Inequality Magic -- What is Z?

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XLogic: Master | Next Rank: 500 Posts; Posts: 127; Joined: Sat Oct 02, 2010 8:55 amFollowed by: 1 member; Thanked: 17 times

by XLogic » Mon Mar 28, 2011 2:11 pm

Please help resolve this data sufficiency question. Provide full explanation.

If z is an integer and 4^z < 213, what is z?

(1) 4^(z + 1) - 4^(z - 1) > 213
(2) 4^(z + 1) + 4^z > 213

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Source: Beat The GMAT — Data Sufficiency | Mon Mar 28, 2011 2:11 pm

ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Mon Mar 28, 2011 2:29 pm

Sometimes I like to think of Data Sufficiency problems as set logic problems (for value DS questions). The question provides you with a set and the statements attempt to restrict that set. If a statement or statements can restrict the set to one value, you have sufficiency.

Looking at this problem in this way, the question

4^z < 213, z is an int

Yields the following set
{...,-1,0,1,2,3}

The first statement

4^(z+1) - 4^(z-1) > 213

Works for z = 3 (you can plug and chug yourself here)

Doesn't work for z=2 and therefore wont work for anything less than z=2 since 4^z only gets smaller as z decreases. Hence (1) is sufficient

The second statement

4^(z+1) + 4(z) > 213

Obviously works for z=3 since this statement will be larger than statement 1

Doesn't work for z=2 and therefore won't work for anything less than z=2.

Hence (2) is sufficient

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XLogic: Master | Next Rank: 500 Posts; Posts: 127; Joined: Sat Oct 02, 2010 8:55 amFollowed by: 1 member; Thanked: 17 times

by XLogic » Mon Mar 28, 2011 2:49 pm

Thanks.

I've done a few practice tests, and I'm scoring 60-80 points below my goal.
I'm scheduled to take the test this Saturday. Any words of advice? Strategies... tactics. too late?

Surprisingly, I'm doing better in DS than PS. But I've been guessing quite a bit on DS.

--Xlogic

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ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

by ldoolitt » Mon Mar 28, 2011 3:04 pm

XLogic wrote:Thanks.

I've done a few practice tests, and I'm scoring 60-80 points below my goal.
I'm scheduled to take the test this Saturday. Any words of advice? Strategies... tactics. too late?

Surprisingly, I'm doing better in DS than PS. But I've been guessing quite a bit on DS.

--Xlogic

Yeah DS is easier to guess on than PS because if you find either statement to be sufficient, you have a 50% chance of getting the question right.

I think the strategy probably depends on your weaknesses. If that were me I would study strategy and practice problems for whatever my weakest area was. Usually that gives you more bang for your buck. For example my weak area in verbal is RC because there isn't a clear cut strategy for it. So I did every RC problem in the OG and the Verbal Review, improved my accuracy from 40% - 65% and it improved my score quite a few points (I don't remember how many).

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Tue Mar 29, 2011 6:00 am

If z is an integer and 4^z < 213, what is z?
z= integer
4^z < 213
4*4=16*4=64*4=256 HENCE z < 4

(1) 4^(z + 1) - 4^(z - 1) > 213
4^z(4^+1 - 4^-1) > 213
4^z(4 - 1/4) > 213
4^z(15/4) > 213
4^z > 213 * 4/15
4^z > 3*71*4*(1/15)
4^z > 284/15
4^z > 56.80
Because z is an integer, then z must be 3!!!

(2) 4^(z + 1) + 4^z > 213
4^z(4+1) > 213
4^z(5) > 213
4^z > 213/5
4^z > 42.6
Because z is an integer, then z must be 3!!!

Correct Answer [spoiler](D)[/spoiler]

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