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Subtracting in-equalities

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by meraGMAT1 » Mon Jan 11, 2010 7:53 pm
Is x-y > r-s?
(1) x > r and y < s?
(2) y = 2, s = 3, r = 5, and x = 6

OA is (D)

My question is:

Subtracting 2 inequalities is WRONG.

Then how is OA (D)

That is:

(1) x > r and y < s?

should not mean

x-y > r-s

Any ideas?

Thanks
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Jan 12, 2010 12:30 pm
meraGMAT1 wrote:Is x-y > r-s?
(1) x > r and y < s
(2) y = 2, s = 3, r = 5, and x = 6
OA is (D)
My question is:
Subtracting 2 inequalities is WRONG.

Then how is OA (D)
That is:
(1) x > r and y < s?
should not mean
x-y > r-s
Any ideas?
Thanks
First, it's useful to recognize that if a>b, then a-b>0 (or a-b is positive)

For this question, it helps to rearrange the terms in the initial question:
If we take "Is x-y > r-s?" and subtract r from both sides and add s to both sides we get
"Is x-y-r+s > 0?" We can rearrange the terms to get
"Is (x-r)+(s-y) >0?"

Statement (1): x > r and y < s
This tells us that x-r is positive and s-y is positive
So, the question "(x-r)+(s-y) >0?" can now be answered since we know that x-r and s-y must both be positive.
SUFFICIENT

Statement (2) is sufficient since we are given the values of all 4 variables.
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by sanju09 » Wed Jan 13, 2010 4:27 am
meraGMAT1 wrote:Is x-y > r-s?
(1) x > r and y < s?
(2) y = 2, s = 3, r = 5, and x = 6

OA is (D)

My question is:

Subtracting 2 inequalities is WRONG.

Then how is OA (D)

That is:

(1) x > r and y < s?

should not mean

x-y > r-s

Any ideas?

Thanks
Like inequalities can be added, though.

(1) If x > r and y < s then x > r and -y > -s, added x - y > r - s, hence a definite YES. Sufficient.

(2) Always sufficient with values given.

D
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by Testluv » Wed Jan 13, 2010 7:58 pm
Subtracting 2 inequalities is WRONG.


If the inequality arrows point in the same direction, then we can add the inequalities but we can't subtract one from the other.

If the inequality arrows point in opposite directions, then we can subtract one inequality from the other, but we can't add them. However, here, it is usually easier to multiply (both sides of) one of the inequalities by -1, which causes the sign to flip, resulting in both arrows pointing in the same direction; then, we can simply add the two inequalities.
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