Is (x-2) (x-3)>0?

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

Is (x-2) (x-3)>0?

by Gmat_mission » Fri May 25, 2018 12:33 am

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Is (x-2) (x-3)>0?

1) x-2 > 0
2) x-3 < 0

[spoiler]OA=C[/spoiler].

Why is each statement alone not sufficient? Could someone give me some help? Please. <i class="em em-frowning"></i>

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Source: Beat The GMAT — Data Sufficiency | Fri May 25, 2018 12:33 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Fri May 25, 2018 2:01 am

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Hello Gmat_mission.

Let's take a look at your question.

1) x-2 > 0

This statement tells us that x > 2, then x can be 2.1 or 4.

If x=2.1 then x-3 < 0, therefore (x-2) (x-3) < 0.

If x=4 then x-3 > 0, therefore (x-2) (x-3) > 0.

Therefore, this statement is not sufficient.

2) x-3 < 0

This statement tells us that x < 3, then x can be 2.5 or 1.

If x=2.5 then x-2 > 0, therefore (x-2) (x-3) < 0.

If x=1 then x-2 < 0, therefore (x-2) (x-3) > 0.

Therefore, this statement is not sufficient.

Using both statements together we get x-2 > 0 and x-3 < 0, hence (x-2)(x-3)<0.

Hence, the answer to the original question is NO. SUFFICIENT.

The correct answer is the option C.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Tue May 29, 2018 4:52 pm

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Gmat_mission wrote:Is (x-2) (x-3)>0?

1) x-2 > 0
2) x-3 < 0

We need to determine whether (x-2) (x-3)>0.

Statement One Alone:

x-2 > 0

Although we know that x - 2 > 0, we do not have any information regarding the sign of the value of x - 3, so statement one is not sufficient to answer the question.

Statement Two Alone:

x-3 < 0

Although we know that x - 3 > 0, we do not have any information regarding the sign of the value of x - 2, so statement one is not sufficient to answer the question.

Statements One and Two Together:

Since x-2 > 0 and x-3 < 0, we see that the product of those two terms will always be less than zero.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]