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# When the integer n is divided by 8, the remainder is 5. Which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 50578
When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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23 Jul 2015, 02:11
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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

Kudos for a correct solution.

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When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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23 Jul 2015, 03:04
Bunuel wrote:
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

Kudos for a correct solution.

Given number = N =8p+5 ---> the number N is odd.

Thus ,

A. n + 3
n+3 = odd + odd = even. Thus not correct.

B. n/2 + 3.5
As n is odd, thus n/2 = abc.5 (where c = even) ---> abc.5+3.5 = abc+3+0.5+0.5 = even+odd+1= odd+1=even. Thus not correct.

C. n – 3
n-3 = odd - odd = even. Thus not correct.

D. 3n + 1
As n =odd, 3n=odd and 3n+1 = odd + odd = even. Thus not correct.

E. 5n + 2
As n =odd, 5n= odd --->5n+2 = odd + even = odd. Thus correct.
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When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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Updated on: 23 Jul 2015, 05:33
1
Bunuel wrote:
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

Kudos for a correct solution.

One possible Value of n = 8 + 5 = 13
Second possible Value of n = 8*2 + 5 = 21

@n = 13

A. n + 3 = 16 = Even
B. n/2 + 3.5 = 13/2+3.5 = 10 = Even
C. n – 3 = 13-3 = 10 = Even
D. 3n + 1 = 3*13+1 = 40 = even
E. 5n + 2 = 5*13+2 = 67 = ODD thus CORRECT OPTION

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Originally posted by GMATinsight on 23 Jul 2015, 05:25.
Last edited by GMATinsight on 23 Jul 2015, 05:33, edited 1 time in total.
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When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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Updated on: 23 Jul 2015, 05:35
1
From question we get n=8Q+5. so we can conclude n is odd

we have to check each option

A. n + 3 odd + odd = Even

B. n/2 + 3.5 take LCM (n+7)/2 Even

C. n – 3 Odd - Odd = Even

D. 3n + 1 Odd + Odd = Even

E. 5n + 2 Odd + Even = Odd (Not Even)

So E is the correct Answer Choice
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Originally posted by cutegirlsimran on 23 Jul 2015, 05:30.
Last edited by cutegirlsimran on 23 Jul 2015, 05:35, edited 1 time in total.
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Re: When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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23 Jul 2015, 05:30
GMATinsight wrote:
Bunuel wrote:
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

Kudos for a correct solution.

One possible Value of n = 8 + 5 = 13
Second possible Value of n = 8*2 + 5 = 21

@n = 13

A. n + 3 = 16 = Even
B. n/2 + 3.5 = 13/2+3.5 = 10 = Even
C. n – 3 = 13-3 = 10 = Even
D. 3n + 1 = 3*8+1 = 25 = Odd thus CORRECT OPTION
E. 5n + 2 = 5*8+2 = 42 = even

GMATinsight, you are using n =13 in options A-C while you use n =8 (an incorrect value) in options D and E.
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Posts: 74
Concentration: Marketing, Healthcare
Re: When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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23 Jul 2015, 05:32
1
Bunuel wrote:
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
Kudos for a correct solution.

n divided by 8 gives a remainder 5

Possible values of n = 5, 13, 21, 29, 37, 45....

A) n + 3 => 8, 16, 24...---- Incorrect

B) n/2 + 3.5 = 1/2(n + 7) = 6, 10...---- Incorrect

C) n - 3 = 2, 10, 18...---- Incorrect

D) 3n + 1 = 16, 40...---- Incorrect

E) 5n + 2 = 27, 67...---- Correct

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When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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23 Jul 2015, 05:37
Engr2012 wrote:
GMATinsight wrote:
Bunuel wrote:
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

Kudos for a correct solution.

One possible Value of n = 8 + 5 = 13
Second possible Value of n = 8*2 + 5 = 21

@n = 13

A. n + 3 = 16 = Even
B. n/2 + 3.5 = 13/2+3.5 = 10 = Even
C. n – 3 = 13-3 = 10 = Even
D. 3n + 1 = 3*8+1 = 25 = Odd thus CORRECT OPTION
E. 5n + 2 = 5*8+2 = 42 = even

GMATinsight, you are using n =13 in options A-C while you use n =8 (an incorrect value) in options D and E.

Haha... I immediately realized and corrected but you are much faster in typing so no kudos for this correction.
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Re: When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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23 Jul 2015, 09:11
Bunuel wrote:
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

Kudos for a correct solution.

n=5,13,21 and so on
if n=5, then
A=n+3=8
B=n/2+3.5=6
C=n-3=2
D=3n+1=16
E=5n+2=27

Math Expert
Joined: 02 Sep 2009
Posts: 50578
Re: When the integer n is divided by 8, the remainder is 5. Which of the  [#permalink]

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26 Jul 2015, 11:15
Bunuel wrote:
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

Kudos for a correct solution.

800score Official Solution:

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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Re: When the integer n is divided by 8, the remainder is 5. Which of the &nbs [#permalink] 26 Jul 2015, 11:15
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