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

 It is currently 02 Jun 2020, 08:00

### 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

# Is x^2 - 4/3*x + 5/12 < 0 ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64172
Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

18 Mar 2015, 04:10
1
9
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:09) correct 57% (02:24) wrong based on 134 sessions

### HideShow timer Statistics

Is x^2 - 4/3*x + 5/12 < 0 ?

(1) 0 <= x
(2) x is an integer

Kudos for a correct solution.

_________________
Manager
Joined: 14 Oct 2014
Posts: 63
Location: United States
GMAT 1: 500 Q36 V23
Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

Updated on: 18 Mar 2015, 16:44
1
(1) Not sufficient. If we take several values of x such as x=1/2, 1, and 0, we get two different answers to the question.
(2) Sufficient. If x = 1, then we get that 1^2-4/3*1+5/12 is positive, hence the answer to the question is no. If x=-1, then (-1)^2-4/3*(-1)+5/12 will also give a positive number and the answer no to the question.

Originally posted by viktorija on 18 Mar 2015, 15:31.
Last edited by viktorija on 18 Mar 2015, 16:44, edited 1 time in total.
Manager
Joined: 14 Sep 2014
Posts: 104
Concentration: Technology, Finance
WE: Analyst (Other)
Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

18 Mar 2015, 16:37
1
(Factoring the equation)
x^2 - 4/3*x + 5/12 < 0?
x^2 - 16/12*x + 5/12 < 0?
12x^2 - 16x + 5 < 0?
(6x - 5)*(2x - 1) < 0?

(1) If we use any positive or negative integer, the signs will be the same for (6x - 5) and (2x - 1) and the equation will be greater than zero. However, if we use x = 1/2, we get -2*0 = 0, so the statement is insufficient.

(2) As mentioned above, using any integer will leave the roots with the same sign, so the product will always be positive. This statement is sufficient.

Manager
Joined: 11 Sep 2013
Posts: 103
Re: Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

18 Mar 2015, 19:19
1
x^2 - 4/3*x + 5/12 < 0 => (X-1/2)(X-5/6)<0 => 1/2<X<5/6)
(1) 0 <= x => Dont know positive or negative
(2) x is an integer => surely it is positive with all the value of x
Senior Manager
Joined: 07 Aug 2011
Posts: 490
GMAT 1: 630 Q49 V27
Re: Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

20 Mar 2015, 05:31
1
Bunuel wrote:
Is x^2 - 4/3*x + 5/12 < 0 ?

(1) 0 <= x
(2) x is an integer

Kudos for a correct solution.

Solving x^2 - 4/3*x + 5/12 < 0
++++++1/2------5/6+++++++
1/2<X<5/6 , note that all the number in this range will be a fraction.

(1) 0 <= x Insufficient as X can be 0 in which case 5/12 is not less than 0. X can be 4/6 in which case x^2 - 4/3*x + 5/12 < 0.
(2) x is an integer . as X do not fall in the above range , the inequality will always yield a positive value.

Math Expert
Joined: 02 Sep 2009
Posts: 64172
Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

23 Mar 2015, 05:10
Bunuel wrote:
Is x^2 - 4/3*x + 5/12 < 0 ?

(1) 0 <= x
(2) x is an integer

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This is a very tricky fraction with quadratics. We know that the lead coefficient, the coefficient of x-squared, is positive, so this is an “upward-facing” parabola, curved side pointing down and “arms” going up.

We can compute that at x = 0, y = +5/12, a positive number. At x = 1, we get y = 1 - 4/3 + 5/12 = 1/12.

At both x = 0 and x = 1, the output is positive. If a = 1 is the coefficient of x-squared, and ( – 4/3) is the coefficient of x, then the line of symmetry of the parabola is given by x = -b/(2a) = (4/3)/2 = 2/3.

The vertex, the lowest point on the parabola, would be at that position. The y-value there would be: y = (2/3)^2 - 4/3*2/3 + 5/12 = 5/12 - 4/3.

We don’t need to continue the calculation any further. A number less than one minus a fraction greater than one will be negative. At x = 2/3, there is a vertex with negative y-value, but the parabola curves up, and by the time it gets to x = 0 or x = 1, it’s already positive and above the x-axis. OK, now we can look at the statements.

Statement #1: 0 ≤ x

Well, if x = 1, then we get a “no” answer, but if x = 2/3, then we get a “yes” answer. Two different answers to the prompt are possible. This statement, alone and by itself, is not sufficient.

Statement #2: x is an integer

This is interesting and subtle. We need to think about the shape of a parabola. This parabola is negative at x = 2/3 and the immediate vicinity, but by the time we get over to either adjacent integer, x = 0 or x = 1, the parabola is already positive.
Attachment:

ghdmpp_img15.png [ 8.49 KiB | Viewed 2375 times ]

Once a parabola is going up, it keeps going, so for any integer to the left of x = 0, or any integer to the right of x = 1, it also will be positive. It is positive for every integer value. That means, we can give a definitive answer of “no” to the prompt question. Because we were able to give a definitive answer, this statement, alone and by itself, is sufficient.

_________________
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Is x^2 - (4/3)x + (5/12) < 0?  [#permalink]

### Show Tags

25 Mar 2015, 09:52
Is $$x^2 - \frac{4}{3}x + \frac{5}{12} < 0$$?

Statement #1: $$0 \leq x$$
Statement #2: x is an integer

For a set of 14 challenging DS questions, including the OE to this particular question, see:
http://magoosh.com/gmat/2015/gmat-data- ... questions/

Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Senior Manager
Joined: 28 Feb 2014
Posts: 288
Location: United States
Concentration: Strategy, General Management
Is x^2 - (4/3)x + (5/12) < 0?  [#permalink]

### Show Tags

25 Mar 2015, 15:08
mikemcgarry wrote:
Is $$x^2 - \frac{4}{3}x + \frac{5}{12} < 0$$?

Statement #1: $$0 \leq x$$
Statement #2: x is an integer

For a set of 14 challenging DS questions, including the OE to this particular question, see:
http://magoosh.com/gmat/2015/gmat-data- ... questions/

Mike

I tested numbers to solve this one

Statement 1:
when x=1/2, 0<0 is false
when x=3/4, (-7/16)+(5/12) < 0 is true
Insufficient

Statement 2:
when x=1, $$x^2 - \frac{4}{3}x + \frac{5}{12} < 0$$ is false
Plugging more integers in for x, $$x^2 - \frac{4}{3}x + \frac{5}{12} < 0$$ seems to be false for all cases
Sufficient

Non-Human User
Joined: 09 Sep 2013
Posts: 15041
Re: Is x^2 - 4/3*x + 5/12 < 0 ?  [#permalink]

### Show Tags

19 May 2020, 16:00
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.
_________________
Re: Is x^2 - 4/3*x + 5/12 < 0 ?   [#permalink] 19 May 2020, 16:00