Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 868
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
04 Jun 2015, 04:41
Question Stats:
57% (02:13) correct 43% (02:27) wrong based on 159 sessions
HideShow timer Statistics
Attachment:
T8783.png [ 10.47 KiB  Viewed 1920 times ]
If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpendicular, what is the length of CM? A. 0.8 B. 1.6 C. 1.8 D. 2.4 E. 2.8 KUDOS for a concise and creative Answer
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



SVP
Joined: 08 Jul 2010
Posts: 2115
Location: India
GMAT: INSIGHT
WE: Education (Education)

If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
04 Jun 2015, 06:13
reto wrote: Attachment: The attachment T8783.png is no longer available If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpendicular, what is the length of CM? A. 0.8 B. 1.6 C. 1.8 D. 2.4 E. 2.8 KUDOS for a concise and creative Answer Answer: Option
Attachments
Sol4.jpg [ 191.15 KiB  Viewed 1868 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 04 May 2014
Posts: 29

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
04 Jun 2015, 06:24
I found a nice way; since the lines are AC and DB are perpendicular, this means that the triangles are proportionate to each other and that they are right triangles. Since we know sides AM and DM we can use pythagorem theorem to solve for AD
1.2 = 6/5 1.8 = 8/5
6/5*6/5 + 8/5*8/5 = 4 which is a perfect square and solves for 2 So AD is 2, we know that CB is proportionate to AD. CB is 1 1/2 x more than AD So CM must be 1 1/2 times more than DM. 6/5 * 3/2 = 18/10 = 1.8 Therefore answer C



Retired Moderator
Joined: 29 Apr 2015
Posts: 868
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
06 Jun 2015, 02:30
reto wrote: Attachment: T8783.png If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpendicular, what is the length of CM? A. 0.8 B. 1.6 C. 1.8 D. 2.4 E. 2.8 KUDOS for a concise and creative Answer Thanks for participating But how about just ballparking and POE this task? Since in Problem Solving Questions, Figures are usually drawn to scale: CM looks a bit longer than AM (1.6). Therefore POE A, B, D, E and choose C.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



Manager
Joined: 26 Mar 2016
Posts: 77
Location: Greece
GPA: 2.9

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
20 Dec 2016, 07:28
Ι took the two similar triangles ADM and BCM: AM/DM=CM/BM. Why am I wrong here?
_________________
+1 Kudos if you like the post



Intern
Joined: 20 Dec 2016
Posts: 3

If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
22 Dec 2016, 17:45
Could some confirm this for me, I couldn't make out the theory that GMATInsight was using in the blue ink, so I don't want to make this assumption if it only holds true here:
If two chords intersect in a circle, are the "vertical" arcs proportional?
I.e. for this example, given the chords AC and DB, are arcs AD and BC similar/proportionate to arcs CD and AB? I guess my question is: is this a theory, or does this proportional relationship happen to be the case because perhaps these chords are perpendicular (or some other relationship that I'm missing)?
Making this assumption, we could the ratio of the hypotenuses are equal to the ratio of the other angles/sides in a "reflective" manner.
EDIT: Another thought/question: Going off that theory, if these were NOT right triangles and they had provided an area for one of the triangles, along the lengths of two related sides, could we calculate the area of the other triangle? Like in this example, if the area of the smaller triangle were X, and they told us CB=3 and AD = 2, could we use that ratio of 3:2 to calculate the area of the larger triangle? I.e. would the area always equal X*(3/2)^2?



Intern
Joined: 12 Jun 2016
Posts: 27
Location: India
Concentration: Entrepreneurship, Finance
GPA: 3.76
WE: Information Technology (Computer Software)

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
22 Dec 2016, 21:37
arven wrote: Ι took the two similar triangles ADM and BCM: AM/DM=CM/BM. Why am I wrong here? This is because the ratio of sides you took is not proper. You can use the below method. Triangles ADM and BCM are similar. Just take any two points at a time for each of the triangle(A,D from first triangle and corresponding B,C from second triangle and so on..) So, AD/BC = DM/CM = AM/BMCheck , the proportion should be DM/AM = CM/BM. But in your case, you have reversed the LHS to AM/DM. Hope this helps.



Math Expert
Joined: 02 Aug 2009
Posts: 5947

If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
23 Dec 2016, 05:52
reto wrote: Attachment: T8783.png If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpendicular, what is the length of CM? A. 0.8 B. 1.6 C. 1.8 D. 2.4 E. 2.8 KUDOS for a concise and creative Answer Hi Another way... when two chords intersect, the product of the segment's is equalHere AM * MC = DM * MB..... 1.6MC=1.2MB......MB=4MC/3.... Take ∆CBM.... \(MC^2+MB^2=CB^2........(\frac{4MC}{3})^2+MC^2=3^2...........\frac{25MC^2}{9}=3^2..... \frac{5MC}{3}=3....... MC=9/5=1.8\) C
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Manager
Joined: 26 Mar 2016
Posts: 77
Location: Greece
GPA: 2.9

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
23 Dec 2016, 06:55
shashank1tripathi wrote: arven wrote: Ι took the two similar triangles ADM and BCM: AM/DM=CM/BM. Why am I wrong here? This is because the ratio of sides you took is not proper. You can use the below method. Triangles ADM and BCM are similar. Just take any two points at a time for each of the triangle(A,D from first triangle and corresponding B,C from second triangle and so on..) So, AD/BC = DM/CM = AM/BMCheck , the proportion should be DM/AM = CM/BM. But in your case, you have reversed the LHS to AM/DM. Hope this helps. I thought I just have to take Base1/Base2=height1/height2 So as I understand do I have to take the sides that are perpendicular to each other?
_________________
+1 Kudos if you like the post



Intern
Joined: 20 Dec 2016
Posts: 3

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
23 Dec 2016, 09:34
arven wrote: shashank1tripathi wrote: arven wrote: Ι took the two similar triangles ADM and BCM: AM/DM=CM/BM. Why am I wrong here? This is because the ratio of sides you took is not proper. You can use the below method. Triangles ADM and BCM are similar. Just take any two points at a time for each of the triangle(A,D from first triangle and corresponding B,C from second triangle and so on..) So, AD/BC = DM/CM = AM/BMCheck , the proportion should be DM/AM = CM/BM. But in your case, you have reversed the LHS to AM/DM. Hope this helps. I thought I just have to take Base1/Base2=height1/height2 So as I understand do I have to take the sides that are perpendicular to each other? I found out the theory in use: When two chords intersect, the product of one chords parts = the product of the other chord's parts. So AM*MC=DM*MB; Therefore, AM/DM = MB/MC; which basically says 2 sides of these triangles are similar. That, along with the similar vertical angle of 90 tells us the triangles are similar. If AM and DM are two parts of a 345, then we know MB and MC have to be parts of a 345. The previous ratio shows which is the 3 and which is the 4 (Numerators are "4s")



Director
Joined: 13 Mar 2017
Posts: 610
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe [#permalink]
Show Tags
21 Aug 2017, 02:05
reto wrote: Attachment: T8783.png If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpendicular, what is the length of CM? A. 0.8 B. 1.6 C. 1.8 D. 2.4 E. 2.8 KUDOS for a concise and creative Answer /_DAC = /_DBC (angle subtended by same arc DC on the circle.) /_ADB = /_ADC (angle subtended by same arc AB on the circle.) /_AMD = /_BMC = 90 deg tria(AMD) ~ tria (BMC) AM/BM = DM/MC = AD/BC 1.6/BM = 1.2/MC = AD/3 AD = \(\sqrt{(AM^2 + DM^2)}\) =\(\sqrt{(1.6^2 + 1.2^2)}\) =2 1.2/MC = 2/3 MC = 1.8 Answer C
_________________
CAT 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".




Re: If in the figure above AM=1.6, DM=1.2 and CB=3. If AC and DB are perpe
[#permalink]
21 Aug 2017, 02:05






