is d negative

[rachelhong2012]

Hi,

I wonder if my approach to this problem is right:

Is d negative?

(1) e + d = -12

(2) e - d < -12



Since either statement alone is sufficient and we must combine them. I wonder if I can add the two statements together and first cancel out d to get:

2e < -24 so e<-12
Then plug that value back into either statement and get: d is a positive number?

Thanks

[tim]

With your approach you can’t just plug e<-12 into either statement, because plugging into statement 2 is inconclusive. However, since you have both statements to use, you still have sufficient information because plugging into 1 tells you d is positive. A better approach though would be to subtract statement 1 from statement 2, getting rid of the e’s you don’t want and keeping the d’s you want:

-2d < 0
d > 0

[rachelhong2012]

With your approach you can’t just plug e<-12 into either statement, because plugging into statement 2 is inconclusive. However, since you have both statements to use, you still have sufficient information because plugging into 1 tells you d is positive. A better approach though would be to subtract statement 1 from statement 2, getting rid of the e’s you don’t want and keeping the d’s you want:

-2d < 0
d > 0

Thanks Tim.

I wonder how did you "subtract" inequality?

I know you can multiple by -1 as a way to "subtract", but you have to switch the sign when you do that.

So I will multiple (e-d<-12) by -1 and get -e + d > 12
combine/add the rephrased inequality with e + d = -12
I will cancel out e and get 2d > 0 hence d>0, am I right?

Thanks again.

[tim]

As a reminder, you should NEVER subtract inequalities. Please take a close look at my post, and you will notice that i did not subtract an inequality.. :)

[shubha2110]

Hi Tim,

Could you please explain further how did you get -2d < 0? I am confused how you got it without subtracting + you say we can't subtract inequalities (why?)

In this question, I found that the 2nd statement tells that d > e.

I solved it as below:

e - d < -12

so, multiplying by -1 on both sides,

d - e > 12

For this to be true, d > e

Then, statement 1 says that e + d = -12. Can i use the fact that d > e in statement 1 to solve conceptually? I think I am missing something.

Hope you can help.

[tim]

i DID subtract; i just didn’t subtract INEQUALITIES. Part of success on the GMAT is being able to identify these subtle differences, so please pay careful attention.. :)

[lj6871849]

Hi tim - just to be sure

(1) e + d = -12

(2) e - d < -12


(2) can be writen as d-e> 12
adding with (1)

e + d = - 12
d - e > 12

2d >= 0

so d >= 0 therefore D is never gonna be negative

and we need EQUAL TO SIGN HERE right? (we n combining stat1 and stat2), in your original post there wasn't an equal to sign hence i had the doubt.

Cheers

[tim]

no, there should not be an equal sign. if the left side is greater than the right and you add equal things to both sides, the left side will still be greater than the right..

[Jazmet]

So the statement (1) e + d = -12 can be re-written as e + d > -12

Am I correct? If yes Please explain why?

[RonPurewal]

So the statement (1) e + d = -12 can be re-written as e + d > -12

no, of course it can't. if my nephew is 12 years old, then he's not more than 12 years old.

what tim is writing above is that, if you take a = b and add it to c > d, then you get a + c > b + d.

note that it's a really bad idea to try to memorize these rules -- that's much too hard, and rather pointless, since all you need to do is think about common-sense examples.

for instance, let's say you spend $50 on groceries (x = 50), and then you spend more than $40 on clothes (y > 40).
in this case, your total amount spent is clearly more than $90 (x + y > 90).
that's how it works.

[Jazmet]

Thank you Ron!

[jlucero]

Glad it helped.

[rustom.hakimiyan]

So the statement (1) e + d = -12 can be re-written as e + d > -12

no, of course it can't. if my nephew is 12 years old, then he's not more than 12 years old.

what tim is writing above is that, if you take a = b and add it to c > d, then you get a + c > b + d.

note that it's a really bad idea to try to memorize these rules -- that's much too hard, and rather pointless, since all you need to do is think about common-sense examples.

for instance, let's say you spend $50 on groceries (x = 50), and then you spend more than $40 on clothes (y > 40).
in this case, your total amount spent is clearly more than $90 (x + y > 90).
that's how it works.

Hi Ron,

This still seems a little convoluted to me.

If I look into adding these two equations - I first have to flip statement 2 to read -e+d>12. Correct?

Then I get:

e+d=-12
-e+d>12
2d>0
d>0

Question 1:

Why do I get rid of the equal sign? I'm trying to draw the analogy from your explanation above but e+d vs. -e+d are throwing me off?

Question 2:

If I don't flip statement number two, can I still add or subtract it? If I do, I get d<0.

e+d=-12
e-d<-12

Subtracting gives me 2d<0, therefore d<0?

Thanks!

[RonPurewal]

Why do I get rid of the equal sign?

When it comes to combining "<", ">", "≤", "≥", and "=" with addition and subtraction, you basically have two options:
- Memorize tons and tons of different combinations;
"- Use common sense.
The latter seems clearly better to me (although there are always students who try the former).

In terms of adding ">" and "=", just think about a real-world example.
My brother and I go to lunch.
"- My lunch costs $8. (x = 8)
"- His lunch costs more than $10. (y > 10)
So... Our combined bill is more than $18. (x + y > 18)

I'm trying to draw the analogy from your explanation above but e+d vs. -e+d are throwing me off?

The +'s and -'s are irrelevant to this issue. You have to add them correctly, of course, but they don't determine which inequality sign will result"”the sum of "=" and ">" will always be ">".

[RonPurewal]

Question 2:

If I don't flip statement number two, can I still add or subtract it?

Use a common-sense analogy again.

"- I want to buy an item that costs $50. (x = 50)
- I have a discount coupon worth less than $10. (y < 10)
- Therefore, when I take the discount (= subtract), the resulting price will be more than $40. (x - y > 40)

So, "=" minus "<" is actually ">".