Inequality

[Imsukhi]

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

[srcc25anu]

a > b and q > p

therefore a + q > b + p
Ans D

[snigdha1605]

Yup I agree... D

[ygdrasil24]

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?

[ganeshrkamath]

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)

[Brent@GMATPrepNow]

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@GMATPrepNow]

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

[subhakam]

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

[Brent@GMATPrepNow]

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

[subhakam]

Brent - Thank you very much
Subhakam