DS 41 from OG quantative

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maria: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Tue May 06, 2008 11:49 am; Thanked: 1 times

DS 41 from OG quantative

by maria » Tue May 27, 2008 8:25 am

if S is a set of four numbers w, x, y and z, is the range of the numbers in S greater than 2?
1. w - z> 2
2. z is the least number in S.

OA is A.
its explanation is:
1. the difference between two of the numbers in the set is greater than 2, which means that the range of the four numbers must also be greater than 2. SUFF.

I agree with the first part, but the second one, I am not quite sure why "which means that the range of the four numbers must also be greater than 2"?

help me, pls.[/quote]

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Source: Beat The GMAT — Data Sufficiency | Tue May 27, 2008 8:25 am

shiraj: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Jan 10, 2008 5:04 am

by shiraj » Wed May 28, 2008 1:53 am

Answer: A

S={w,x,y,z}

(1) w - z > 2 => w > z + 2

Now we can hav the following cases -

Case a) Say z is the least and w is greatest.
Then, to the answer to range of the numbers in S greater than 2 is YES

Case b) Say z is the least and w is not the greatest.
You have at least another number which is greater than w.
Then, to the answer to range of the numbers in S greater than 2 is YES

Case c) Say z is not the least and w is greatest.
You have at least another number which is less than z.
Then, to the answer to range of the numbers in S greater than 2 is YES

Case d) Say z is not the least and w is not the greatest.
You have at least another number which is less than z, and
at least another number which is greater than w.
Then, to the answer to range of the numbers in S greater than 2 is YES

Thus condition (1) is sufficient to answer it.

(2) Z is least. But no information regarding the other nos.
You do not know, by how much they are greater.

So the answer is A

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

by camitava » Wed May 28, 2008 4:03 am

Good explanation, Shiraj... Carry on, man.

Correct me If I am wrong

Regards,

Amitava

Quote

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: DS 41 from OG quantative

by Stuart@KaplanGMAT » Wed May 28, 2008 11:49 am

maria wrote:if S is a set of four numbers w, x, y and z, is the range of the numbers in S greater than 2?
1. w - z> 2
2. z is the least number in S.

OA is A.
its explanation is:
1. the difference between two of the numbers in the set is greater than 2, which means that the range of the four numbers must also be greater than 2. SUFF.

I agree with the first part, but the second one, I am not quite sure why "which means that the range of the four numbers must also be greater than 2"?

help me, pls.

[/quote]

Range is the difference between the smallest and largest numbers in a set.

We have no clue if w and z are the two furthest apart numbers in the set.

If they are the furthest apart, then the range will be |w - z| which we know is > 2.

If they aren't the furthest apart, then the range will be even bigger, so we also know that it will be > 2.

Either way, the range is > 2... sufficient.