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 Your Progress
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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
16 Jun 2012, 15:00
2
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) --> \(qa=80\) --> so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 --> this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 --> this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
17 Jun 2012, 07:36
Bunuel wrote:
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) --> \(qa=80\) --> so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 --> this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 --> this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear.
Dear Bunuel, i am not able to understand the st. 2 analysis. (ofcourse i understood what you have written.) one doubt remains like: if it is said x/y leaves a remainder of 10, can i consider values of x/y as 10/20 and like that?
Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
17 Jun 2012, 07:40
1
kashishh wrote:
Bunuel wrote:
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) --> \(qa=80\) --> so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 --> this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 --> this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear.
Dear Bunuel, i am not able to understand the st. 2 analysis. (ofcourse i understood what you have written.) one doubt remains like: if it is said x/y leaves a remainder of 10, can i consider values of x/y as 10/20 and like that?
Yes, 10 divided by 20 yields the remainder of 10.
THEORY: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).
For example positive integer n is divided by 25 yields the remainder of 13 can be expressed as: \(n=25q+13\). Now, the lowest value of \(q\) can be zero and in this case \(n=13\) --> 13 divided by 25 yields the remainder of 13. Generally when divisor (25 in our case) is more than dividend (13 in our case) then the reminder equals to the dividend. For example: 3 divided by 24 yields a reminder of 3 --> \(3=0*24+3\); or: 5 divided by 6 yields a reminder of 5 --> \(5=0*6+5\),
Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
24 Jun 2013, 12:02
Bunuel wrote:
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) --> \(qa=80\) --> so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 --> this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 --> this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear.
Thanks for the solution
I have one doubt ... as per the 2nd statement when 40 is divided by a remainder is 40 i.e. 40 = aq +40 or aq =0 ?
can you please explain this also .. _________________
Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
24 Jun 2013, 12:16
ichauhan.gaurav wrote:
Bunuel wrote:
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) --> \(qa=80\) --> so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 --> this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 --> this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear.
Thanks for the solution
I have one doubt ... as per the 2nd statement when 40 is divided by a remainder is 40 i.e. 40 = aq +40 or aq =0 ?
can you please explain this also ..
Yes, "the remainder when 40 is divided by a is 40" can be written as \(40=ap+40\) --> \(ap=0\). What is the point of confusion here?
_________________
Re: If a is a positive integer and 81 divided by a results in a [#permalink]
Show Tags
25 Jun 2013, 05:24
Bunuel wrote:
ichauhan.gaurav wrote:
Bunuel wrote:
If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?
Given: \(81=qa+1\) --> \(qa=80\) --> so, \(a\) is a factor of 80: 2, 4, 5, 8, 10, 16, 20, 40, or 80.
(1) The remainder when a is divided by 40 is 0 --> this basically tells us that \(a\) is a multiple of 40, so \(a\) could be either 40 or 80 (from the above). Not sufficient.
(2) The remainder when 40 is divided by a is 40 --> this basically means that \(a\) is greater than 40 (for example, the remainder upon division 40 by 50 is 40). Now, the only factot of 80 which is greater than 40 is 80 itself. So, \(a=80\). Sufficient.
Answer: B.
Hope it's clear.
Thanks for the solution
I have one doubt ... as per the 2nd statement when 40 is divided by a remainder is 40 i.e. 40 = aq +40 or aq =0 ?
can you please explain this also ..
Yes, "the remainder when 40 is divided by a is 40" can be written as \(40=ap+40\) --> \(ap=0\). What is the point of confusion here?
close
58% (01:20) correct 
