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# If a + b = 20, then what is the value of c − d?

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Math Expert
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If a + b = 20, then what is the value of c − d?  [#permalink]

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13 Dec 2015, 04:57
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If a + b = 20, then what is the value of c − d?

(1) ac − bd + bc − ad = 60
(2) d = 4

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If a + b = 20, then what is the value of c − d?  [#permalink]

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Updated on: 15 Dec 2015, 09:04
1
[Corrected] Our Apology for being careless! We read the question wrongly!

If a + b = 20, then what is the value of c − d?

(1) ac − bd + bc − ad = 60
(2) d = 4

Looking at original condition, a+b=20,, then asking c-d,
If we factorize (1), (a+b)c-(a+b)d=60, (a+b)(c-d)=60.
(2) is d=4, c-d is question then if we substutute a+b=20,
In (1), from 20(c-d)=60, c-d=3. It is unique so sufficient.
In (2), d=4, it is not unique so not sufficient.

"Variable approach method 1" is to "modify the original condition and the question" then we can solve approximately 30% of DS questions.
Factorization is one of examples as shown above.
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Originally posted by MathRevolution on 13 Dec 2015, 20:45.
Last edited by MathRevolution on 15 Dec 2015, 09:04, edited 1 time in total.
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Posts: 38
Re: If a + b = 20, then what is the value of c − d?  [#permalink]

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13 Dec 2015, 20:59
1
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a + b = 20, then what is the value of c − d?

(1) ac − bd + bc − ad = 60
(2) d = 4

In the original condition, there are 4 variables(a,b,c,d) and 1 equation(a+b=20), which should match with the number of equations. So you need 3 more equation. For 1) 1 equation, for 2) 1 equation and you need 1 more equation, which is likely to make E the answer. In 1) & 2), it is ac-bd+bc-ad=60, (a+b)(c-d)=60, 20(c-4)=60, which is not unique and therefore not sufficient. So, the answer is E.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

I think answer for this question is option A. As questions is asking value of C-D
from statement -1
(a+b)c-(b+a)d= 60
=> c-d=3(since a+b=20 )
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Joined: 10 Dec 2015
Posts: 5
Re: If a + b = 20, then what is the value of c − d?  [#permalink]

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14 Dec 2015, 06:05
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a + b = 20, then what is the value of c − d?

(1) ac − bd + bc − ad = 60
(2) d = 4

In the original condition, there are 4 variables(a,b,c,d) and 1 equation(a+b=20), which should match with the number of equations. So you need 3 more equation. For 1) 1 equation, for 2) 1 equation and you need 1 more equation, which is likely to make E the answer. In 1) & 2), it is ac-bd+bc-ad=60, (a+b)(c-d)=60, 20(c-4)=60, which is not unique and therefore not sufficient. So, the answer is E.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

I agree with sharma 123. Statement 1 sufficiently provides the value of c-d which 3. Let me know what you think?
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If a + b = 20, then what is the value of c − d?  [#permalink]

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15 Dec 2015, 07:15
1
Statement 1 is definitely sufficient.

ac-bd+bc+ad=60 can either be solved by factoring out (a+b) like sharma did or by factoring out (c-d).

Lets factor out (c-d):
a(c-d)+b(c-d)=60
From the promp we know that a+b=20
Since we have two (c-d), they will both be the same value. Thus, you could write (c-d)=x (this is only for better understanding of the next step and is no necessary)

(c-d)=x
-> ax+bx=60 -> we know that a+b=20 -> 20x=60 -> x=3 -> x=(c-d) -> thus (c-d)=3

Statement 2 is obviously not sufficient, since it doesnt tell us anything about c. Thus, the final answer is A.

I would be very careful with assuming 2 Variables -> 2 Equations needed etc. The Gmat knows that you think that way and most of the time it will punish you for such a lazy approach.
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Re: If a + b = 20, then what is the value of c − d?  [#permalink]

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15 Dec 2015, 08:02
(1) ac − bd + bc − ad = 60
which can be written as (a+b)(c-d)=60, we know the value of (a+b), so we can find the value of (c-d). Sufficient
(2) d = 4...Value of c unknown...Insuff

Ans: A
Math Expert
Joined: 02 Aug 2009
Posts: 7200
Re: If a + b = 20, then what is the value of c − d?  [#permalink]

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15 Dec 2015, 08:43
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a + b = 20, then what is the value of c − d?

(1) ac − bd + bc − ad = 60
(2) d = 4

In the original condition, there are 4 variables(a,b,c,d) and 1 equation(a+b=20), which should match with the number of equations. So you need 3 more equation. For 1) 1 equation, for 2) 1 equation and you need 1 more equation, which is likely to make E the answer. In 1) & 2), it is ac-bd+bc-ad=60, (a+b)(c-d)=60, 20(c-4)=60, which is not unique and therefore not sufficient. So, the answer is E.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

the colored portion is unique and can have an answer as 3 only .. so would be suff..
ans A
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If a + b = 20, then what is the value of c − d?  [#permalink]

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15 Dec 2015, 09:09
1
Math Revolution Team apologizes for posting wrong answer by wrong reading of the question! We corrected it and A is the answer.
Please see our posting again above ! We believe that Variable approach can still solve all DS questions.
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Re: If a + b = 20, then what is the value of c − d?  [#permalink]

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28 Dec 2017, 05:11
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Re: If a + b = 20, then what is the value of c − d? &nbs [#permalink] 28 Dec 2017, 05:11
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