If x is an integer, what is the value of x?

Question

Competition Mode Question

(1) (2x + 1)(x – 2) < 0
(2) x^2 < 2

gurmukh · Answer

From statement 1
x can be 0 or 1
Insufficient
From statement 2
x can be -1,0, 1
Insufficient
Combining also they are insufficient
Answer is E

Posted from my mobile device

yashikaaggarwal · Answer

IMO E,

(1) (2x + 1)(x – 2) < 0
=> X < -1/2 & 2
=> X < -1/2 (not sufficient, because values can vary till -infinity)

(2) x^2 < 2
=> ±X < √2
=> X<√2 & X>-√2
=> -√2<x<√2 ( not sufficient, since different values lies in between the given constraint)

1&2 : X>-1.4 and X<-0.5
(-1.4)-------x-------(-0.5)
There are still many values lies in between the constraint.

So answer is supposedly E

Posted from my mobile device

ArunSharma12 · Answer

If x is an integer, what is the value of x?

(1) (2x + 1)(x – 2) < 0
(2) x^2 < 2

statement 1: (2x + 1)(x – 2) < 0
case A:
2x + 1 < 0; x < -1/2: [-1,-2,-3,...]
x - 2 > 0; x > 2; [3,4,5...]
no value of x is possible

case B:
2x + 1 > 0; x > -1/2: [0,1,2,...]
x -2 < 0: x < 2 [1,0,-1...]
x can be [0,1]

statement 2:
x^2 - 2 < 0
-1.4 < x < 1.4
x can be [-1,0,1]

combining both statements,
x can be [0,1].
Ans: E

NitishJain · Answer

Nothing is given in qtn stem, lets jump to statements:

Statement (1):: (2x + 1)(x – 2) < 0 ==> -1/2 < x < 2 ==> x = 0 ,1; Not unique value, NOT SUfficient
Statement (2):: x^2 < 2 ==> (x^2 - 2) < 0 ==> -sqrt(2) < x < sqrt(2) ==> x = -1, 0, 1 Not unique value, NOT SUfficient

Lets combine both statements: x = 0,1 Not unique value, NOT SUfficient

E

firas92 · Answer

(1) (2x + 1)(x – 2) < 0

-1/2<x<2 so x can be 0 or 1

Not sufficient

(2) x^2 < 2

x can be -1, 0 or 1

Not sufficient

(1)+(2)

x can still be 0 or 1

Not sufficient

Answer is (E)

Posted from my mobile device

exc4libur · Answer

(1) insufic "<" means the range in-between (2x + 1)(x – 2) < 0 2x+1>0, x>-0.5 x-2<0, x<2 -0.5

freedom128 · Answer

Q. If x is an integer, what is the value of x?

(1) (2x + 1)(x – 2) < 0
-0.5 < x < 2 --> x= 0 or 1. We don't know which one.
NOT SUFFICIENT

(2) x^2 < 2
-1.4 < x < 1.4 --> x= -1, 0, or 1. We don't know which one.
NOT SUFFICIENT

(1)+(2)
Even we combine both statements, we can only deduce that x= 0 or 1. We don't know which one.
NOT SUFFICIENT

FINAL ANSWER IS (E)

Posted from my mobile device

MayankSingh · Answer

IMO E

If x is an integer, what is the value of x?

(1) (2x + 1)(x – 2) < 0
 -∞ ........+Ve........... (-1/2) ...... -Ve ........ (2)............. +Ve
so, -1/2 < x < 2
x= { 0, 1 }
Not sufficient

(2) x^2 < 2
-√2 < x < √2
x= { 0, 1 }
Not sufficient

Together, x= { 0, 1 }
Not sufficient

HoneyLemon · Answer

Ans Should be E.

If x is an integer, what is the value of x?

St (1): 
 (2x + 1)(x – 2) < 0

Either   or

so -0.5 < x < 2 i.e X could be 0 or 1 . Since we don't have an conclusive ans . Its st 1 is insuffi.

St (2):
 x^2 < 2

-1.41 < x < 1.41 .

again x can be 0 or 1 . Again we don't have an conclusive ans . Its st 2 is insuffi.

By Combining st 1 and 2 also it's insuffi.. ,since x can be 0 or 1 . 
So ans is E , IMO .

minustark · Answer

If x is an integer, what is the value of x?

(1) (2x + 1)(x – 2) < 0
(2) x^2 < 2

1) when 2x + 1 < 0, x < -1/2 (x can be -1, -2...as its an integer), but in that case (x -2) will also be negative, so x has to be either 0 or positive. Again, when x -2 < 0 or, x < 2, both 0 and 1 will satisfy the condition. not sufficient
2) x^2 < 2, |x| < 1.41. not sufficient
Together, x can be either 0 or 1. Not sufficient
E is the answer

ApoorvaChouhan7 · Answer

I choose E.

Statement 1: 
Intersection for (2x+1) to be positive and (x-2) to be negative is -1< x < 2. Giving possible integers 0,1

Not Suff.

Statement 2

X can take -1,0,1
Not suff.

Combining the two still leaves us with 1,0 
Not suff.

Hence, E.

Posted from my mobile device

debjit1990 · Answer

Ans: E
x=int
1)(2x + 1)(x – 2) < 0
-1/2<x<2..so X can be 0 and 1..not sufficient
2)x^2 < 2 
-root2<x<root2..so x can be -1,0,1..not sufficient
combine..both 0 and 1 are possible..not sufficient

Bunuel · Answer

If x is an integer, what is the value of x?

(1) (2x + 1)(x – 2) < 0
(2) x^2 < 2

statement 1: (2x + 1)(x – 2) < 0
case A:
2x + 1 < 0; x < -1/2: [-1,-2,-3,...]
x - 2 > 0; x > 2; [3,4,5...]
no value of x is possible

case B:
2x + 1 > 0; x > -1/2: [0,1,2,...]
x -2 < 0: x < 2 [1,0,-1...]
x can be [0,1]

statement 2:
x^2 - 2 < 0
-1.4 < x < 1.4
x can be [-1,0,1]

combining both statements,
x can be [0,1].
Ans: E

If x is an integer, what is the value of x?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If x is an integer, what is the value of x?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards