Last visit was: 19 Jun 2024, 14:21 It is currently 19 Jun 2024, 14:21
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
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93791
Own Kudos [?]: 633153 [17]
Given Kudos: 82365
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6811
Own Kudos [?]: 30589 [2]
Given Kudos: 799
Location: Canada
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6811
Own Kudos [?]: 30589 [1]
Given Kudos: 799
Location: Canada
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5232
Own Kudos [?]: 4072 [1]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: If x^2 + 4x + n > 13 for all x, then which of the following must be tr [#permalink]
1
Kudos
Bunuel wrote:
If \(x^2 + 4x + n > 13\) for all x, then which of the following must be true ?

A. n > 17
B. n = 20
C. n = 17
D. n < 11
E. n = 13


Are You Up For the Challenge: 700 Level Questions


\(x^2 + 4x + n > 13\)
\((x+2)^2 > 17-n\)
If n=17; x=-2
But if n>17; 17-n <0; (x+2)^2> 17-n for all values of x

IMO A
VP
VP
Joined: 10 Jul 2019
Posts: 1389
Own Kudos [?]: 561 [0]
Given Kudos: 1656
Send PM
Re: If x^2 + 4x + n > 13 for all x, then which of the following must be tr [#permalink]
Concept: the Graph of a Quadratic Expression will produce a Parabola in the coordinate plane in which the Input values (x) will produce corresponding Output values (y) such that the graph will be “U-shaped”

Step 1: change the quadratic expression into Vertex Form

(x)^2 + 4x + n > 13

(x)^2 + 4x + 4 - 4 + n > 13

(x + 2)^2 - 4 + n > 13

(x + 2)^2 - 17 + n > 0

step 2: analyze the Parabola

since the coefficient in front of the (x)^2 term is Positive, this will be an upwards opening parabola in which the Vertex will be the MINIMUM Point on the parabola.

Therefore, the minimum output value will be y = -17 at the coordinate point (-2 , -17)

In other words, the minimum output value from any corresponding X-input value will be ——-> -17

Therefore, to ensure that the output value is (+)positive, we need to Shift the Parabola upwards along the Y Axis

If we Add + 17 outside the square’s term, this will shift the parabola upwards such that the vertex will now fall on the X-axis. That means we can still get an output of 0

So to ensure that we always have an output of greater than > 0

We must shift the parabola up by a little more than 17 units

And to do that we need to insert a value into n that is greater than > 17

n > 17

Posted from my mobile device
GMAT Club Bot
Re: If x^2 + 4x + n > 13 for all x, then which of the following must be tr [#permalink]
Moderator:
Math Expert
93791 posts