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Inequality

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by Imsukhi » Fri Jun 28, 2013 9:35 pm
if a>b and p<q then which of the following is true?

A) a-q <b-p

B) a-p>b-q

C) b+p>a-q

D) b+p<a+q

E) a+p>b-q

Pls explan
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by srcc25anu » Fri Jun 28, 2013 9:47 pm
a > b and q > p

therefore a + q > b + p
Ans D
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by snigdha1605 » Fri Jun 28, 2013 10:08 pm
Yup I agree... D
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by ygdrasil24 » Fri Jun 28, 2013 11:20 pm
srcc25anu wrote:a > b and q > p

therefore a + q > b + p
Ans D
p,q can be re written as p>-q or -p>q
so taking a> b and p> -q
a+p>b-q Can't it be true as well?
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by ganeshrkamath » Thu Jul 04, 2013 3:18 am
Imsukhi wrote:if a>b and p<q then which of the following is true?

A) a-q <b-p

B) a-p>b-q

C) b+p>a-q

D) b+p<a+q

E) a+p>b-q

Pls explan
a > b
q > p
(a + q) > (b + p)
So (D)
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by Brent@GMATPrepNow » Thu Jul 04, 2013 6:22 am
Imsukhi wrote:if a>b and p<q then which of the following is true?

A) a-q <b-p

B) a-p>b-q

C) b+p>a-q

D) b+p<a+q

E) a+p>b-q

Pls explan

Important: We can ADD inequalities, but we cannot subtract them.
In order to add inequalities, the inequality signs must be facing in the same direction.

So, take a > b and rewrite it as b < a

Now add the two inequalities:
b < a
p < q
b+p < a+q

Answer: D

Cheers,
Brent
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by Brent@GMATPrepNow » Thu Jul 04, 2013 6:28 am
ygdrasil24 wrote:
p,q can be rewritten as p>-q or -p>q
so taking a> b and p> -q
a+p>b-q Can't it be true as well?
We cannot take p < q and rewrite it as p > -q

It appears that you have multiplied only one side of the inequality by -1. If you're going to multiply by -1, you must multiply both sides (and reverse the inequality).
So, if we take p < q and multiply both sides by -1, we get -p > -q

Cheers,
Brent
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by subhakam » Thu Sep 05, 2013 1:37 pm
Brent@GMATPrepNow wrote:
Imsukhi wrote:if a>b and p<q then which of the following is true?

A) a-q <b-p

B) a-p>b-q

C) b+p>a-q

D) b+p<a+q

E) a+p>b-q

Pls explan

Important: We can ADD inequalities, but we cannot subtract them.
In order to add inequalities, the inequality signs must be facing in the same direction.

So, take a > b and rewrite it as b < a

Now add the two inequalities:
b < a
p < q
b+p < a+q

Answer: D

Cheers,
Brent
Brent - is this universally true statement ?
"We can ADD inequalities, but we cannot subtract them" OR are you just referring to the above case - why we cannot subtract inequalities?
x>y
z>w
x-z>y-w -> does that not hold true?
Please let me know - if that is the case then conceptually it is confusing
7>3
2>1
7-2>3-1
Thanks
Subhakam
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by Brent@GMATPrepNow » Thu Sep 05, 2013 3:38 pm
subhakam wrote: Brent - is this universally true statement ?
"We can ADD inequalities, but we cannot subtract them" OR are you just referring to the above case - why we cannot subtract inequalities?
x>y
z>w
x-z>y-w -> does that not hold true?
Please let me know - if that is the case then conceptually it is confusing
7>3
2>1
7-2>3-1
Thanks
Subhakam
Hi Subhakam,

Yes, this is a universally true statement.

If we subtract inequalities, the result need not be true.
The example you provide is one that works, but in order for a rule to be a rule, it must always work.

Check out this one:

30 > 20
29 > 1
BUT we can't say that 30-29 > 20-1

So, we can add inequalities, but we can't subtract them.

Cheers,
Brent
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by subhakam » Fri Sep 06, 2013 5:49 am
Brent - Thank you very much
Subhakam
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