February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
Author 
Message 
TAGS:

Hide Tags

Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 88
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31 GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)

In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
10 Dec 2010, 10:03
Question Stats:
62% (01:42) correct 38% (01:44) wrong based on 418 sessions
HideShow timer Statistics
In the xyplane, a parabola intersects with axisy at point (0,y). Is y < 0 ? (1) The vertex of parabola is (2,5) (2) The parabola intersects with axisx at point (2,0) and (6,0)
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: #32 parabola intersts Y axis
[#permalink]
Show Tags
10 Dec 2010, 12:52
aalriy wrote: In the xyplane, a parabola intersects with axisy at point (0,y). Is y<0.
I. The vertex of parabola is (2,5) II. The parabola intersects with axisx at point (2,0) and (6,0) Though it's possible to solve this question algebraically the easiest way will be to visualize it and draw on a paper. (1) The vertex of parabola is (2,5) > the vertex is in the IV quadrant: if the parabola is downward it'll have negative yintercept, but if it's upward then it can have positive as well as negative yintercept. Not sufficient. (2) The parabola intersects with axisx at point (2,0) and (6,0) > now if the vertex is above xaxis then parabola will have positive yintercept and if its vertex is below xaxis it'll have negative yintercept. Not sufficient. (1)+(2) As from (1) the vertex is below xaxis then from (2) we'll have that parabola must have negative yintercept. Sufficient. You can look at the diagram below to see that a parabola passing through the given three points must have negative yintercept only. Attachment:
MSP139819db6ebe95a9e2a900005889a632a09g5628.gif [ 3.25 KiB  Viewed 9090 times ]
Answer: C. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 12 Jul 2011
Posts: 86
Concentration: Operations, Strategy
WE: Engineering (Telecommunications)

Re: #32 parabola intersts Y axis
[#permalink]
Show Tags
20 Oct 2011, 21:12
Thanks Bunuel for the explanation, I was thinking since option B gives us (2,0) and (6,0) vertices, with this we can assume that the parabola is directed upwards and it's Y intersect will be ve and hence sufficient, but after reading your explanation I understand it better 1+ Kudos to you.



Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
27 Jun 2013, 21:30



Intern
Joined: 08 Nov 2012
Posts: 5

Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
27 Oct 2013, 23:40
Hi Bunuel
What is wrong in the following approach
1) Insufficient The vertex of parabola is (2,5) > the vertex is in the IV quadrant: if the parabola is downward it'll have negative yintercept, but if it's upward then it can have positive as well as negative yintercept. Not sufficient
I was thinking from option 2 we can find the product of the roots and sum of the roots product of roots = c/a = 12
and sum of roots = b/a = 4
hence come up with an equation y = x^24x12
and from the question stem we have that it intercepts at 0,y
Putting x = 0 we get y = 12 (negative) and B alone is sufficient .



Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
28 Oct 2013, 00:13
sr2013 wrote: Hi Bunuel
What is wrong in the following approach
1) Insufficient The vertex of parabola is (2,5) > the vertex is in the IV quadrant: if the parabola is downward it'll have negative yintercept, but if it's upward then it can have positive as well as negative yintercept. Not sufficient
I was thinking from option 2 we can find the product of the roots and sum of the roots product of roots = c/a = 12
and sum of roots = b/a = 4
hence come up with an equation y = x^24x12
and from the question stem we have that it intercepts at 0,y
Putting x = 0 we get y = 12 (negative) and B alone is sufficient . How did you get y=x^24x12 from c/a=12 and b/a=4? You cannot solve c/a=12 and b/a=4 to get unique values of a, b, and c. For example if a=2, c=12, and b=4 you'll get 2x^224x8=0: Attachment:
MSP2141ga1ih773ii7e3di00002h2000h2fiibia6c.gif [ 3.51 KiB  Viewed 7619 times ]
If a=1, c=12, and b=4 you'll get x^2+4x+12=0: Attachment:
MSP24971d0ia65iig79i4gg000037eb4cg662i7adih.gif [ 3.44 KiB  Viewed 7622 times ]
Or in other words infinitely many parabolas have x intercepts at 2 and 6. You cannot get unique equation only from that info.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 11 Apr 2014
Posts: 9

Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
15 Oct 2014, 00:53
Bunuel wrote: sr2013 wrote: Hi Bunuel
What is wrong in the following approach
1) Insufficient The vertex of parabola is (2,5) > the vertex is in the IV quadrant: if the parabola is downward it'll have negative yintercept, but if it's upward then it can have positive as well as negative yintercept. Not sufficient
I was thinking from option 2 we can find the product of the roots and sum of the roots product of roots = c/a = 12
and sum of roots = b/a = 4
hence come up with an equation y = x^24x12
and from the question stem we have that it intercepts at 0,y
Putting x = 0 we get y = 12 (negative) and B alone is sufficient . How did you get y=x^24x12 from c/a=12 and b/a=4? You cannot solve c/a=12 and b/a=4 to get unique values of a, b, and c. For example if a=2, c=12, and b=4 you'll get 2x^224x8=0: Attachment: MSP2141ga1ih773ii7e3di00002h2000h2fiibia6c.gif If a=1, c=12, and b=4 you'll get x^2+4x+12=0: Attachment: MSP24971d0ia65iig79i4gg000037eb4cg662i7adih.gif Or in other words infinitely many parabolas have x intercepts at 2 and 6. You cannot get unique equation only from that info. Hi Bunuel I have tried solving it using standard expressions for parabola For parabola y= ax2+ bx+ c, standard vertex is located at point (\frac{b}{2a}, c\frac{b^2}{4a}). From a) we know the value of vertex as (2,5) by putting the value in standard vertex we can get c=4 it is also given in the question stem that parabola intersects y axis at (0,y) from this we can get the value of y as 4. which is sufficient to answer the question. Please let me know whats wrong with this approach.



Math Expert
Joined: 02 Sep 2009
Posts: 52906

In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
15 Oct 2014, 01:59
kd1989 wrote: Bunuel wrote: sr2013 wrote: Hi Bunuel
What is wrong in the following approach
1) Insufficient The vertex of parabola is (2,5) > the vertex is in the IV quadrant: if the parabola is downward it'll have negative yintercept, but if it's upward then it can have positive as well as negative yintercept. Not sufficient
I was thinking from option 2 we can find the product of the roots and sum of the roots product of roots = c/a = 12
and sum of roots = b/a = 4
hence come up with an equation y = x^24x12
and from the question stem we have that it intercepts at 0,y
Putting x = 0 we get y = 12 (negative) and B alone is sufficient . How did you get y=x^24x12 from c/a=12 and b/a=4? You cannot solve c/a=12 and b/a=4 to get unique values of a, b, and c. For example if a=2, c=12, and b=4 you'll get 2x^224x8=0: Attachment: MSP2141ga1ih773ii7e3di00002h2000h2fiibia6c.gif If a=1, c=12, and b=4 you'll get x^2+4x+12=0: Attachment: MSP24971d0ia65iig79i4gg000037eb4cg662i7adih.gif Or in other words infinitely many parabolas have x intercepts at 2 and 6. You cannot get unique equation only from that info. Hi Bunuel I have tried solving it using standard expressions for parabola For parabola y= ax2+ bx+ c, standard vertex is located at point (\frac{b}{2a}, c\frac{b^2}{4a}). From a) we know the value of vertex as (2,5) by putting the value in standard vertex we can get c=4 it is also given in the question stem that parabola intersects y axis at (0,y) from this we can get the value of y as 4. which is sufficient to answer the question. Please let me know whats wrong with this approach. The post you are quoting has an answer to your question. You cannot solve for c. P.S. Please read this: rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 (Writing Mathematical Formulas on the Forum)
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 22 Nov 2014
Posts: 60

In the xy plane,a parabola intersects with axisy at point (0,y).
[#permalink]
Show Tags
12 May 2016, 18:49
In the xy plane,a parabola intersects with axisy at point (0,y). is y<0?
1. The vertex of the parabola is (2,5) 2. The parabola intersects with axis X at point (2,0) and (6,0)



Math Expert
Joined: 02 Aug 2009
Posts: 7334

Re: In the xy plane,a parabola intersects with axisy at point (0,y).
[#permalink]
Show Tags
12 May 2016, 19:55
ruchi857 wrote: In the xy plane,a parabola intersects with axisy at point (0,y). is y<0?
1. The vertex of the parabola is (2,5) 2. The parabola intersects with axis X at point (2,0) and (6,0) A parabola has a vertex and a similar curve on both sides.. the vertex can be MIN or MAX value depending on the way parabola opens up...1. The vertex of the parabola is (2,5)we know vertex lies below the xaxis, but  a) if it opens upwards the intersect with yaxis can be either below xaxis or above it.. b) if it opens downwards the intersect with yaxis will be below xaxis .. Insuff 2. The parabola intersects with axis X at point (2,0) and (6,0)we know vertex would lie at (2+6)/2 = 2 as x, BUT we cannot determine if VERTEX is above or below xaxis.. whereever vertex lies, the intersect will lie on that point ..since the curve moves from 2 to 2 in that Quadrant  a) if it opens upwards the intersect with yaxis will be below x axis, as the vertex will be below xaxis.. b) if it opens downwards the intersect with yaxis will be above xaxis, as the vertex will be above xaxis .. combined statement I tells us that the vertex is below the xaxis and statement II tells us that if vertex is below x axis the intersect is also below xaxis.. so y<0.. Suff C
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Math Expert
Joined: 02 Sep 2009
Posts: 52906

Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
12 May 2016, 23:06



NonHuman User
Joined: 09 Sep 2013
Posts: 9838

Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
Show Tags
17 Oct 2018, 19:50
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In the xyplane, a parabola intersects with axisy at point
[#permalink]
17 Oct 2018, 19:50






