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Is a + b > c + d?

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Joined: 02 Aug 2009
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Is a + b > c + d?  [#permalink]

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New post 24 Dec 2017, 04:13
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

48% (01:38) correct 52% (01:10) wrong based on 77 sessions

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Is \(a+b>c+d\)?

(1) \(a>c+d\)
(2) \(a+b>2c+d\)

new tricky Question - self made

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is a + b > c + d?  [#permalink]

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New post 24 Dec 2017, 04:39
1
chetan2u wrote:
Is \(a+b>c+d\)?
(1) \(a>c+d\)
(2) \(a+b>2c+d\)

new tricky Question - self made


Statement 1: \(a>c+d\). Nothing mentioned about \(b\). Insufficient

Statement 2: \(a+b>2c+d=>a+b>c+d+c\). but we don't know the value of any variable. Hence Insufficient

Combining 1 & 2 we still do not know the values of variables.

For eg. if \(a=1, b=c=-1\) and \(d=1\), then

\(1>-1+1=>1>0\) and \(1-1>-2+1=>0>-1\) but the stem will be \(1-1>-1+1\), which is not possible. Hence we have a NO here

But if \(a=3, b=c=-1\) & \(d=1\), then

\(3>-1+1=>3>0\) and \(3-1>-2+1=>2>1\) and the stem will be \(3-1>-1+1=>2>0\). Hence we have a Yes. So, Insufficient

Option E
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Re: Is a + b > c + d?  [#permalink]

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New post 24 Dec 2017, 10:24
chetan2u wrote:
Is \(a+b>c+d\)?

(1) \(a>c+d\)
(2) \(a+b>2c+d\)

new tricky Question - self made


Since all our inequalities are very similar to each other, we'll try transforming (1) and (2) into our original inequality.
This is a Precise approach.

To change (1) into the original inequality we'd need to add b to the left-hand side.
But as we don't know if b is negative or non-negative we don't know how this will affect the inequality.
Insufficient.

To change (2) into the original inequality we'd need to subtract c from the right-hand side.
Similarly to the above, without knowing if c is negative or non-negative we don't know what this will do.
Insufficient.

Combining the two, we can try subtracting inequality (1) from inequality (2).
This gives b > c. But - we still don't know if b and c are positive or negative so cannot answer the question.

(E) is our answer.
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Re: Is a + b > c + d?  [#permalink]

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New post 13 Jan 2018, 11:04
Statement 1: a > c + d => no info about b => insuff
Statement 2: a + b > 2c + d
=> a + b > c + c + d
(very tempting to consider it as sufficient, but NOT to be)
c can be negative, in which case, it could c + c + d < a + b < c + d
=> insufficient
1 + 2
adding two inequalities
2a + b > 3c + 2d
still not sufficient to say a + b > c + d => (E)
Re: Is a + b > c + d? &nbs [#permalink] 13 Jan 2018, 11:04
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