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# Is a + b > c + d?

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Math Expert
Joined: 02 Aug 2009
Posts: 7458
Is a + b > c + d?  [#permalink]

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24 Dec 2017, 04:13
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Difficulty:

65% (hard)

Question Stats:

52% (02:14) correct 48% (01:29) wrong based on 81 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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Re: Is a + b > c + d?  [#permalink]

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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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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.

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Re: Is a + b > c + d?  [#permalink]

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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
2a + b > 3c + 2d
still not sufficient to say a + b > c + d => (E)
Re: Is a + b > c + d?   [#permalink] 13 Jan 2018, 11:04
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