GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 23:52 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # When the integer k is divided by 7, the remainder is 5. Which of the f

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64248
When the integer k is divided by 7, the remainder is 5. Which of the f  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 69% (01:59) correct 31% (02:27) wrong based on 192 sessions

### HideShow timer Statistics

Tough and Tricky questions: Remainders.

When the integer k is divided by 7, the remainder is 5. Which of the following expressions below when divided by 7, will have a remainder of 6?

I. 4k + 7
II. 6k + 4
III. 8k + 1

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

Kudos for a correct solution.

Source: Chili Hot GMAT

_________________
Manager  Joined: 12 Sep 2014
Posts: 138
GMAT 1: 740 Q49 V41
GPA: 3.94
Re: When the integer k is divided by 7, the remainder is 5. Which of the f  [#permalink]

### Show Tags

1
The options for the integer k are 5, 12, 19, 26...

Let's look at each of the three cases:
1. 4k+7 yields 27, 55... yes
2. 6k + 4 yields 34, 76... yes
3. 8k + 1 yields 41, 97... yes

I didn't try anymore and concluded that they all work. Choice E.
Manager  Joined: 13 Jun 2013
Posts: 248
Re: When the integer k is divided by 7, the remainder is 5. Which of the f  [#permalink]

### Show Tags

3
Bunuel wrote:

Tough and Tricky questions: Remainders.

When the integer k is divided by 7, the remainder is 5. Which of the following expressions below when divided by 7, will have a remainder of 6?

I. 4k + 7
II. 6k + 4
III. 8k + 1

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

Kudos for a correct solution.

Source: Chili Hot GMAT

k= 7t+5 where t can be 0,1,2,----
I. 4k+7= 4(7t+5) + 7 = 28t + 27
28t is completely divisible by 7. thus remainder when 28t+27 is divided by 7 = 27/7 = 6

II. 6k+4= 6(7t+5) +4 = 42t+34
again 42t is completely divisible by 7. thus remainder when 42t+34 is divided by 7 = 34/7 = 6

II. 8k+1 = 8(7t+5)+1 = 56t+41
again by using similar analogy remainder = 41/7 =6

now, since each I,II and III leaves a remainder of 6. hence answer must be E
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1708
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: When the integer k is divided by 7, the remainder is 5. Which of the f  [#permalink]

### Show Tags

1
Answer = E) I, II and III

Place k = 12

I: 4(12) + 7 = 55 = 56-1 >> Remainder = 6

II: 6(12) + 4 = 72 + 4 = 76 = (77-1) >> Remainder = 6

III: 8(12) + 1 = 96 + 1 = 97 = (96-1) >> Remainder = 6
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10602
Location: United States (CA)
Re: When the integer k is divided by 7, the remainder is 5. Which of the f  [#permalink]

### Show Tags

Bunuel wrote:

Tough and Tricky questions: Remainders.

When the integer k is divided by 7, the remainder is 5. Which of the following expressions below when divided by 7, will have a remainder of 6?

I. 4k + 7
II. 6k + 4
III. 8k + 1

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

k can be values such as 5, 12, 19, 26, etc.

Let’s test the answers using 5 and 12 as the values of k.

I. 4k + 7

When k = 5, 4k + 7 is 27, which does have a remainder of 6 when divided by 7.

When k = 12, 4k + 7 is 55, which does have a remainder of 6 when divided by 7

We can keep testing values but we will get 6 as the remainder. So I is true.

II. 6k + 4

When k = 5, 6k + 4 is 34, which does have a remainder of 6 when divided by 7.

When k = 12, 6k + 4 is 76, which does have a remainder of 6 when divided by 7

We can keep testing values, but we will get 6 as the remainder. So II is true.

III. 8k + 1

When k = 5, 8k + 1 is 41, which does have a remainder of 6 when divided by 7.

When k = 12, 8k + 1 is 97, which does have a remainder of 6 when divided by 7

We can keep testing values, but we will get 6 as the remainder. So III is true.

Alternate Solution:

Let’s note the following fact: If the remainder when n is divided by 7 is 6, then n + 1 is divisible by 7.

Since k produces a remainder of 5 when divided by 7, we can write k = 7s + 5 for some positive integer s. We will test each Roman numeral, but rather than testing whether the remainder is 6, we will use the above fact and test whether one more than that expression is divisible by 7.

I. 4k + 7

Let’s test whether 4k + 8 is divisible by 7. Substituting k = 7s + 5, we get:

4k + 8 = 4(7s + 5) + 8 = 28s + 28.

Since 28s + 28 is divisible by 7, 4k + 7 will produce a remainder of 6 when divided by 7.

II. 6k + 4

Let’s test whether 6k + 5 is divisible by 7. Substituting k = 7s + 5, we get:

6k + 5 = 6(7s + 5) + 5 = 42s + 35

Since 42s + 35 is divisible by 7, 6k + 4 will produce a remainder of 6 when divided by 7.

III. 8k + 1

Let’s test whether 8k + 2 is divisible by 7. Substituting k = 7s + 5, we get:

8k + 2 = 8(7s + 5) + 2 = 56s + 42

Since 56s + 42 is divisible by 7, 8k + 1 will produce a remainder of 6 when divided by 7.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: When the integer k is divided by 7, the remainder is 5. Which of the f   [#permalink] 11 Aug 2019, 18:18

# When the integer k is divided by 7, the remainder is 5. Which of the f   