odd = odd

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