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CAT question !

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Intern
Joined: 28 Apr 2009
Posts: 4

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30 Oct 2011, 00:39
1. Q. can be answered using statement 1 alone.
2. Q. can be answered using statement 2 alone.
3. Statement 1 & 2 both are needed to answer the Q.
4. Q. can’t be answered even using both the statements

Q. Given that, X and Y are non negative. What is the value of X?
1. 2X+2Y <=40
2. X-2Y>=20

a) 1 b) 2 c) 3 d) 4

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Joined: 20 Dec 2010
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30 Oct 2011, 02:45
Sids wrote:
1. Q. can be answered using statement 1 alone.
2. Q. can be answered using statement 2 alone.
3. Statement 1 & 2 both are needed to answer the Q.
4. Q. can’t be answered even using both the statements

Q. Given that, X and Y are non negative. What is the value of X?
1. 2X+2Y <=40
2. X-2Y>=20

a) 1 b) 2 c) 3 d) 4

1. x+y<=20
x=0; y=1;
x=1; y=1
Not Sufficient.

2. x-2y>=20
x=20; y=0;
x=21; y=0
Not Sufficient.

Both;
x+y-(x-2y)<=20-20
3y<=0
y<=0
OR
y=0, as y is non-negative.

Substituting y=0,
x<=20 AND x>=20; thus, x=20

Ans: "C"
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Intern
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30 Oct 2011, 03:28
Thanks Fluke, I too was happy with "c". Wanted conformation from another mind as well, just in case if, I am missing anything.... Thanks!

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Veritas Prep GMAT Instructor
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31 Oct 2011, 22:27
Sids wrote:
1. Q. can be answered using statement 1 alone.
2. Q. can be answered using statement 2 alone.
3. Statement 1 & 2 both are needed to answer the Q.
4. Q. can’t be answered even using both the statements

Q. Given that, X and Y are non negative. What is the value of X?
1. 2X+2Y <=40
2. X-2Y>=20

a) 1 b) 2 c) 3 d) 4

This is how I deal with this question:
If I am to get a value of X from 2 inequalities, I will get it from the border conditions. So more than anything, I will focus on the 'equal to' sign.
It is clear that either one of the inequalities will not give me the value of X. I have to see whether both together give me a value.
1. X + Y <= 20
2. X - 2Y >= 20
When Y is added to X, it is LESS than or equal to 20. When twice of Y is subtracted from X, it is GREATER than or equal to 20! Since Y cannot be negative, it must be 0 to give 20 in both cases. That is the only way in which both these conditions can be met. Hence, X must be 20.

fluke: Of course, your solution is absolutely correct and spot on. I am giving this method only to encourage you guys to think in terms of the 'big picture'. Very often, it helps you logically deduce your answer without much mathematical work.
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Re: CAT question !   [#permalink] 31 Oct 2011, 22:27
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