Inequalities: If x is a positive integer, is x<1 ?

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Thu Dec 27, 2007 3:07 pm

If x is a positive integer, is X<1 ?

(1) 2x < 1
(2) 2x <= 2

(A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
(B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
(D) Each statement ALONE is sufficient
(E) Statements (I) and (II) TOGETHER are NOT sufficient

Can you please let me know how you come to the answer ?
Thanks in advance.
II

Last edited by II on Tue Apr 29, 2008 5:37 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 27, 2007 3:07 pm

StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Thu Dec 27, 2007 3:45 pm

Is the answer B ?

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Thu Dec 27, 2007 7:02 pm

StarDust845 wrote:Is the answer B ?

How did you come to that answer ?
And no ... answer is not A.

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sujaysolanki: Master | Next Rank: 500 Posts; Posts: 214; Joined: Wed Nov 14, 2007 6:30 am; Thanked: 15 times

by sujaysolanki » Thu Dec 27, 2007 11:07 pm

From 1 we get X < 0.5 so X definitely less < 1 Hence sufficient

From 2 x could be =1 or less than 1 Hence Insufficient

Hence A

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Thu Dec 27, 2007 11:50 pm

If x is a positive integer, is X<1 ?

(1) 2x < 1
(2) 2x <= 2

In the Qs, it is saying that X is a positive number and according to the conclusion X < 1. So X has to be 0 only.
Now by 1, X <1> Which proves X < 1
But by 2, 2X <2> X <1> Which is saying that X can be equal to 1 or less than 1. So no direct conclusion you can draw.
So IMO A.

Correct me If I am wrong

Regards,

Amitava

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StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Fri Dec 28, 2007 7:18 am

I disagree with sujaysolanki's and camitava's solution.

In the stem it states that x is a positive integer (0 is not). That means x is 1,2,3 etc.

From (1) I know that x < 0.5, but is there a solution to this inequality given the stem? NO. If there is no solution how can you say that it proves X < 1?????

But from (2) I know x <= 1 and from stem x can't be 0 (0 is not a positive integer) hence x must be 1 and hence the answer is B.

What's the official answer?

Thanks,
Calista.

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