It is currently 26 Jan 2022, 03:21 |

Customized

for You

Track

Your Progress

Practice

Pays

- Jan
**28**### GRE Success with ScholarDen

08:00 PM PST

-10:00 PM PST

Read about this users success story with ScholarDen. They helped make his GRE Prep Journey easier. Hear from past users and their GRE Prep Journey's - Jan
**31**### How Do the Best GRE Tutors Help You Improve Your GRE Score?

06:00 PM PST

-07:00 PM PST

If you want to improve your GRE score, you have many options at your disposal. You can self-study using free or extremely low-cost GRE prep materials from ETS, invest in a slightly more expensive self-paced GRE course, and more. - Jan
**31**### Decoding the HBS Interview presented by mbaMission

08:00 PM EST

-09:00 PM EST

Join mbaMission for this workshop Thursday, January 31st at 8 PM ET | 5 PM PT. - Feb
**07**### TTP helped Brian score 338 on the GRE

07:00 PM PST

-09:00 PM PST

Studying for the GRE is no easy task, especially while serving in the military, but with the help of TTP, Brian scored an impressive 338 on his GRE. See for yourself why we’re changing the way students study for the GRE with a 5-day trial for just $1.

The function f is defined for all numbers x by f (x) = x2 +
[#permalink]
17 Feb 2017, 06:48

Expert Reply

2

Bookmarks

Question Stats:

The function \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\). If t is a number such that \(f(2t) = 30\), which two of the following could be the number \(t\) ?

Indicate two such numbers.

❑ \(- 5\)

❑ \(- 3\)

❑ \(-\frac{1}{2}\)

❑ \(2\)

❑ \(\frac{5}{2}\)

_________________

GRE Prep Club OFFICIAL Android App

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4804**

WE:**Business Development (Energy and Utilities)**

Re: The function f is defined for all numbers x by f (x) = x2 +
[#permalink]
27 Feb 2017, 16:00

2

Expert Reply

Explanation

Here we have the expression \(f(x)= x^2 + x\). This can be rewritten as \(f(x)= x(x+1)\). Now putting x = 2t in the expression we can rewrite the expression as:

\(f(2t)=2t(2t+1)\).

Our best strategy for this question is to put the option values and check if \(f(2t) = 30\).

❑ —5........... \(f(2*-5)= -10(-10+1) = -90\) NO

❑ —3........... \(f(2*-3)= -6(-6+1) = 30\) YES

❑ \(\frac{1}{2}\).......... \(f(2*\frac{1}{2})= 1(1+1) = 2\) No

❑ 2...........\(f(2*2)= 4(4+1) = 20\) NO

❑ \(\frac{5}{2}\).......... \(f(2*\frac{5}{2})= 5(5+1) = 30\) YES

Hence B and E are correct options.

_________________

Here we have the expression \(f(x)= x^2 + x\). This can be rewritten as \(f(x)= x(x+1)\). Now putting x = 2t in the expression we can rewrite the expression as:

\(f(2t)=2t(2t+1)\).

Our best strategy for this question is to put the option values and check if \(f(2t) = 30\).

❑ —5........... \(f(2*-5)= -10(-10+1) = -90\) NO

❑ —3........... \(f(2*-3)= -6(-6+1) = 30\) YES

❑ \(\frac{1}{2}\).......... \(f(2*\frac{1}{2})= 1(1+1) = 2\) No

❑ 2...........\(f(2*2)= 4(4+1) = 20\) NO

❑ \(\frac{5}{2}\).......... \(f(2*\frac{5}{2})= 5(5+1) = 30\) YES

Hence B and E are correct options.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: The function f is defined for all numbers x by f (x) = x2 +
[#permalink]
24 Mar 2017, 15:04

3

Expert Reply

Carcass wrote:

The function f is defined for all numbers x by f (x) = x² + x. If t is a number such that f (2t) = 30, which two of the following could be the number t ?

Indicate two such numbers.

❑ —5

❑ —3

❑ \(\frac{1}{2}\)

❑ 2

❑ \(\frac{5}{2}\)

Show: :: OA

B and D

If f(x) = x² + x, then f(2t) = (2t)² + 2t

Since f(2t) = 30, we know that: (2t)² + 2t = 30

Simplify: 4t² + 2t = 30

Subtract 30 from both sides: 4t² + 2t - 30 = 0

Divide both sides by 2 to get: 2t² + t - 15 = 0

Factor to get: (2t - 5)(t + 3) = 0

So, EITHER 2t - 5 = 0 OR t + 3 = 0

If 2t - 5 = 0, then t = 5/2

If t + 3 = 0, then t = -3

Answer:

Show: ::

B and E

_________________

Moderator

Joined: **02 Jan 2020 **

Status:**GRE Quant Tutor**

Posts: **431**

Location: **India**

Concentration: **General Management**

Schools: **XLRI Jamshedpur, India - Class of 2014**

GMAT 1: **700 Q51 V31**

GPA: **2.8**

WE:**Engineering (Computer Software)**

Re: The function f is defined for all numbers x by f (x) = x2 +
[#permalink]
15 Dec 2021, 08:47

Given that \(f\) is defined for all numbers \(x\) by \(f(x) = x^2 + x\) and t is a number such that \(f(2t) = 30\). And we need to find values of t

Let's start by finding the value of f(2t)

To find f(2t) we need to substitute x = 2t in \(f(x) = x^2 + x\)

=> f(2t) = \((2t)^2 + 2t\) = \(4t^2 + 2t\) = 30 (given)

=> \(4t^2 + 2t - 30 = 0\)

Divide both the sides by 2 we get

=> \(2t^2 + t - 15 = 0\)

=> \(2t^2 + 6t - 5t - 15 = 0\)

=> \(2t(t + 3 ) - 5(t + 3) = 0\)

=> (t + 3) * (2t - 5) = 0

=> t = -3 or t = \(\frac{5}{2}\)

So, Answer will be B and E

Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

_________________

Let's start by finding the value of f(2t)

To find f(2t) we need to substitute x = 2t in \(f(x) = x^2 + x\)

=> f(2t) = \((2t)^2 + 2t\) = \(4t^2 + 2t\) = 30 (given)

=> \(4t^2 + 2t - 30 = 0\)

Divide both the sides by 2 we get

=> \(2t^2 + t - 15 = 0\)

=> \(2t^2 + 6t - 5t - 15 = 0\)

=> \(2t(t + 3 ) - 5(t + 3) = 0\)

=> (t + 3) * (2t - 5) = 0

=> t = -3 or t = \(\frac{5}{2}\)

So, Answer will be B and E

Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

_________________

Ankit

to My YouTube Channel to get Your Regular Math Doze!!!

How to Solve :

Circles || Equilateral Triangle in a Circle || Arithmetic and Geometric Progression || Divisibility Rules || Absolute Value || Inequalities || Statistics || Functions and Custom Characters || Remainders || LCM and GCD || Stem & Leaf Plot || Box And Whisker Plot

GRE Club Topic Wise Problems

GRE Quant - 2019 Ed

GRE Verbal - 2019 Ed

The Princeton Review Quantitative Directory

The 5 lb. Book of GRE Practice Problems (2nd Ed.) - QUANT

GRE - PowerPrep® The FREE Practice Tests Explained 2019

to My YouTube Channel to get Your Regular Math Doze!!!

How to Solve :

Circles || Equilateral Triangle in a Circle || Arithmetic and Geometric Progression || Divisibility Rules || Absolute Value || Inequalities || Statistics || Functions and Custom Characters || Remainders || LCM and GCD || Stem & Leaf Plot || Box And Whisker Plot

GRE Club Topic Wise Problems

GRE Quant - 2019 Ed

GRE Verbal - 2019 Ed

The Princeton Review Quantitative Directory

The 5 lb. Book of GRE Practice Problems (2nd Ed.) - QUANT

GRE - PowerPrep® The FREE Practice Tests Explained 2019

gmatclubot

Moderators:

Multiple-choice Questions — Select One or More Answer Choices |
||