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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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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I'd appreciate if you could explain what you did for st 2.. how did you get x/8 ?

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.

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.

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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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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why did you consider N as an integer.it was not given in the question?

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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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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Don't see how S) 1 is sufficient.

x/16 gives remainder 2.

Hence X = 16q + 2

if q=0,
x= 16(0) + 2
=2

if q=1
x= 16 + 2
= 18

lets take x=2. 2/8 gives 0 remainder 8.
lets take x=18 18/8 gives 2 remainder 2.

Insufficient.

S) 2 on the other hand..

X = 24p + 10

if p=0
x= 10

p=1
x = 34

10/8 gives remainder 2
34/8 gives remainder 2.

Statement 2 works, but 1 doesn't.

PierTotti17 All is good in what you wrote, except, 2/8 gives a remainder of 2, not 8. Hence 1 is sufficient as well.

Easy to prove sufficiency with number picking, just plug in 2, 18 for St 1) you will get remainder 2 both times when dividing by 8.
St 2) must give the same remainder... you get 2 when dividing by 8 as well, plug in 2 and 34.
This is because both 16 and 24 are multiples of 8 so they all share the same remainder when dividing X. As chetan2u mentioned the only thing is to make sure remainder/divisor is in the most reduced form.

My two cents' worth here, probably a rehash of what the experts have expounded on above:

In both statements, the divisors 16, 24 (in relation and including the divisor '8' in the stem) are all multiples of the smallest of the divisors: '8'.

If so, we can possibly infer that all outcomes when divided by the divisors (=8K) would yield the same remainder; without calculating, I would pick 'D'.

Here are some numbers to try out e.g. 2,4,8 as divisors; the same numerator X=17 is tested.
17/2 with R=1
17/4 with R=1
17/8 with R=1

Each statement is sufficient on its own, hence D.

Hi GMATPrepNow, I know its an easy question but still I am little confused about the method. Can you please help?
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Target question: What is the remainder when x is divided by 8?

Statement 1: When x is divided by 16, the remainder is 2
In other words, x is 2 greater than some multiple of 16
In other words, x = 16k + 2 (for some integer k)
Rewrite this as: x = (8)(2k) + 2
This tells us that x is 2 greater than some multiple of 8
This means we get a remainder of 2 when x is divided by 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When x is divided by 24, the remainder is 10
In other words, x is 10 greater than some multiple of 24
In other words, x = 24j + 10 (for some integer j)
In other words, x = 24j + 8 + 2 (for some integer j)
Rewrite this as: x = 8(3j + 1) + 2
This tells us that x is 2 greater than some multiple of 8
This means we get a remainder of 2 when x is divided by 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
RELATED VIDEO FROM MY COURSE

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\((x/16) = Q + (2/16)\)

X = 16Q + 2

\((x/24) = Q + (10/24)\)

X = 24Q + 10

Divide both by 8: remainder of 2 and 2