How in the world?

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notgoodinmath: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue Jul 08, 2008 1:29 pm

How in the world?

by notgoodinmath » Tue Jul 08, 2008 3:48 pm

Can someone please tell me what is the best strategy to use when answering these questions:

If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative

I only
II only
III only
I and II
II and III

Thanks!

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Source: Beat The GMAT — Problem Solving | Tue Jul 08, 2008 3:48 pm

tanviet: Legendary Member; Posts: 1404; Joined: Tue May 20, 2008 6:55 pm; Thanked: 18 times; Followed by:2 members

by tanviet » Tue Jul 08, 2008 7:25 pm

pick the specific numbers . OA is 3 only

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preetha_85: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sun Jul 06, 2008 6:41 am; Location: INDIA; Thanked: 2 times

Solution

by preetha_85 » Tue Jul 08, 2008 8:30 pm

you have got to pick nos. and check

case 1 : both x&y are positive
assume x=6;y=-2.
then x-y=6-(-2)=8

Hence 1 is not the answer.

Case 2 : If x is positive ,y must be positive
Not necessary.. from the example above

Case 3: If x is negative y must be negative
Assume x=-7;then y has to be negative for the answer to be positive.
since only then will the sins cancel out for the no. to be positive.
So in this case if y=-15
x-y= -7-(-15) = 8

Hence option 3 is right

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VP_Jim: GMAT Instructor; Posts: 1223; Joined: Thu May 01, 2008 3:29 pm; Location: Los Angeles, CA; Thanked: 185 times; Followed by:15 members

by VP_Jim » Tue Jul 08, 2008 8:36 pm

I agree with the above - the best way to do this (and most other problems involving variables) is to pick numbers.

This question tells us that x-y=8. So, we can pick numbers such as:

x=10, y =2
x = 4, y = -4
x = -2, y=-10

etc. etc.

Then, plug these numbers into the answer choices and eliminate ones that come out "false". You may have to do multiple iterations of this before you arrive at the correct answer.

Jim S. | GMAT Instructor | Veritas Prep

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amitdgr: Master | Next Rank: 500 Posts; Posts: 228; Joined: Sun Jun 29, 2008 8:47 pm; Thanked: 15 times; Followed by:1 members

Re: How in the world?

by amitdgr » Wed Jul 09, 2008 5:14 am

Take case I : Both x and y are positive ----- Need not be, Y can be negative eg. x=4 and y=-4 => x-y = 4+4 = 8

Take Case II : If x is positive, y must be positive ----- Disproved above

Case III - If x is negative, y must be negative ----- If x is negative and y is positive, then -x-y will give a negative result. This shows that if x is negative, y must be negative so that the eqn becomes -x+y which gives us a possibility of having positive result.

Right answer is C. III only

HTH

Amit

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notgoodinmath: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Tue Jul 08, 2008 1:29 pm

by notgoodinmath » Wed Jul 09, 2008 11:48 am

Thanks Guys! time consuming for sure

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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

by Stuart@KaplanGMAT » Wed Jul 09, 2008 1:36 pm

notgoodinmath wrote:Thanks Guys! time consuming for sure

Most roman numeral questions are susceptible to a strategic attack - GMAC wants to reward strategic thinkers!

Start by looking at the choices and (usually) begin with the roman numeral that appears most frequently. As you deal with each roman numeral, eliminate choices as you go.

In this question, II is the most frequent among the choices. Once we see that II is not a MUST be true, we eliminate (b), (d) and (e) - worst case, we have a 50/50 shot.

The remaining choices are:

(a) I only; and
(c) III only.

Since they appear an equal number of times, we just work with the one that seems easier, which in this case will be I, since in all likelihood the numbers you picked to show that II doesn't have to be true will also show that I doesn't have to be true.

Once we elminate I (and (a)), the only answer choice left is (c) III only. We can confidently pick (c) without even thinking about III.

So, if you attacked this question strategically, you probably only needed to pick 1 set of numbers.