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

 It is currently 18 Oct 2019, 22:06

### 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

# Suppose a and b are single-digit positive integers chosen independentl

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
Suppose a and b are single-digit positive integers chosen independentl  [#permalink]

### Show Tags

31 Mar 2019, 22:12
00:00

Difficulty:

85% (hard)

Question Stats:

22% (01:32) correct 78% (02:37) wrong based on 36 sessions

### HideShow timer Statistics

Suppose a and b are single-digit positive integers chosen independently and at random. What is the probability that the point (a, b) lies above the parabola y = ax^2 - bx ?

A. 11/81
B. 13/81
C. 5/27
D. 17/81
E. 19/81

_________________
Manager
Joined: 01 Feb 2017
Posts: 242
Re: Suppose a and b are single-digit positive integers chosen independentl  [#permalink]

### Show Tags

14 Apr 2019, 04:28
4
Total possible values for each a and b, from 1 to 9= 9*9 = 81

As a is a positive integer, parabola is curving upwards.
Any point that lies above the parabola must satisfy inequality: y>ax^2 - bx
Now, as all such points have coordinates (a,b), inequality becomes: b>a*a^2 - b*a i.e b>a^3 - ab
Rewriting inequality: b > a^3/(a+1)

for a=1, b>1/2 : possible values of b=1 to 9
for a=2, b>8/3 : possible values of b=3 to 9
for a=3, b>27/4 : possible values of b=7 to 9
for a=4, b>64/5 : not possible, as max b cannot exceed 9
so, a cannot have values above 3

total possible coordinates: (1,1-9) + (2,3-9) + (3,7-9) = 9+7+3 = 19

Probability= 19/81
Ans E
Re: Suppose a and b are single-digit positive integers chosen independentl   [#permalink] 14 Apr 2019, 04:28
Display posts from previous: Sort by