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

It is currently 06 Dec 2019, 03:02

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

The height of a model rocket in feet, x, t seconds after its launch is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59568
The height of a model rocket in feet, x, t seconds after its launch is  [#permalink]

Show Tags

New post 28 Nov 2019, 00:42
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:33) correct 44% (01:48) wrong based on 26 sessions

HideShow timer Statistics

The height of a model rocket in feet, x, t seconds after its launch is modeled by the equation \(x=-t^2+bt+a\), where a and b are positive integers. At what value of t does the rocket reach its maximum height?

(1) \(b=10\)

(2) \(a=125\)


Are You Up For the Challenge: 700 Level Questions
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: The height of a model rocket in feet, x, t seconds after its launch is  [#permalink]

Show Tags

New post 28 Nov 2019, 03:14
\(x=-t^2+bt+a\)
\(x=-t(t+b)+a\)

#1\(b=10\)
a is not know insufficient
#2
at t=0
we get height = 125
IMO B

Bunuel wrote:
The height of a model rocket in feet, x, t seconds after its launch is modeled by the equation \(x=-t^2+bt+a\), where a and b are positive integers. At what value of t does the rocket reach its maximum height?

(1) \(b=10\)

(2) \(a=125\)


Are You Up For the Challenge: 700 Level Questions
Director
Director
avatar
P
Joined: 18 May 2019
Posts: 524
GMAT ToolKit User Premium Member CAT Tests
Re: The height of a model rocket in feet, x, t seconds after its launch is  [#permalink]

Show Tags

New post 28 Nov 2019, 05:56
1
Given x=-t^2+bt+a
we are to determine at which time, t, x is maximum.

Given a function f(t)=mx^2+nx+k
the maximum/minimum value occurs at t=-n/ma
when m<0, then we have a maximum function and when m>0, then we have a minimum function.
From the given function x=-t^2+bt+a,
m=-1; n=b
we know that x has a maximum function since m=-1.
All we need in order to determine the time,t, at which the maximum function occurs is b. because t=-b/(2*-1) = b/2

Statement 1: b=10
This sufficient since we can determine the time that x is maximum occurs is =10/2 = 5.

Statement 2: a=125
This is insufficient since we don't b, which is necessary to determine the time, t, at which x is maximum.

The answer therefore option A.

Alternatively, you can use calculus to solve this question easily.
x=-t^2+bt+a
differentiating x with respect to t yields dx/dt=-2t+b
The function x is maximum when dx/dt=0
therefore -2t+b=0
t=b/2
from this we know we only need b in order to determine the time at which x is maximum.

Statement 1: b=10
so we can determine t=10/2=5
statement 1 is therefore sufficient.

Statement 2: a=125
Not sufficient, since we don't need a to determine the time at which x is maximum. We need b and we don't b.

The answer is therefore A.
GMAT Club Bot
Re: The height of a model rocket in feet, x, t seconds after its launch is   [#permalink] 28 Nov 2019, 05:56
Display posts from previous: Sort by

The height of a model rocket in feet, x, t seconds after its launch is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne