GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Feb 2019, 10:15

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# When the positive integer n is divided by 7, the quotient is q and the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53020
When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 01:49
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:46) correct 27% (01:41) wrong based on 49 sessions

### HideShow timer Statistics

When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

_________________
VP
Joined: 31 Oct 2013
Posts: 1138
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 01:54
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

$$\frac{n}{7}$$= q + 4

n = 7q + 4

2n = 14q + 8

$$\frac{2n}{7}$$ =$$\frac{(14q + 8 )}{7}$$

we have remainder 1 but quotient 2q.

SVP
Joined: 18 Aug 2017
Posts: 1883
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 05:46
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

lets use some no to solve
When the positive integer n is divided by 7, the quotient is q and the remainder is 4.
n=7q+4
n=11
q=1

now
when When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

22=7*3+1
q=3
out of given options
D sufficies relation
IMO D
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4387
Location: India
GPA: 3.5
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 07:00
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 andthe quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

Let $$n = 11$$, So $$q = 1$$ and $$r = 4$$

When $$2n$$ is divided by $$7$$ then we have $$\frac{22}{7} = 7*3(q) + 1(r)$$

Thus, the value of quotient in terms of $$q(3)$$ = $$2*1(q) + 1$$, Answer must be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 07:13
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

IMO D

Plug in some values n = 11, q = 1, remainder = 4

Now n becomes 2n = 22 here q = 3, remainder = 1

So only D satisfies the above relation

2*1 + 1 = 3
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 07:35
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

Two ways..

(I) Algebraic
the positive integer n is divided by 7, the quotient is q and the remainder is 4 MEANS n=7q+4.
2n is divided by 7, the remainder is 1 and the quotient, in terms of q..2n=7x+1.
substitute $$n=7q+4, .....2(7q+4)=7x+1......14q+8=7x+1......7x=14q+8-1=14q+7.......x=2q+1$$
D

(II) Substitute n as some value..
take q as 2, so n=7*2+4=18..
so 2n = 2*18=36
36=7x+1.......7x=35..x=5

Substitute q as 2 and see which choice gives you 5 ..
2q+1=2*2+1=5

so D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Manager
Joined: 20 Mar 2018
Posts: 52
Location: Ghana
Concentration: Finance, Real Estate
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

06 Feb 2019, 11:35
Let quotient interms of q =?
Now since dividend is n ,divisor is 7 ,quotient is q and remainder being 4 can be in this form ,n=7q+4.......(1)
Now second statement says ,
2n=?+1.....(2)
Multiply eqn.....(1) by 2
2n=14q+8
2n=?+1 —> 14q+8=?+1 —> 14q+7=? —> 7(2q+1)=?
Haha so there we have it divisor*quotient ,so quotient interms of q is (2q+1)
Hope this helps .

Posted from my mobile device
Manager
Joined: 12 Sep 2017
Posts: 135
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

13 Feb 2019, 16:18
Hello everyone!

Could someone please tell me if my logic is good or it was just a coincidence?

"the remainder is 1.."

So in my head, I just canceled out A, C and E because they do not hold a remainder of 1.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4938
Location: United States (CA)
Re: When the positive integer n is divided by 7, the quotient is q and the  [#permalink]

### Show Tags

15 Feb 2019, 17:38
Bunuel wrote:
When the positive integer n is divided by 7, the quotient is q and the remainder is 4. When 2n is divided by 7, the remainder is 1 and the quotient, in terms of q, is

A. q/2

B. q/2 + 1

C. 2q

D. 2q+1

E. 2q+2

We can create the equations:

n/7 = q + 4/7

n = 7q + 4

and

2n/7 = z + 1/7

2n = 7z + 1

Multiplying the first equation by 2, we have:

2n = 14q + 8

Setting the two equations equal to each other, we have:

14q + 8 = 7z + 1

14q + 7= 7z

2q + 1 = z

Alternate Solution:

Since the remainder is 4 when n is divided by 7, we see that n could be 11, 18, 25, 32, …

For simplicity’s sake, let’s let n = 11. When 11 is divided by 7, the quotient q is 1, with a remainder of 4.

Now, we see that 2n = 22. When 22 is divided by 7, the quotient is 3, with a remainder of 1.

The original quotient q is 1, and the new quotient is 3. Of the answer choices, only D. 2q + 1 gives us an answer of 3 when q = 1.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: When the positive integer n is divided by 7, the quotient is q and the   [#permalink] 15 Feb 2019, 17:38
Display posts from previous: Sort by