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# Is a + b > c + d ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Is a + b > c + d ?  [#permalink]

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20 Mar 2016, 23:43
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Difficulty:

5% (low)

Question Stats:

88% (00:41) correct 12% (00:38) wrong based on 119 sessions

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Is a + b > c + d ?

(1) a > c

(2) d < b

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Re: Is a + b > c + d ?  [#permalink]

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23 Mar 2016, 06:22
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Is a + b > c + d ?

(1) a > c

(2) d < b

St 1 : a > c, No information on b and d, hence insufficient
St 2 : d < b or b > d , No information on a and b, hence insufficient
Both statements : Since a > c and b > d, add both statements then a + b > c + d, which is our answer. Sufficient.

Solution: C
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Re: Is a + b > c + d ?  [#permalink]

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22 Mar 2018, 07:34
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Top Contributor
Bunuel wrote:
Is a + b > c + d ?

(1) a > c

(2) d < b

Target question: Is a + b > c + d ?

Statement 1: a > c
Since we have no information about b or d, we cannot determine whether a + b > c + d
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: d < b
Since we have no information about a or c, we cannot determine whether a + b > c + d
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a > c
Statement 2 tells us that b > d (NOTE: I rewrote the inequality so that the inequality symbol is facing the other direction)
Since the two inequality symbols are facing in the SAME DIRECTION, we can ADD THEM to get: a + b > c + d
PERFECT.
We can now say, with certainty that the answer to the target question is YES, a + b IS greater than c + d
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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Re: Is a + b > c + d ?  [#permalink]

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24 Mar 2018, 18:47
Bunuel wrote:
Is a + b > c + d ?

(1) a > c

(2) d < b

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 4 variables (a, b, c and d) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since a > c and b > d, we have a + b > c + d by adding two inequalities.
Thus, both conditions together are sufficient.

Since this question is an inequality question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since we don't have any information about b and d, the condition 1) is not sufficient.

Condition 2)
Since we don't have any information about a and c, the condition 1) is not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: Is a + b > c + d ?  [#permalink]

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25 Mar 2018, 07:59
Bunuel wrote:
Is a + b > c + d ?

(1) a > c

(2) d < b

1. no info b,d ----> NS
2. no info a,c ----> NS

1+2 (a-c) + (b-d) = +ve + +ve and hence GT )
Hence a+c >b+d ....................Sufficient
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Re: Is a + b > c + d ?  [#permalink]

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25 Sep 2019, 06:45
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Re: Is a + b > c + d ?   [#permalink] 25 Sep 2019, 06:45
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