fskilnik wrote:
GMATH practice exercise (Quant Class 16)
The sum of all integers between 500 and 2500 that are divisible by both 18 and 75 is:
(A) 6750
(B) 6300
(C) 5400
(D) 4050
(E) 3150
\(? = \sum N \,\,\,::\,\,\,\left\{ \matrix{
\,500 < N\,\,{\mathop{\rm int}} < 2500\,\,\,\,\left( * \right) \hfill \cr
\,{N \over {2 \cdot {3^2}}} = {\mathop{\rm int}} \,\,\,;\,\,\,{N \over {3 \cdot {5^2}}} = {\mathop{\rm int}} \,\,\,\,\left( {**} \right) \hfill \cr} \right.\)
\(\left( {**} \right)\,\,\,\, \Rightarrow \,\,\,\,N = k \cdot LCM\left( {2 \cdot {3^2};3 \cdot {5^2}} \right) = k \cdot 2 \cdot {3^2} \cdot {5^2} = 450 \cdot k\,\,\,\,\,\left( {k\,\,{\mathop{\rm int}} } \right)\)
\(\left\{ \matrix{
\,450 \cdot 2 = 900 \hfill \cr
\,\left( {450 \cdot 2} \right) \cdot 3 = 2700 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,k = 2,3,4,5\)
\(? = 450\,\left( {2 + 3 + 4 + 5} \right)\,\,\, = \,\,\,6300\)
The correct answer is (B).
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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