The remainder when N is divided by 18 is 16, translated : \(N=18k+16\)

\(\frac{N}{4}\) is divided by 18 means what is the remainder of \(\frac{N}{4*18}\)?

Given that N is a multiple of 28, translated: \(N=28m\)

\(\frac{N}{4*18}\) with \(N=28m\) is \(\frac{28m}{4*18}\) or \(\frac{7m}{18}\) and its "form" can be written as \(7m=18q+R\) ( or 14m=36q+2R, this will be useful later)

Going back to the first equation \(N=18k+16\) = \(28m=18k+16\) = \(14m=9k+8\). From the equation before is its "useful" form 14m=36q+2R

so puttin them together \(9k+8=36q+2R\)

all the numbers k,q,R must be integer \(8-2R=36q-9k\)

if q and r are 0 \(8-2R=0\) so \(R=4\)

value #1the other possible value of R (because must be positive, it's a reminder) will be in the case 9k>36q

The difference \(36q-9k\) can be (36-45) = -9 but \(8-2R=-9\) means R=17/2 no integer

difference -18 => R = 5

value #2difference -27 => R = 33/2 no integer

difference -36 => R=21 out of range 0,18

We can stop here bigger differences mean R out of 0,18 range

2 values,

B(I am not sure of my method though, the Master Mind could help here and +1 to the question! it took me 10 minutes to came up with a solution!)

_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My QuantRules for Posting in the Verbal Forum -

Rules for Posting in the Quant Forum[/size][/color][/b]