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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.
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.
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
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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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.
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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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
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83% (01:26) correct 
