If xy is less than 3, is x less than 1
1) y is greater than 3
2) x is less than 3
thanks.
Inequalities: If xy is less than 3, is x less than 1
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II, the Qs is saying -II wrote:If xy is less than 3, is x less than 1
1) y is greater than 3
2) x is less than 3
thanks.
xy <3> 3 let say y = 4 and xy = 2 so x = 1/2
Again, y = 3.1 and xy = 2.9 so x = 0.935
So x <1> SUFF
stmt - 2, x < 3. But x can be between 1 and 3 or x can be less than 1.
So it is INSUFF.
So IMO A.
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
You can break it out into equations.
Given
x*y < 3 Need to know if x < 1
Therefore... let's look at various possible y
Positive y: x < 3 / y
y = 0 : x can be anything
Negative y: x > 3 / y (remember to flip the signs)
Statement 1:
y > 3. This is the positive case above. Therefore:
x < 3 / y
For all y greater than 3, 3 / y is going to be less than 1. Therefore:
x < 1 SUFFICIENT
Statement 2:
x < 3
Obviously this practically tells you that you do not know whether it is less than 1 or not. All you have to do is a logic check to confirm that there is no other information that can block 1 < x < 3 from being a real answer.
Nothing to our knowledge. There is some y that can be multiplied by 1 < x < 3 and be less than 3.
Therefore INSUFFICIENT
So the answer is (A)
Given
x*y < 3 Need to know if x < 1
Therefore... let's look at various possible y
Positive y: x < 3 / y
y = 0 : x can be anything
Negative y: x > 3 / y (remember to flip the signs)
Statement 1:
y > 3. This is the positive case above. Therefore:
x < 3 / y
For all y greater than 3, 3 / y is going to be less than 1. Therefore:
x < 1 SUFFICIENT
Statement 2:
x < 3
Obviously this practically tells you that you do not know whether it is less than 1 or not. All you have to do is a logic check to confirm that there is no other information that can block 1 < x < 3 from being a real answer.
Nothing to our knowledge. There is some y that can be multiplied by 1 < x < 3 and be less than 3.
Therefore INSUFFICIENT
So the answer is (A)
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Stmt IIs there another approach to solving this, apart from plugging in numbers ?
xy<3 (1)
y>3 i.e
3<y (2)
Add I and II
xy+3<3+y
xy-y<0
y(x-1) < 0
Either y<0 or x-1 < 0
Given y>3 so x-1<0 or x<1
SUFF
Another simple approach for Stmt I
xy<3
xy-3<0 (1)
3<y (2)
Add 1) and 2) (inqualities facing same direction)
xy-3+3<0+y
xy<y
Divide by y since we know y is positive(doesnt change the inequality )
x<1
SUFF
Stmt II
Pick numbers to prove insuff
A)
Last edited by cramya on Mon Dec 15, 2008 11:45 pm, edited 1 time in total.
- logitech
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Sexy..cramya wrote:
Another simple approach for Stmt I
xy<3
xy-3<0 (1)
3<y (2)
Add 1) and 2) (inqualities facing same direction)
xy-3+3<0+y
xy<y
Divide by y since we know y is positive(doesnt change the inequality )
x<1
SUFF )
LGTCH
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Ronnie,x*y < 3
1: y is positive
so x < 3/y
so x < 1
Suff...
Good to see a nice approach for a change rather than a IMO.
Jus kidding!
I try not be blunt unlike my buddy Logitech!!!
Good luck with ur preps and keep up the good work!
Regards,
Cramya
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xy < 3 Given
From 1 : y>3 , Let's say y=3 then to satisfy the above equation x<1 and since y>3 x has to be < 1. Sufficient
From 2 : x<3 doesn't mention anything about y and so x can take any value less than 3 : Insufficient
hence A. Loved the other approaches mentioned here.
- pradeep
From 1 : y>3 , Let's say y=3 then to satisfy the above equation x<1 and since y>3 x has to be < 1. Sufficient
From 2 : x<3 doesn't mention anything about y and so x can take any value less than 3 : Insufficient
hence A. Loved the other approaches mentioned here.
- pradeep
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We are given that the product of x and y is less than 3 and must determine whether x < 1.II wrote:If xy is less than 3, is x less than 1
1) y is greater than 3
2) x is less than 3
Statement One Alone:
y is greater than 3.
We are given that y is greater than 3. If x is greater than or equal to 1, then xy will be greater than 3. Therefore, in order for xy to be less than 3, x must be less than 1. Statement one alone is sufficient to answer the question.
Statement Two Alone:
x is less than 3.
The information in statement two is not sufficient to answer the question. For instance, if x = 2, and y = 1, then xy = 2(1) = 2. However, if x = 1/2 and y = 4, then xy = (1/2)(4) = 2. In the former case, x > 1; in the latter case, x < 1. Statement two alone is not sufficient to answer the question.
Answer: A
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