GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 18:32

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter...

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Feb 2018
Posts: 10
In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter...  [#permalink]

### Show Tags

Updated on: 30 Jan 2019, 08:14
2
5
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:35) correct 36% (02:02) wrong based on 47 sessions

### HideShow timer Statistics

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 [ 78.65 KiB | Viewed 726 times ]

Source: Manhattan Review

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.
Math Expert
Joined: 02 Aug 2009
Posts: 7954
Re: In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter...  [#permalink]

### Show Tags

25 Jan 2019, 11:06
2
jpfg259 wrote:
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

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 $$\frac{AQ}{AC}=\frac{AQ}{AQ+QC}=\frac{AQ}{AQ+2AQ}=\frac{AQ}{3AQ}=\frac{1}{3}$$
Attachments

Screen Shot 2019-01-25 at 3.50.29 PM.png [ 61.58 KiB | Viewed 674 times ]

_________________
Intern
Joined: 22 Feb 2018
Posts: 10
Re: In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter...  [#permalink]

### Show Tags

29 Jan 2019, 08:05
chetan2u wrote:
jpfg259 wrote:
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

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 $$\frac{AQ}{AC}=\frac{AQ}{AQ+QC}=\frac{AQ}{AQ+2AQ}=\frac{AQ}{3AQ}=\frac{1}{3}$$

That was a great explanation, thank you so much!
Director
Joined: 12 Feb 2015
Posts: 915
Re: In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter...  [#permalink]

### Show Tags

05 Feb 2019, 09:48
jpfg259 wrote:
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

Source: Manhattan Review

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
_________________
"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"
Re: In a parallelogram ABCD, P is the midpoint of AB. Diagonal AC inter...   [#permalink] 05 Feb 2019, 09:48
Display posts from previous: Sort by