In the figure above, △IGH is inscribed in △ABC in such a way that HG||

Question

https://gmatclub.com/forum/download/file.php?id=58150 In the figure above, △IGH is inscribed in △ABC in such a way that HG||BC, AB||GI, and HI||AC. What is the length of AB times the length of HG? (1) AB = 10 (2) BC*GI = 24 Untitled.png

GMATinsight · Answer

This question should be answered more logically than mathematically.

Here we can see that since sides of △IGH are parallel with sides of △ABC so the two triangles are Similar.

Now we need to take the ratio of corresponding sides in which two ratios will give us AB*HG

i.e. to answer the question we need the product of two other corresponding sides of the two triangles

Statement 1: AB = 10

clearly NOT sufficient because any lenght of side can not give us answer.

Statement 2: BC*GI = 24

Must be Sufficient because the other two corresponding sides of AB anf GH will be BC and GI

i.e. their product will be equal i.e. BC*GI = AB*HG = 24

SUFFICIENT

Answer: Option B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the figure above, △IGH is inscribed in △ABC in such a way that HG||

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards