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

 It is currently 14 Nov 2019, 04:45

### 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 the value of x less than 0? (1) The product of x and y is negative

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59034
Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

17 Oct 2019, 21:19
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:28) correct 45% (01:19) wrong based on 44 sessions

### HideShow timer Statistics

Competition Mode Question

Is the value of x less than 0?

(1) The product of x and y is negative.
(2) The difference between x and its reciprocal is positive.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8161
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

17 Oct 2019, 21:27
1
Is the value of x less than 0?

Is x<0?

(1) The product of x and y is negative.
xy is negative. So one of x or y is negative and other positive.
If y>0, x<0, but if y<0, x>0.

(2) The difference between x and its reciprocal is positive.
$$x-\frac{1}{x}>0...\frac{x^2-1}{x}>0$$
If $$x>0..x^2-1>0..x>1$$....$$x=2....2-\frac{1}{2}=\frac{3}{2}$$....x>0
If $$x<0..x^2-1<0....x<0$$...$$x=-\frac{1}{2}...-\frac{1}{2}-(-2)=\frac{3}{2}$$....x<0

Combined..
x<0 or x>1
Insuff

E
_________________
Retired Moderator
Joined: 27 Oct 2017
Posts: 1272
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

17 Oct 2019, 21:41
1
Is the value of x less than 0?

(1) The product of x and y is negative.

it means x and y are of opposite sign. but since no other info is given, it is NOT SUFFICIENT.

(2) The difference between x and its reciprocal is positive.

The difference between any 2 numbers is always non-negative.
It is zero if the numbers are equal. Otherwise always positive.

The difference between two numbers is defined as the distance between the two numbers on the number line.

Statement 2 states that the x is not equal to 1/x or x is not equal to 1 or -1.
No other info, hence NOT SUFFICIENT.

Even after combining 2 statements, we are unable to conclude anything.
Hence it is E
_________________
Senior Manager
Joined: 18 May 2019
Posts: 440
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

17 Oct 2019, 21:51
1
We are to determine if x is less than 0.

Statement 1: xy<0
Clearly insufficient. This is because x can be either positive or negative depending on whether y is positive or negative. When y is positive, x is negative, and when y is negative, x is positive. The answer is, therefore, yes and no.

Statement 2: The difference between x and it's reciprocal is positive.
Statement 2 is not sufficient. This is because x can be 51, implying its reciprocal is 15. 51-15=36, leading to answer No to the question posed. X can also be -15, and its reciprocal is -51. -15--51=36 satisfying the given condition and this now leads to the answer Yes to the question posed.

1+2
Still insufficient. Both statements do not restrict the value of x to less than 0, equal to 0, or greater than 0. When y is negative, x=51 satisfies statement 1 and statement 2, and leads to the answer No to the question asked.
On the other hand, when y>0 x can equal -15, which satisfies both statements and leads to the answer Yes.

The right answer in my view is E.
Senior Manager
Joined: 01 Mar 2019
Posts: 264
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

Updated on: 19 Oct 2019, 02:11
1
(1) The product of x and y is negative.....Clearly insufff.....Either of x,y can be +ve,-ve
(2) The difference between x and its reciprocal is positive.....x-1/x can be positive if x is positive(1,2...) also for x=-1/2,-4/3....So instuff

OA:E

Posted from my mobile device

Originally posted by madgmat2019 on 17 Oct 2019, 21:57.
Last edited by madgmat2019 on 19 Oct 2019, 02:11, edited 1 time in total.
VP
Joined: 20 Jul 2017
Posts: 1061
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

17 Oct 2019, 23:06
1
(1) The product of x and y is negative.
--> x & y have opposite signs (If x > 0, y < 0 or of x <0, y > 0) --> Insufficient

(2) The difference between x and its reciprocal is positive.
--> x - 1/x > 0
--> (x^2 - 1)/x > 0

Formula: If A/B > 0 --> Either both A>0 & B>0 or both A<0 & B<0
Similarly, if (x^2 - 1)/x > 0

Case 1: x^2 - 1 > 0 & x > 0
--> x > 1 (x is positive)

Case 2: x^2 - 1 < 0 & x < 0
--> -1 < x < 0 (x is negative)
--> Insufficient

Combining (1) & (2),

Also, x can be either positive or negative --> Insufficient

IMO Option E
Senior Manager
Joined: 07 Mar 2019
Posts: 378
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

17 Oct 2019, 23:20
Is the value of x less than 0?
x < 0 ?

(1) The product of x and y is negative.
$$x.y < 0$$
(+).(-), x < 0 NO
OR
(-).(+), x < 0 YES

INSUFFICIENT.

(2) The difference between x and its reciprocal is positive
$$x - \frac{1}{x}$$ > 0
It's possible only when x > 0 since x < 0 results in a negative difference.

Let x = 2 then $$2 - \frac{1}{2} = \frac{3}{2}$$ > 0
x = -2 then $$-2 - \frac{1}{(-2)} = \frac{-3}{2}$$ < 0
Hence x has to be positive. x < 0 NO

SUFFICIENT.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager
Joined: 05 Aug 2018
Posts: 72
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 01:09
1
Is the value of x less than 0?

Is x < 0?

(1) The product of x and y is negative.
xy < 0
x < 0 or y < 0
insufficient

(2) The difference between x and its reciprocal is positive.

x - 1/x > 0
x2 -1 > 0
(x+1)(x-1) >0
x< -1 or x> 1 - we get that x can be both positive or negative

insufficient

taken (1) + (2) together, x can still be both positive and negative - insufficient
Thus, E is the correct answer
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 01:18
1
#1
The product of x and y is negative.
either of x&y is -ve insufficient
#2

The difference between x and its reciprocal is positive.
x=2 ; reciprocal 1/2
∆ ; 2-1/2 ; 3/2
x=-1/2 ; reciprocal ; -2
∆ -1/2+2 ; 3/2
insufficient
from 1 &2
nothing conclusive
IMO E

Is the value of x less than 0?

(1) The product of x and y is negative.
(2) The difference between x and its reciprocal is positive.
Senior Manager
Joined: 10 Apr 2018
Posts: 279
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34
GPA: 3.3
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 02:14
1
Quote:
Is the value of x less than 0?

(1) The product of x and y is negative.
(2) The difference between x and its reciprocal is positive.

We have to find whether or not x<0.

(1) xy<0
=> Either of x and y is negative and the other is positive.
So, we do not have sufficient information to find out whether or not x<0.
Thus, insufficient.

(2) x-$$\frac{1}{x}$$<0
=> $$\frac{(x^2-1)}{x}$$<0
=> x>1 or -1<x<0
So, x can be positive or negative.
Thus, insufficient.

From (1) and (2) together, we do not have sufficient information to find out whether or not x<0.
Thus, insufficient.

Therefore, the correct answer is option E.
SVP
Joined: 03 Jun 2019
Posts: 1838
Location: India
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 02:22
1
Asked: Is the value of x less than 0?

(1) The product of x and y is negative.
xy < 0
x<0;y>0 or y<0;x>0
NOT SUFFICIENT

(2) The difference between x and its reciprocal is positive.
x - 1/x > 0
(x^2 - 1)/x > 0
(x-1)(x+1)/x >0
x> 1 or -1<x<0
NOT SUFFICIENT

(1) + (2)
(1) The product of x and y is negative.
xy < 0
x<0;y>0 or y<0;x>0
(2) The difference between x and its reciprocal is positive.
x - 1/x > 0
(x^2 - 1)/x > 0
(x-1)(x+1)/x >0
x> 1 or -1<x<0
x may or may not be <0
NOT SUFFICIENT

IMO E
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Manager
Joined: 22 Feb 2018
Posts: 207
Location: India
Concentration: Entrepreneurship, Healthcare
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 03:53
1
Imo. E

Is the value of x less than 0?
Is x = -ve?

(1) The product of x and y is negative.
xy<0, x can or can not be -ve. Insufficient.

(2) The difference between x and its reciprocal is positive.
x-1/x = +ve
x can be 2 or -1/2, So x can be or can not be -ve. Insufficient.

1 + 2)
X can be or can not be -ve. Insufficient.
Manager
Joined: 07 Apr 2018
Posts: 101
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 05:27
1
Q : x<0 ?
Q type: Y/N

a) xy<0 => x and y have opposite signs. Either of them can be negative. Insufficient

b) The difference between x and its reciprocal is positive. => (x - 1/x) > 0 => (x^2 -1) > 0
or, x^2 >1
x can be positive or negative. (e.g. If x^2 =4, the x can have two values +2 or -2) Insufficient

a) + b) = x can be positive or negative.

Director
Joined: 24 Nov 2016
Posts: 762
Location: United States
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 06:43
1
Quote:
Is the value of x less than 0?

(1) The product of x and y is negative.
(2) The difference between x and its reciprocal is positive.

(1) The product of x and y is negative. insufic.

$$xy<0:[x>0,y<0]…or…[x<0,y>0]$$

(2) The difference between x and its reciprocal is positive. insufic.

$$x-\frac{1}{x}>0…\frac{x^2-1}{x}>0…\frac{(x-1)(x+1}{x}>0…[x<-1,x>1]$$

(1 & 2): insufic.

Senior Manager
Joined: 25 Jul 2018
Posts: 338
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 13:27
1
x< 0 ???

(Statement1): x*y< 0
—> either x or y could be positive or negative to get this inequality correct.
Insufficient

(Statement2): $$x—\frac{1}{x}$$>0

$$\frac{(x^{2}—1)}{x}$$>0

$$\frac{(x+1)(x—1)}{x}$$> 0
—> —1<x <0 and x>1
Clearly insufficient

Taken together 1&2,
—> it depends on statement1
If x< 0, then Yes
If x>0, then No

Insufficient

Posted from my mobile device
Manager
Joined: 17 Jan 2019
Posts: 127
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 21:49
1
Is the value of x less than 0?

is X negative?

(1) The product of x and y is negative.
meaning either x or y is negative.
we don't know which one.
Therefore, insuffucient

(2) The difference between x and its reciprocal is positive.
x- (1/x) is positive
(1/x)-x is positive
there is no such number that will give those both statement true
insufficient

together, we know y doesn't give anything and with those statement in b doesn't add any value.

Therefore, E
Intern
Joined: 05 Oct 2019
Posts: 3
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 22:47
1. xy<0 means either x or y is negetive. so it is not enough

2. the reciprocal of x is 1/x
so x-1/x is positive. here this is positive result as x is larger then 1/x. but if the value of x is negetive then the result will be negetive. so this is also wrong

Posted from my mobile device
Manager
Joined: 19 Jan 2019
Posts: 110
Re: Is the value of x less than 0? (1) The product of x and y is negative  [#permalink]

### Show Tags

18 Oct 2019, 23:11
The trap here is to blindly assume value of X to be an integer.

Statement 1 is clearly not sufficient as X can be greater than 0 or less than 0. Not sufficient.

Statement 2-.. tricky part.

Let's see , X -1/X >0
(X^2-1)/X > 0, at first one might think for this expression to be true, X has to be positive.. and if one thinks that way, he/she has made a wrong assumption of X to be a positive integer..

Take X = 4
(16-1)/4 > 0, I get a no
Take X = -0.5
(0.25-1)/-0.5 > 0, but X is less than 0 and I get a yes . This statement is not sufficient as well .

Combining both statements is of no use because X can be positive or X can be negative.. eliminate C and E is the right answer..

Posted from my mobile device
Re: Is the value of x less than 0? (1) The product of x and y is negative   [#permalink] 18 Oct 2019, 23:11
Display posts from previous: Sort by