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If a is a positive integer and 81 divided by a results in a

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If a is a positive integer and 81 divided by a results in a [#permalink] New post 16 Jun 2012, 13:48
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If a is a positive integer and 81 divided by a results in a remainder of 1, what is the value of a?

(1) The remainder when a is divided by 40 is 0
(2) The remainder when 40 is divided by a is 40
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 16 Jun 2012, 14:00
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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.
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 17 Jun 2012, 06:36
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?
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 17 Jun 2012, 06:40
Expert's post
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,

Hope it's clear.
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 17 Jun 2012, 20:17
B. But is it a 700+ level question??i doubt!
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 24 Jun 2013, 11:02
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 .. :(
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 24 Jun 2013, 11:16
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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?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 25 Jun 2013, 04:24
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?


thanks :)
I got it ... :)
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Re: If a is a positive integer and 81 divided by a results in a [#permalink] New post 07 Oct 2014, 02:46
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Re: If a is a positive integer and 81 divided by a results in a   [#permalink] 07 Oct 2014, 02:46
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