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# What is the value of DE/FG ?

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
What is the value of DE/FG ?  [#permalink]

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27 Feb 2019, 15:52
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:48) correct 44% (01:59) wrong based on 36 sessions

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GMATH practice exercise (Quant Class 17)

What is the value of $$DE/FG$$ ?

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

Attachment:

27-Feb19-3j.gif [ 6.45 KiB | Viewed 415 times ]

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: What is the value of DE/FG ?  [#permalink]

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28 Feb 2019, 07:07
fskilnik wrote:
GMATH practice exercise (Quant Class 17)

What is the value of $$DE/FG$$ ?

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

$$\Delta ADE\,\,\, \cong \,\,\,\Delta AFG\,\,\, \cong \,\,\,\Delta ABC$$

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

$$\left( 1 \right)\,\,\,{{AD} \over {AB}} = {1 \over 5}\,\,\,\,\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.\,\,\,\,\left( {{\rm{images}}} \right)$$

$$\left( 2 \right)\,\,AD = FB\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.\,\,\,\,\left( {{\rm{images}}} \right)$$

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

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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: What is the value of DE/FG ?   [#permalink] 28 Feb 2019, 07:07
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