If x and y are integers and x > 0, is y > 0?
(1) 7x - 2y > 0
(2) -y < x
By me Ans shoud be :- A as it fits all the parameters of being positive.
But ans given by test makers is :- E
Inequality ques???
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- asamaverick
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What made you go for a A?
(1) gives is 7x > 2y
Consider these x = 1, = 2. Yes y > 0
x = 2, y = -1. No y < 0
So A is not the right answer.
We can easily prove that (2) alone is not sufficient.
Combining the two:
7x -2y > 0
x + y > 0
Multiply second one by 2 and add. This gives.
9 x > 0
So all we know is x is positive. This still is not enough to say if y > 0. Hence E.
(1) gives is 7x > 2y
Consider these x = 1, = 2. Yes y > 0
x = 2, y = -1. No y < 0
So A is not the right answer.
We can easily prove that (2) alone is not sufficient.
Combining the two:
7x -2y > 0
x + y > 0
Multiply second one by 2 and add. This gives.
9 x > 0
So all we know is x is positive. This still is not enough to say if y > 0. Hence E.
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We are being asked if y is positive - given the parameters that x is positive and 7x-2y>0 this is an algebra inequality so we have to be careful about signs and may need to solve for actual values.
1 says 7x>2y - which means that 7/2(x)>y = so we know that some positive number is greater than y - this doesn't tell us whether y is positive or negative so it is insufficient. BCE
2. Says that -y<x - we know here that x is positive so we know that -y is less than a positive number. This still leaves both positive and negative options open - either y is negative so basically the positive value of y is less than another positive - or y is positive and teh negative value of y is less thana positive number - this isn't enough information.
if you put them together both statements allow for positive and negative values for y -and together they offer no new information - so the answer is E.
1 says 7x>2y - which means that 7/2(x)>y = so we know that some positive number is greater than y - this doesn't tell us whether y is positive or negative so it is insufficient. BCE
2. Says that -y<x - we know here that x is positive so we know that -y is less than a positive number. This still leaves both positive and negative options open - either y is negative so basically the positive value of y is less than another positive - or y is positive and teh negative value of y is less thana positive number - this isn't enough information.
if you put them together both statements allow for positive and negative values for y -and together they offer no new information - so the answer is E.
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Master GMAT Instructor
The Princeton Review
Irvine, CA
So why can't you multiply the 2nd equation by 7 which will give you:asamaverick wrote: Combining the two:
7x -2y > 0
x + y > 0
Multiply second one by 2 and add. This gives.
9 x > 0
So all we know is x is positive. This still is not enough to say if y > 0. Hence E.
7x - 2y > 0
7x + 7y > 0
and then subtract the 2 eqns which will give you -9y > 0 i.e. y HAS to be < 0 in which case the answer has to be C.
I'm guessing there's something I'm missing out when solving the 2 inequalities simultaneously. Can someone help me understand what it is? Should you NOT solve inequalities simultaneously? Thanks.
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As a general rule, you can add inequalities but not subtract them.jube wrote:
So why can't you multiply the 2nd equation by 7 which will give you:
7x - 2y > 0
7x + 7y > 0
and then subtract the 2 eqns which will give you -9y > 0
For example, consider:
6 > 4 and
4 > 1
we can add them and know that:
10 > 5
but we can't subtract them and get:
2 > 3