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

 It is currently 20 Jan 2019, 22:31

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# When positive integer x is divided by 7 the quotient is q

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Nov 2013
Posts: 28
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

18 Nov 2013, 07:55
4
10
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:00) correct 57% (02:15) wrong based on 321 sessions

### HideShow timer Statistics

When positive integer x is divided by 7 the quotient is q and the remainder is 1. What is the remainder when x is divided by 10?

(1) When x is divided by 5 the quotient is q and the remainder is 1
(2) x is less than 50

-----------------------------
I got the correct answer but took quite a while. I listed out all the possible value of x and realize remainder when x is divided by 10 has to be 1. Any other faster method?

8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85
6, 11, 16, 21, 26, 31, 36, 41, 46, 56, 61, 71
Math Expert
Joined: 02 Sep 2009
Posts: 52298
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

21 May 2014, 05:36
4
1
seabhi wrote:
Hi,
IMO C. Please correct me if I am wrong.

from stmt 1: x = 7q+1 and x=5q+1 which leads to .. x=35Q+36 as the general formula.
hence multiple values of x will satisfy this. 36, 71, 106 .. you cannot say if the remainder will be 1 or 6.

from stmt2 x < 50 .. not sufficient.

from stmt1 and stmt 2 .. x can be only 36. Hence C.

No, the correct answer is A.

When positive integer x is divided by 7 the quotient is q and the remainder is 1. What is the remainder when x is divided by 10?

When positive integer x is divided by 7 the quotient is q and the remainder is 1 --> x = 7q + 1 --> x could be 1, 8, 15, 22, ...

(1) When x is divided by 5 the quotient is q and the remainder is 1 --> x = 5q + 1 --> subtract this from the equation from the stem: 0 = 2q --> q = 0 --> x = 1. 1 divided by 10 gives the remainder of 1. Sufficient.

(2) x is less than 50 --> if x = 1, then the remainder upon division 1 by 10 is 1 but if x = 8, then the remainder upon division 8 by 10 is 8. Not sufficient.

Hope it helps.
_________________
##### General Discussion
Manager
Joined: 15 Aug 2013
Posts: 53
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 02:56
2
from the ques stem we know-
x= 7q + 1
from 1) x = 5q + 1
subtracting we get x =1. hence when we divide x i.e. 1 by 10 we get remainder 1. sufficient.
stmt 2 is clearly insufficient. lots of possible values for x.
Intern
Joined: 16 Nov 2013
Posts: 28
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 07:29
zerosleep wrote:
from the ques stem we know-
x= 7q + 1
from 1) x = 5q + 1
subtracting we get x =1. hence when we divide x i.e. 1 by 10 we get remainder 1. sufficient.
stmt 2 is clearly insufficient. lots of possible values for x.

What do you mean? Subtracting we get x = 1 ?
Manager
Joined: 26 Sep 2013
Posts: 193
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 09:11
1
zerosleep wrote:
from the ques stem we know-
x= 7q + 1
from 1) x = 5q + 1
subtracting we get x =1. hence when we divide x i.e. 1 by 10 we get remainder 1. sufficient.
stmt 2 is clearly insufficient. lots of possible values for x.

You don't get x=1 when you subract, you'd get 0=2q....also when you divide 1 by 10 the remainder is 10..
Intern
Joined: 20 Nov 2012
Posts: 15
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 10:20
N=7q+1
N=5q+1

Therefore: N=35X +1

The remeinder could be 1 or 6. for Example if X=0 then the remeinder is 1, but when X=1 then the remeinder is 6.
Director
Joined: 25 Apr 2012
Posts: 683
Location: India
GPA: 3.21
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 23:16
bluecatie1 wrote:
N=7q+1
N=5q+1

Therefore: N=35X +1

The remeinder could be 1 or 6. for Example if X=0 then the remeinder is 1, but when X=1 then the remeinder is 6.

Precisely what i thought but from Question stem and St 1 we have
but note that it is for the same value of q that we get the remainder 1

x= 7q+1 and x=5q+1 -------> For the same value of q

Also 7q+1=5q+1 --------> 2Q=0 or q=0

Thus the number is 1 and when divided by 10 the remainder is 1 only.

Ans A is correct

if the Question would have stated x= 7q+1 and x=5a+1 then x= 35C+1 and possible value of x = 1,36,71, 106,141.....

then even taking statement 2 the answer would be E. The Question stem needs to mention that x is a 2 digit number.

Hope it helps
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Director
Joined: 25 Apr 2012
Posts: 683
Location: India
GPA: 3.21
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 23:21
registerincog wrote:
When positive integer x is divided by 7 the quotient is q and the remainder is 1. What is the remainder when x is divided by 10?

(1) When x is divided by 5 the quotient is q and the remainder is 1
(2) x is less than 50

-----------------------------
I got the correct answer but took quite a while. I listed out all the possible value of x and realize remainder when x is divided by 10 has to be 1. Any other faster method?

8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85
6, 11, 16, 21, 26, 31, 36, 41, 46, 56, 61, 71

For the 2 values highlighted in bold, the remainders will be 6 and 1 respectively.

You need to consider 1 as well the possible value of x....here's why

x=7q+1 when q=0, x=1
q=1,x=8

Similarly x =5q+1, q=0, x=1
q=2,,x=6....and so on
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

19 Nov 2013, 23:31
registerincog wrote:
When positive integer x is divided by 7 the quotient is q and the remainder is 1. What is the remainder when x is divided by 10?

(1) When x is divided by 5 the quotient is q and the remainder is 1
(2) x is less than 50

From the question stem, x =7q+1.

F.S 1 states that x = 5q+1. Thus, we know that 7q+1=5q+1 --> q=0.Note that q is also an integer. Thus, x=1.Remainder when 1 is divided by 10 is 1. Sufficient.

F.S 2 for x=8, remainder when divided by 10 is 8.However, when x=15,the remainder when x is divided by 10 is 5. 2 different numerical values, hence Insufficient.

A.

AccipiterQ wrote:
when you divide 1 by 10 the remainder is 10..

Nope . This is incorrect.
_________________
Manager
Joined: 15 Aug 2013
Posts: 53
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

20 Nov 2013, 05:08
AccipiterQ wrote:
zerosleep wrote:
from the ques stem we know-
x= 7q + 1
from 1) x = 5q + 1
subtracting we get x =1. hence when we divide x i.e. 1 by 10 we get remainder 1. sufficient.
stmt 2 is clearly insufficient. lots of possible values for x.

You don't get x=1 when you subract, you'd get 0=2q....also when you divide 1 by 10 the remainder is 10..

Hi,

I meant if you subtract these equations you get q =0. Now put q =0 in any equation and you will get x =1. Hence the no is 1. Now when you divide x (which is 1) by 10, you will get remainder 1. Sorry for the confusion.
Manager
Joined: 15 Aug 2013
Posts: 53
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

20 Nov 2013, 05:10
registerincog wrote:
zerosleep wrote:
from the ques stem we know-
x= 7q + 1
from 1) x = 5q + 1
subtracting we get x =1. hence when we divide x i.e. 1 by 10 we get remainder 1. sufficient.
stmt 2 is clearly insufficient. lots of possible values for x.

What do you mean? Subtracting we get x = 1 ?

Hi,
Full solution to avoid any confusion-
x= 7q + 1
from 1) x = 5q + 1
Now subtracting these two equations yields q =0. Now put q=0 in any equation and you will get x=1. hence the no is 1. Now if we divide x (which is nothing but 1) we will remainder as 1.
Manager
Joined: 25 Oct 2013
Posts: 148
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

26 Dec 2013, 05:55
1
Stmt 1 made it so simple that I assumed there must be typo in the question and solved with x=5p+1 and got C as the answer

if x = 7q+1 and x=5q+1 only value that q can take is ZERO!!! How can stmt 1 be so simple
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Manager
Joined: 21 Aug 2013
Posts: 78
Schools: ISB '15
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

21 May 2014, 04:02
1
Hi,
IMO C. Please correct me if I am wrong.

from stmt 1: x = 7q+1 and x=5q+1 which leads to .. x=35Q+36 as the general formula.
hence multiple values of x will satisfy this. 36, 71, 106 .. you cannot say if the remainder will be 1 or 6.

from stmt2 x < 50 .. not sufficient.

from stmt1 and stmt 2 .. x can be only 36. Hence C.
_________________

Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Intern
Joined: 08 Jun 2011
Posts: 18
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

02 Jul 2017, 09:03
3
x= 7q + 1
from 1) x = 5q + 1
subtracting eqn 1 from given, we get x =1. hence when we divide x i.e. 1 by 10 we get remainder 1. Sufficient.
stmt 2 is clearly insufficient.
Hence, A
Senior Manager
Joined: 26 Dec 2015
Posts: 256
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

08 Aug 2017, 20:26
Bunuel wrote:
seabhi wrote:
Hi,
IMO C. Please correct me if I am wrong.

from stmt 1: x = 7q+1 and x=5q+1 which leads to .. x=35Q+36 as the general formula.
hence multiple values of x will satisfy this. 36, 71, 106 .. you cannot say if the remainder will be 1 or 6.

from stmt2 x < 50 .. not sufficient.

from stmt1 and stmt 2 .. x can be only 36. Hence C.

No, the correct answer is A.

When positive integer x is divided by 7 the quotient is q and the remainder is 1. What is the remainder when x is divided by 10?

When positive integer x is divided by 7 the quotient is q and the remainder is 1 --> x = 7q + 1 --> x could be 1, 8, 15, 22, ...

(1) When x is divided by 5 the quotient is q and the remainder is 1 --> x = 5q + 1 --> subtract this from the equation from the stem: 0 = 2q --> q = 0 --> x = 1. 1 divided by 10 gives the remainder of 1. Sufficient.

(2) x is less than 50 --> if x = 1, then the remainder upon division 1 by 10 is 1 but if x = 8, then the remainder upon division 8 by 10 is 8. Not sufficient.

Hope it helps.

Bunuel the method you mentioned in response to seabhi has been discussed above. i'm curious -- if he's wrong, how were his calculations incorrect? i built out the #s given from the formulas and got the same thing as him (see below):

- x=5q+1, so: 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71
- x = 7q+1, so: 8, 15, 22, 29, 36, 43, 50, 57, 64, 71
Intern
Joined: 23 Jul 2015
Posts: 34
When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

07 Apr 2018, 11:46
2
1
LakerFan24 wrote:
Bunuel wrote:
seabhi wrote:
Hi,
IMO C. Please correct me if I am wrong.

from stmt 1: x = 7q+1 and x=5q+1 which leads to .. x=35Q+36 as the general formula.
hence multiple values of x will satisfy this. 36, 71, 106 .. you cannot say if the remainder will be 1 or 6.

from stmt2 x < 50 .. not sufficient.

from stmt1 and stmt 2 .. x can be only 36. Hence C.

No, the correct answer is A.

When positive integer x is divided by 7 the quotient is q and the remainder is 1. What is the remainder when x is divided by 10?

When positive integer x is divided by 7 the quotient is q and the remainder is 1 --> x = 7q + 1 --> x could be 1, 8, 15, 22, ...

(1) When x is divided by 5 the quotient is q and the remainder is 1 --> x = 5q + 1 --> subtract this from the equation from the stem: 0 = 2q --> q = 0 --> x = 1. 1 divided by 10 gives the remainder of 1. Sufficient.

(2) x is less than 50 --> if x = 1, then the remainder upon division 1 by 10 is 1 but if x = 8, then the remainder upon division 8 by 10 is 8. Not sufficient.

Hope it helps.

Bunuel the method you mentioned in response to seabhi has been discussed above. i'm curious -- if he's wrong, how were his calculations incorrect? i built out the #s given from the formulas and got the same thing as him (see below):

- x=5q+1, so: 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71
- x = 7q+1, so: 8, 15, 22, 29, 36, 43, 50, 57, 64, 71

Hi,

I think the confusion with this problem is that you neglecting that q in the question stem and in the first statement (1) have to be the same value.

So, from the question stem $$\frac{x}{7}$$ = q remainder 1. Or x = 7q+1
which means when q=0 then x = 1. And when q=5, then x =36.

And from statement (1) $$\frac{x}{5}$$ = q remainder 1. Or x=5q+1
Thus from this statement if q=0 then x = 1 and if q=7 then x =36

Now, what students are doing incorrectly is assuming since x = 1 and x=36 so they are marking this as insuff. "the quotient is q" in the question stem and "the quotient is q" in statement (1) are of the same value. So when x=1, then q = 0 both in question stem and statement (1). But when x=36, then q = 5 in the question stem and q = 7 in statement (1), so q is not of the same value, and we can ignore x = 36 as a valid solution and only take x = 1 as a valid solution. And of course x=1 divided by 10 leaves remainder of 1.
Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 987
Location: India
GPA: 3.64
When positive integer x is divided by 7 the quotient is q  [#permalink]

### Show Tags

04 Aug 2018, 07:09
Official Explanation from Veritasprep:

In quotient remainder problems, number picking is often a valid technique to show patterns and answer the question. For this problem, however, it is not very helpful as the question is really testing a tricky property of division with integers.

From statement one, you learn that when x is divided by 5 the quotient is q and the remainder is 1. In the question stem, you learned that when x
is divided by 7 the quotient is also q and the remainder is also 1. Most students understand that if you divide a number by two different divisors and get the same remainder, you must be at the LCM (lowest common multiple) of those two numbers plus the remainder (and then at the same location down the number line to infinity). For instance if you divide a number by 5 and 7 and get a remainder of 1, then that can happen at 35+1, 70+1, 105+1, etc. However, if you read carefully you see that the quotient is the same in both operations, a puzzling result. Clearly if you divide 36 by 7 it will give you a different quotient then when you divide 36 by 5. The only way this can happen is if x is equal to 1. Remember that when a smaller integer is divided by a larger integer, the quotient is always 0 and the remainder is the dividend itself. Here when 1 is divided by 7 the quotient is 0 and the remainder is 1 and when 1 is divided by 5 the quotient is also 0 and the remainder is 1. Statement 1 is sufficient as x must be 1 and the remainder when x is divided by 10 is also 1.

Statement 2 is clearly not sufficient by itself so the answer is A. This statement is here for people who miss that the quotient is the same and think that x could be any multiple of 35+1. By knowing that x is less than 50 it would lock in the value at 36. However, from the discussion above it is clear that this would be incorrect.
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

When positive integer x is divided by 7 the quotient is q &nbs [#permalink] 04 Aug 2018, 07:09
Display posts from previous: Sort by