Data Sufficiency

Veritas Prep

If q is a six-digit integer between 200,000 and 201,000, what is the units digit of q?

1) The remainder when q is divided by 5 is 4.
2) The tens digit of 2(5q + 1.5) is 9.

OA B

AAPL wrote:Veritas Prep

If q is a six-digit integer between 200,000 and 201,000, what is the units digit of q?

1) The remainder when q is divided by 5 is 4.
2) The tens digit of 2(5q + 1.5) is 9.

$$200,000 < q\,\,{\mathop{\rm int}} \,\, < \,\,201,000$$
$$? = \left\langle q \right\rangle $$
$$\left( 1 \right)\,\,q = 5M + 4\,\,,\,\,\,M\,\,{\mathop{\rm int}} \,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,M = 40,000\,\,\,\, \Rightarrow \,\,\,q = 200,004\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 4 \hfill \cr
\,{\rm{Take}}\,\,M = 40,001\,\,\,\, \Rightarrow \,\,\,q = 200,009\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9 \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\left\langle {{{10q + 3} \over {10}}} \right\rangle \,\, = \,\,9\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {q + {3 \over {10}}} \right\rangle = 9\,\,\,\,\,\mathop \Rightarrow \limits^{q\,\,{\mathop{\rm int}} } \,\,\,\,\,? = 9$$


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.