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Concentration: Entrepreneurship, General Management
GPA: 3.49
When positive integer x is divided by 7 the quotient is q [#permalink]
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18 Nov 2013, 08:55
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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?
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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19 Nov 2013, 03:56
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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.
Concentration: Entrepreneurship, General Management
GPA: 3.49
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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19 Nov 2013, 08:29
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.
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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19 Nov 2013, 10:11
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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..
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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20 Nov 2013, 00:21
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?
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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20 Nov 2013, 00:31
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.
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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20 Nov 2013, 06:08
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.
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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20 Nov 2013, 06:10
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.
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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21 May 2014, 05:02
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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.
_________________
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.
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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08 Oct 2015, 08:03
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Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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25 Oct 2016, 06:52
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Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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02 Jul 2017, 10:03
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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
Re: When positive integer x is divided by 7 the quotient is q [#permalink]
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08 Aug 2017, 21:26
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.
Answer: A.
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):
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44% (01:25) correct
