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

 It is currently 18 Jun 2019, 18:11 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  What is the smallest possible distance between the point (0, 5) and an

Author Message
TAGS:

Hide Tags

Senior RC Moderator V
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2759
Location: Pakistan
GPA: 3.39
What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

8 00:00

Difficulty:   55% (hard)

Question Stats: 55% (01:29) correct 45% (01:42) wrong based on 103 sessions

HideShow timer Statistics

What is the smallest possible distance between the point (0, 5) and any point on the line y = -x + 3?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2

Source: Experts Global GMAT
Difficulty Level: 600

_________________
New Project RC Butler 2019 - Practice 2 RC Passages Everyday
Final days of the GMAT Exam? => All GMAT Flashcards.
This Post Helps = Press +1 Kudos
Best of Luck on the GMAT!!

Last edited by SajjadAhmad on 06 Jan 2019, 20:16, edited 4 times in total.
RC Moderator V
Joined: 24 Aug 2016
Posts: 804
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

3
What is the smallest possible distance between the point (0, 5) and any point on the line y = -x + 3?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2

EG

Method 01 :

Distance from a pt (x,y) from line am+bn+c=0 is $$\frac{|ax+by+c|}{\sqrt{(a^2 +b^2)}}$$
Eqn: x+y-3=0 Hence Distance = $$\frac{|0*1 +5*1-3|}{\sqrt{(1^2 +1^2)}}$$ = $$\sqrt{2}$$

Or Alternatively , Method 02: Picture
Attachments IMG_0382.jpg [ 74.27 KiB | Viewed 997 times ]

_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Manager  G
Joined: 24 Jun 2013
Posts: 141
Location: India
Schools: ISB '20, GMBA '20
Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

2
1
What is the smallest possible distance between the point (0, 5) and any point on the line y = -x + 3?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2

EG

smallest possible distance is always when line from that point meets at 90deg to other line.

From above we know the both lines will be perpendicular to each other.

if two lines are perpendicular to each other then their slope are negative reciprocal.

let L1 = y = -x + 3 ==> m1 (slope) = -1
let L2 (line from point 0,5 to L1) = y=m2 x + C ; we also know from above that m2 = 1

so the equation of L2 becomes = y = x + 5 (C=5, we can substitute (0,5) in L2 equation to get value of C)

now both line meet at (-1,4) you could get this point by equating both line equation to find intersecting x,y co ordinates.

now the distance between (0,5) and (-1,4) will be the smallest distance and can be calculated by using distance formula

$$\sqrt{(x2-x1)^2 + (y2-y1)^2}$$ = $$\sqrt{2}$$
_________________
If this post helped you learn something pls give kudos
Manager  B
Joined: 18 Apr 2018
Posts: 94
Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

u1983, doomedcat I keep getting 1 as answer using method 1 stated by u1983. Pls what am I doing wrong? Or is the method wrong?
From the diagram posted by u1983 point (0,5) is on the x-axis instead of the y axis.. sorry I asking all these questions, this is because I am not an expert and just need clarification on whether the explanation is accurate. Thanks.
Posted from my mobile device
RC Moderator V
Joined: 24 Aug 2016
Posts: 804
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

Kem12 wrote:
u1983, doomedcat I keep getting 1 as answer using method 1 stated by u1983. Pls what am I doing wrong? Or is the method wrong?
From the diagram posted by u1983 point (0,5) is on the x-axis instead of the y axis.. sorry I asking all these questions, this is because I am not an expert and just need clarification on whether the explanation is accurate. Thanks.
Posted from my mobile device

Hi Kem12 ...please post the calculation you are doing. We will try to find the confusion point.
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Manager  B
Joined: 18 Apr 2018
Posts: 94
Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

u1983 (|0*1+5*1-3|)/(1^2+1^2) this equals 1.

Posted from my mobile device
RC Moderator V
Joined: 24 Aug 2016
Posts: 804
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16 Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

1
Kem12 wrote:
u1983 (|0*1+5*1-3|)/(1^2+1^2) this equals 1.

Posted from my mobile device

Hello Kem12 ...Thanks.

The mistake is at my end. I missed out on the sq root at the denominator while typing the soln. Sorry for taking things granted .
I have corrected it now.
SO, now following the formula you should get $$\sqrt{2}$$.
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Intern  B
Joined: 18 Nov 2018
Posts: 6
Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

1
Please the graph doesn’t make any sense.

When I graph I see 2 points between (0,5) and (0,3) and the perpendicular from (0,5) hits the line at x=-2, giving a 2,2,2root2 90degree triangle between 0,5 and 0,3(on the line).

Where am I wrong?

Or should I just memorize the formula and move on

Posted from my mobile device
Manager  B
Joined: 14 Feb 2016
Posts: 71
Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

1
u1983 wrote:
What is the smallest possible distance between the point (0, 5) and any point on the line y = -x + 3?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2

EG

Method 01 :

Distance from a pt (x,y) from line am+bn+c=0 is $$\frac{|ax+by+c|}{\sqrt{(a^2 +b^2)}}$$
Eqn: x+y-3=0 Hence Distance = $$\frac{|0*1 +5*1-3|}{\sqrt{(1^2 +1^2)}}$$ = $$\sqrt{2}$$

Or Alternatively , Method 02: Picture

I am a bit confused by your graph. If the coordinates are (0,5);(x1, y1). Then why is the coordinate (0,5) not posted on the y-axis?
_________________
Please provide kudos if you liked my post! I would really like to use the PDF file!!
Intern  B
Joined: 18 Nov 2018
Posts: 6
Re: What is the smallest possible distance between the point (0, 5) and an  [#permalink]

Show Tags

Please the graph doesn’t make any sense.

When I graph I see 2 points between (0,5) and (0,3) and the perpendicular from (0,5) hits the line at x=-2, giving a 2,2,2root2 90degree triangle between 0,5 and 0,3(on the line).

Where am I wrong?

Or should I just memorize the formula and move on

u1983 wrote:
What is the smallest possible distance between the point (0, 5) and any point on the line y = -x + 3?

A. 0
B. $$\frac{1}{\sqrt{2}}$$
C. 1
D. $$\sqrt{2}$$
E. 2

EG

Method 01 :

Distance from a pt (x,y) from line am+bn+c=0 is $$\frac{|ax+by+c|}{\sqrt{(a^2 +b^2)}}$$
Eqn: x+y-3=0 Hence Distance = $$\frac{|0*1 +5*1-3|}{\sqrt{(1^2 +1^2)}}$$ = $$\sqrt{2}$$

Or Alternatively , Method 02: Picture

Posted from my mobile device Re: What is the smallest possible distance between the point (0, 5) and an   [#permalink] 07 Jan 2019, 12:06
Display posts from previous: Sort by

What is the smallest possible distance between the point (0, 5) and an  