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605-655 (Medium)|   Geometry|      
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jpfg259
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In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter... Updated on: 30 Jan 2019, 08:14
Originally posted by jpfg259 on 25 Jan 2019, 07:54.
Last edited by jpfg259 on 30 Jan 2019, 08:14, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

64% (01:43) correct 36% (01:55) wrong based on 85 sessions

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In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC intersects PD at Q. What proportion of AC is AQ?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

Attachment:
Screen Shot 2019-01-25 at 3.50.29 PM.png
Screen Shot 2019-01-25 at 3.50.29 PM.png [ 78.65 KiB | Viewed 3275 times ]

Thank you in advance!

Source: Manhattan Review
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B
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GMAT Focus 1: 735 Q90 V89 DI81
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In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter... 25 Jan 2019, 11:06
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jpfg259
In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC intersects PD at Q. What proportion of AC is AQ?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

Attachment:
The attachment Screen Shot 2019-01-25 at 3.50.29 PM.png is no longer available

Thank you in advance!
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Triangles APQ and CDQ are similar triangles as AP is parallel to CD...
The corresponding sides are in same ratio...
so \(\frac{AP}{CD}=\frac{PQ}{DQ}=\frac{AQ}{CQ}\) means \(\frac{AP}{CD}=\frac{AQ}{CQ}... =>\frac{x}{2x}=\frac{AQ}{CQ}....=>CQ=2AQ\)..
We are looking for \(\frac{AQ}{AC}=\frac{AQ}{AQ+QC}=\frac{AQ}{AQ+2AQ}=\frac{AQ}{3AQ}=\frac{1}{3}\)
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Screen Shot 2019-01-25 at 3.50.29 PM.png
Screen Shot 2019-01-25 at 3.50.29 PM.png [ 61.58 KiB | Viewed 3164 times ]

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jpfg259
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In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter... 29 Jan 2019, 08:05
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chetan2u
jpfg259
In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC intersects PD at Q. What proportion of AC is AQ?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

Attachment:
Screen Shot 2019-01-25 at 3.50.29 PM.png

Thank you in advance!


Triangles APQ and CDQ are similar triangles as AP is parallel to CD...
The corresponding sides are in same ratio...
so \(\frac{AP}{CD}=\frac{PQ}{DQ}=\frac{AQ}{CQ}\) means \(\frac{AP}{CD}=\frac{AQ}{CQ}... =>\frac{x}{2x}=\frac{AQ}{CQ}....=>CQ=2AQ\)..
We are looking for \(\frac{AQ}{AC}=\frac{AQ}{AQ+QC}=\frac{AQ}{AQ+2AQ}=\frac{AQ}{3AQ}=\frac{1}{3}\)
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That was a great explanation, thank you so much!
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CAMANISHPARMAR
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In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter... 05 Feb 2019, 09:48
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jpfg259
In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC intersects PD at Q. What proportion of AC is AQ?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

Attachment:
Screen Shot 2019-01-25 at 3.50.29 PM.png

Thank you in advance!

Source: Manhattan Review
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Important thing to note in this question is that triangles QDC & QPA are similar. Since P is the mid point; AP:DC is 1:2; Hence AQ:QC is 1:2 or AQ:AC is 1:3

Corect ans is Option B
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In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter... 29 Dec 2020, 17:25
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