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
Inequality
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- snigdha1605
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p,q can be re written as p>-q or -p>qsrcc25anu wrote:a > b and q > p
therefore a + q > b + p
Ans D
so taking a> b and p> -q
a+p>b-q Can't it be true as well?
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a > bImsukhi 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
q > p
(a + q) > (b + p)
So (D)
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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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We cannot take p < q and rewrite it as p > -qygdrasil24 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?
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
Brent - is this universally true statement ?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
"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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Hi Subhakam,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
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