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

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

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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.
[Reveal] Spoiler: OA

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

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New post 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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New post 23 Jul 2015, 05:25
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

Answer: option E
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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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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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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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New post 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

Answer: option D


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

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New post 23 Jul 2015, 05:32
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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


Hence answer is E

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

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New post 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

Answer: option D


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. :) :wink:
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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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New post 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

Answer E

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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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New post 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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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