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

 It is currently 11 Dec 2019, 22:19

### 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

# The above equations define how the function f varies with x. Is –0.9 <

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4587
GPA: 3.39
The above equations define how the function f varies with x. Is –0.9 <  [#permalink]

### Show Tags

04 Oct 2019, 07:08
9
00:00

Difficulty:

95% (hard)

Question Stats:

9% (02:13) correct 91% (02:32) wrong based on 54 sessions

### HideShow timer Statistics

$$f(x) = x^2$$ for $$|x| ≤ 1$$

$$f(x) = \frac{1}{x^2}$$ for $$x > 1$$

The above equations define how the function f varies with $$x.$$ Is $$–0.9 < a < 0.9$$?

(1) $$f(–a) = \frac{1}{f(b)}$$

(2) $$a = \frac{1}{b}$$

Source: Nova GMAT

_________________
Intern
Joined: 01 Jul 2019
Posts: 3
Re: The above equations define how the function f varies with x. Is –0.9 <  [#permalink]

### Show Tags

02 Dec 2019, 08:28
1
-0.9<a<0.9 means that f(a)= X^2

1. f(-a)=1/f(b)
suppose b is postive that is Greater than 1
Therefore , f(b)= 1/x^2 and
1/f(b) = x^2.
But f(-a)= x^2 since a is negative .So it has to 1/x^2.
Hence f(-a)= 1/f(b) where b more than 1 and a is between -0.9<a<0.9. Only then statement 1 holds true.

Stat 2 - Insuff .

IMO - A

VP
Joined: 19 Oct 2018
Posts: 1171
Location: India
The above equations define how the function f varies with x. Is –0.9 <  [#permalink]

### Show Tags

02 Dec 2019, 11:20
2
f(x)= x^2 for x ≤ 1
$$f(x) = \frac{1}{x^2}$$ for $$x > 1$$

Range of f(x)- [0, 1]
Range of 1/f(x)- [1, infinity)

Statement 1-
$$f(–a) = \frac{1}{f(b)}$$

As value of LHS is between 0 and 1( both inclusive) and value of RHS is equal to or greater than 1, LHS is equal to RHS if and only both are equal to 1.

f(-a)=1, if a=1 or -1.

Hence, a can never lies in range (-0.9, 0.9)

Sufficient

Statement 2- a*b=1

Case 1- a=2 and b=1/2

Case 2- a=1/2 and b=2

Insufficient

$$f(x) = x^2$$ for $$|x| ≤ 1$$

$$f(x) = \frac{1}{x^2}$$ for $$x > 1$$

The above equations define how the function f varies with $$x.$$ Is $$–0.9 < a < 0.9$$?

(1) $$f(–a) = \frac{1}{f(b)}$$

(2) $$a = \frac{1}{b}$$

Source: Nova GMAT
GMAT Tutor
Joined: 17 Sep 2014
Posts: 290
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
The above equations define how the function f varies with x. Is –0.9 <  [#permalink]

### Show Tags

05 Dec 2019, 07:24
2
$$f(x) = x^2$$ for $$|x| ≤ 1$$

$$f(x) = \frac{1}{x^2}$$ for $$x > 1$$

The above equations define how the function f varies with $$x.$$ Is $$–0.9 < a < 0.9$$?

(1) $$f(–a) = \frac{1}{f(b)}$$

(2) $$a = \frac{1}{b}$$

Source: Nova GMAT

Analyzing the question:
One thing to note is that the highest value of the function is 1. For x between -1 and 1 the function value is at it's lowest for x = 0 and highest at |x| = 1. After we go into the x > 1 range the function value starts dropping as $$1/x^2$$ is decreasing with x. Hence we are UNABLE to determine where x is according to the value of f(x). There are 3 such values for f(x) = 0.5 for example, two of them within -1 < x < 1 and another with x > 1.

Statement 1:
We noted earlier that the maximum value of this function is 1, so the left side f(-a) must be at most 1. The right side has 1 / f(b), which must exceed 1 unless f(b) = 1. So we must have f(b) = f(-a) = 1. Also note f(-a) = f(a) since the function always squares the input. So f(a) = f(b) = 1. This can only happen when the input is either -1 or 1. Since $$a$$ cannot be in range of -0.9 to 0.9, this is sufficient.

Statment 2:
Insufficient.

Ans: A
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
The above equations define how the function f varies with x. Is –0.9 <   [#permalink] 05 Dec 2019, 07:24
Display posts from previous: Sort by