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# Is 3 >= X >=2? A. (X-3)*(X-2)*(X-1) > 0 B. X > 1

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Director
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Is 3 >= X >=2? A. (X-3)*(X-2)*(X-1) > 0 B. X > 1 [#permalink]

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06 Apr 2007, 18:08
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Is 3 >= X >=2?

A. (X-3)*(X-2)*(X-1) > 0
B. X > 1
Director
Joined: 14 Jan 2007
Posts: 775
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06 Apr 2007, 19:36

Stmt 1: (X-3)*(X-2)*(X-1) > 0
for (X-3)*(X-2)*(X-1) to be +ve , there will be following possibilities-
X-3, X-2, X-1
+ + + ===> X>3
- - + ====> X<2
- + - ====> X<1
+ - - ====> X<1

X does not lie between 2 and 3 inclusive. Hence SUFF

Stmt2: X >1
X may or may not be in range of 2 to 3.
Hence INSUFF
GMAT Club Legend
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Location: Singapore
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06 Apr 2007, 20:14
Is x between 2 and 3?

St1:
If x is positive, it has to be greater than 3. So it's not between 2 and 3. Sufficient.

St2:
x>1 can be any value greater than 1. Insufficient.

Ans A
Senior Manager
Joined: 20 Feb 2007
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06 Apr 2007, 23:30
One more A

The question says is x = 2, 2.5 (or any fraction between 2 and 3) or 3.

x can not be 3 or 2 or 1 in stmt 1 since it will make the LHS value = 0.....even if we take x a fraction number from 2 to 3....answer is a negative value which is not true......So A is SUFF

second stmt doesn't provide enough info.....INSUFF
Manager
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28 Apr 2007, 11:10

Stmt 1: [b](X-3)*(X-2)*(X-1) > 0[/b]
for (X-3)*(X-2)*(X-1) to be +ve , there will be following possibilities-
X-3, X-2, X-1
+ + + ===> X>3
- - + ====> X<2
- + - ====> X<1
+ - - ====> X<1

X does not lie between 2 and 3 inclusive. Hence SUFF

Stmt2: [b]X >1[/b]
X may or may not be in range of 2 to 3.
Hence INSUFF[/quote]

Can anyone explain how to get the ranges in Stmt 1?
Manager
Joined: 11 Nov 2006
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28 Apr 2007, 11:12

Stmt 1: [b](X-3)*(X-2)*(X-1) > 0[/b]
for (X-3)*(X-2)*(X-1) to be +ve , there will be following possibilities-
X-3, X-2, X-1
+ + + ===> X>3
- - + ====> X<2
- + - ====> X<1
+ - - ====> X<1

X does not lie between 2 and 3 inclusive. Hence SUFF

Stmt2: [b]X >1[/b]
X may or may not be in range of 2 to 3.
Hence INSUFF[/quote]

Can anyone explain how to get the ranges in Stmt 1?
Current Student
Joined: 22 Apr 2007
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28 Apr 2007, 12:32
(1) x should be either greater than 3, or between 2 and 1 for the LHS to be greater than 0

Sufficient

(2) Clearly insufficient

Current Student
Joined: 28 Dec 2004
Posts: 3363
Location: New York City
Schools: Wharton'11 HBS'12
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29 Apr 2007, 08:23
yup A it is..

for 1) to be >0

(x-3) has to be postive
(x-2) has to be positive
(x-1) has to be positive... which clearly says X is greater than 3

if any of the term becomes negative ..the whole equation becomes negative..

2) does mean much..

A it is..
29 Apr 2007, 08:23
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