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M10-12

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M10-12 [#permalink]

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If \(X\) is a positive integer, what is the remainder of \(\frac{X}{8}\)?


(1) The remainder of \(\frac{X}{16}\) is 2.

(2) The remainder of \(\frac{X}{24}\) is 10.

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Re M10-12 [#permalink]

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Official Solution:


Statement (1) by itself is sufficient. From S1 it follows that \(X = 16N + 2\) where \(N\) is an integer. Thus, the remainder of \(\frac{X}{8}\) is 2.

Statement (2) by itself is sufficient. From S2 it follows that \(X = 24N + 10 = (24N + 8) + 2\) where \(N\) is an integer. Thus, the remainder of \(\frac{X}{8}\) is 2.


Answer: D
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Re: M10-12 [#permalink]

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New post 09 Nov 2014, 08:07
I'd appreciate if you could explain what you did for st 2.. how did you get x/8 ?
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Re: M10-12 [#permalink]

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Split 24N + 10 ==> (24N+8) + 2

It can further be written as 8(3N+1) + 2. When this is divided by 8 the remainder is 2.
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Re: M10-12 [#permalink]

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New post 23 Feb 2016, 00:48
Bunuel wrote:
Official Solution:


Statement (1) by itself is sufficient. From S1 it follows that \(X = 16N + 2\) where \(N\) is an integer. Thus, the remainder of \(\frac{X}{8}\) is 2.

Statement (2) by itself is sufficient. From S2 it follows that \(X = 24N + 10 = (24N + 8) + 2\) where \(N\) is an integer. Thus, the remainder of \(\frac{X}{8}\) is 2.


Answer: D


Hi

I think I am missing some concept here. I framed equations like this:
Stem=X=8a+R; To find R=X-8a
Stmt1=X=16b+2
Stmt2=X=24c+10

Hence got E as cant find a or X from any of the stmts. I knw logically what I did is not wrong but dont know how to proceed from here. Read something about primes but how does the concept come about? Pls elaborate. Thanks.
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M10-12 [#permalink]

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sinhap07 wrote:
Bunuel wrote:
Official Solution:


Statement (1) by itself is sufficient. From S1 it follows that \(X = 16N + 2\) where \(N\) is an integer. Thus, the remainder of \(\frac{X}{8}\) is 2.

Statement (2) by itself is sufficient. From S2 it follows that \(X = 24N + 10 = (24N + 8) + 2\) where \(N\) is an integer. Thus, the remainder of \(\frac{X}{8}\) is 2.


Answer: D


Hi

I think I am missing some concept here. I framed equations like this:
Stem=X=8a+R; To find R=X-8a
Stmt1=X=16b+2
Stmt2=X=24c+10

Hence got E as cant find a or X from any of the stmts. I knw logically what I did is not wrong but dont know how to proceed from here. Read something about primes but how does the concept come about? Pls elaborate. Thanks.


Hi,
NOTE:-
whatever is the remainder by an integer, the remainder will remain teh same if div by its factors..
only thing to check is if the R is further div by that factor

what you should have done after making your statements..
Stmt1=X=16b+2
we do not require X or a, we are interested in R..
so what does x/8 mean..
(16b+2)/8=16b/8 + 2/8..
16b is div by 8 so will not leave any remainder but 2/8 will leave a remainder of 2..
suff

Stmt2=X=24c+10

same way ( 24c+10)/8= 3c +10/8..
when 10 is div by 8, it will give us 2 as remainder ..
again suff

D

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Re: M10-12 [#permalink]

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New post 03 May 2016, 06:09
could someone explain to me how does it follow from statement 1 that

that X=16N+2X=16N+2 where N is an integer?
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Re: M10-12 [#permalink]

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New post 03 May 2016, 06:22
nausherwan wrote:
could someone explain to me how does it follow from statement 1 that

that X=16N+2X=16N+2 where N is an integer?


hi
I. (1) The remainder of \(\frac{X}{16}\) is 2...
it can be written as -- when x is divided by 16, the remainder is 2...
we do not know the quotient(Q) here but just know the remainder..
how do I write it in a equation-
x = 16a + 2..
a is the quotient and 2 is the remainder..
say a is 5.. so x= 5*16 +2 = 82..
I can write it as-- the remainder of 82/16 is 2..

so x=16n+2 is just another way of writing -- The remainder of \(\frac{X}{16}\) is 2
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Re: M10-12 [#permalink]

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nausherwan wrote:
could someone explain to me how does it follow from statement 1 that

that X=16N+2X=16N+2 where N is an integer?


Check the links below:
Divisibility and Remainders on the GMAT

Theory on remainders problems

Tips on remainders

Cyclicity on the GMAT

Units digits, exponents, remainders problems

Hope it helps.
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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

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Re: M10-12 [#permalink]

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New post 14 Nov 2016, 22:58
why did you consider N as an integer.it was not given in the question?
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Re: M10-12 [#permalink]

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New post 27 May 2017, 10:08
Another approach - Write out few of the Numbers and check

S1: The Remainder of \(\frac{X}{16}= 2\)
This means X = 2, 18, 34...
Remainders when divided by 8 in all the cases = 2
Suff

S2: The Remainder of \(\frac{X}{24}= 10\)
This means X = 10, 34, 58...
Remainder when X is divided by 8 in all cases = 2
Suff

Final answer : D
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Re M10-12 [#permalink]

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New post 31 Jan 2018, 00:53
I think this is a high-quality question and I don't agree with the explanation. what if we take x=14 for statement 1.
then 14/16 gives rem as 2
but 14/8 gives rem as 6.
so the correct answer should be B.
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Re: M10-12 [#permalink]

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New post 31 Jan 2018, 01:49
muditsingh0616 wrote:
I think this is a high-quality question and I don't agree with the explanation. what if we take x=14 for statement 1.
then 14/16 gives rem as 2
but 14/8 gives rem as 6.
so the correct answer should be B.


14 divided by 16 gives the remainder of 14, not 2. From (1) x could be 2, 18, 34, 50, 66, ... Each of these values gives a remainder of 2 when divided by 8, so (1) is sufficient.
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GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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: M10-12   [#permalink] 31 Jan 2018, 01:49
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