GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Aug 2020, 01:13

### 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

# For how many values of a greater than 0

Author Message
TAGS:

### Hide Tags

PS Forum Moderator
Joined: 18 Jan 2020
Posts: 1546
Location: India
GPA: 4
For how many values of a greater than 0  [#permalink]

### Show Tags

07 Jul 2020, 08:44
4
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:20) correct 30% (01:37) wrong based on 23 sessions

### HideShow timer Statistics

For how many values of a greater than 0 (A>0), both the roots of ax^2 - (a+1)x + (a-2) = 0, are greater than 3?

A. 1
B. 0
C. 4
D. 5
E. 2

Posted from my mobile device
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 2062
Location: India
Re: For how many values of a greater than 0  [#permalink]

### Show Tags

07 Jul 2020, 10:36
1
Since both roots are greater than 3, sum of roots must be greater than 6.

$$\frac{a+1}{a} >6$$

$$a<\frac{1}{5 }$$.......(1)

Also,

$$y= ax^2 - (a+1)x + (a-2$$) is an upward parabola, since a>0.
Attachment:

Untitled.png [ 5.33 KiB | Viewed 371 times ]

f(3) > 0, since both roots are greater than 3.

9a-3(a+1)+a-2 >0

$$a> \frac{5}{7}$$.......(2)

We can see that equation (1) and (2) both are contradictory. No such value of a is possible.

B

yashikaaggarwal wrote:
For how many values of a greater than 0 (A>0), both the roots of ax^2 - (a+1)x + (a-2) = 0, are greater than 3?

A. 1
B. 0
C. 4
D. 5
E. 2

Posted from my mobile device
Senior Manager
Status: Student
Joined: 14 Jul 2019
Posts: 453
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Re: For how many values of a greater than 0  [#permalink]

### Show Tags

07 Jul 2020, 11:26
1
yashikaaggarwal wrote:
For how many values of a greater than 0 (A>0), both the roots of ax^2 - (a+1)x + (a-2) = 0, are greater than 3?

A. 1
B. 0
C. 4
D. 5
E. 2

Posted from my mobile device

Product of the roots = (a-2)/a
Sum of the roots = - (a+1)/a
We have to find when, -a -1 / a > 6 or, -a -1 > 6a or, -1 > 6a, since a is greater than 1. there is no such value.
and (a-2)/a > 9 or, 9a< a-2, or, 8a < -2, no value of a is possible.

Manager
Joined: 15 Nov 2017
Posts: 245
Location: India
Concentration: Operations, Marketing
GPA: 4
WE: Operations (Retail)
Re: For how many values of a greater than 0  [#permalink]

### Show Tags

07 Jul 2020, 12:20
minustark wrote:
yashikaaggarwal wrote:
For how many values of a greater than 0 (A>0), both the roots of ax^2 - (a+1)x + (a-2) = 0, are greater than 3?

A. 1
B. 0
C. 4
D. 5
E. 2

Posted from my mobile device

Product of the roots = (a-2)/a
Sum of the roots = - (a+1)/a
We have to find when, -a -1 / a > 6 or, -a -1 > 6a or, -1 > 6a, since a is greater than 1. there is no such value.
and (a-2)/a > 9 or, 9a< a-2, or, 8a < -2, no value of a is possible.

Sum of the roots would be (a+1)/a
_________________
Manager
Joined: 05 Jan 2020
Posts: 142
Re: For how many values of a greater than 0  [#permalink]

### Show Tags

09 Jul 2020, 22:17
1
ax^2 - (a+1)x + (a-2) = 0 and both roots are greater than 3.

product of roots = c/a = (a-2)/a

Since each root is greater than 3, thus the product of the roots will be greater than 9.
=> (a-2)/a > 9
=> a-2 > 9a
=> a < -1/4

but a is greater than 0 (stated in question) => no such value of 'a' for which both roots are greater than 3.

Ans: B
Re: For how many values of a greater than 0   [#permalink] 09 Jul 2020, 22:17