What is the value of DE/FG ?

[fskilnik@GMATH]

GMATH practice exercise (Quant Class 17)



What is the value of DE/FG ?

(1) AB/AD = 5
(2) AD = FB

Answer: [spoiler]____(C)__[/spoiler]

[fskilnik@GMATH]

GMATH practice exercise (Quant Class 17)



What is the value of DE/FG ?

(1) AB/AD = 5
(2) AD = FB

$$\Delta ADE\,\,\, \cong \,\,\,\Delta AFG\,\,\, \cong \,\,\,\Delta ABC$$
$$? = \frac{{DE}}{{FG}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,?\,\, = \,\,\,\Delta ADE:\Delta AFG\,\,\,{\text{ratio}}\,\,{\text{of}}\,\,{\text{similarity}}\,\,{\text{ = }}\,\,\,\frac{{AD}}{{AF}}\,\,\left( { = \frac{{AE}}{{AG}}} \right)\,\,}$$



$$\left( 1 \right)\,\,\,{{AD} \over {AB}} = {1 \over 5}\,\,\,\,\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.\,\,\,\,\left( {{\rm{images}}} \right)$$
$$\left( 2 \right)\,\,AD = FB\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.\,\,\,\,\left( {{\rm{images}}} \right)$$
$$\left( {1 + 2} \right)\,\,\,\,? = {{AD} \over {AF}} = {{AD} \over {AB - BF}}\,\,\mathop = \limits^{\left( 2 \right)} \,\,{{AD} \over {AB - AD}}\,\,\mathop = \limits^{\left( * \right)} \,\,{k \over {5k - k}} = {1 \over 4}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

The correct answer is (C).


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

Regards,
Fabio.