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# If a > b, how much greater than b is a ?

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Director
Status: I don't stop when I'm Tired,I stop when I'm done
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If a > b, how much greater than b is a ?  [#permalink]

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27 Aug 2015, 10:46
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:03) correct 27% (00:49) wrong based on 82 sessions

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If a > b, how much greater than b is a ?

(1) b is one-fourth the value of a.
(2) The sum of a and b is 100.

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Re: If a > b, how much greater than b is a ?  [#permalink]

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27 Aug 2015, 19:24
2
We have been given that a > b
We have been asked how much greater than b is a.
This simply means what is a - b.

Statement 1:
b = a/4
Hence, a - b = a - a/4 = 3a/4
But this does not gives us the value.
Not Sufficient

Statement 2:
a+b = 100
Not sufficient

Combining both the statements:
We can find the value of a and b seperately by combining the following equations:
b = a/4 and a+b = 100
Hence we can find the value of a-b.
Sufficient. Thus the answer is C
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If a > b, how much greater than b is a ?  [#permalink]

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28 Aug 2015, 07:59
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 equations ensures a solution.

If a > b, how much greater than b is a ?

(1) b is one-fourth the value of a.
(2) The sum of a and b is 100.

==> since there are 2 variables in the original condition, to match the number of variables and you need 2 equations. Since there is 1 each in 1) and 2), the answer is likely C.
In actual calculation, we can get a+b = 100, b = a/4 from 1) & 2) and a = 4b, 4b + b = 5b = 100 ==> b = 20, a = 80. thus a- b = 80 - 20 = 60, therefore the answer is C.
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Re: If a > b, how much greater than b is a ?  [#permalink]

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26 Sep 2016, 00:00
OptimusPrepJanielle wrote:
We have been given that a > b
We have been asked how much greater than b is a.
This simply means what is a - b.

How can you tell that the question is asking for a value and not a percentage?

For instance, in terms of percentage greater, it would mean that we need to solve for (A-B)/B, which is equivalent to = (A/B) - 1

With item (1), we are told (B=A/4), so therefore rewritten it can be used to show the ratio (A/B) = 4. Therefore, in terms of percentage greater, (A/B)-1 = 3, or 300%

Wouldn't A is 300% greater than B be a valid answer, thus making Statement 1 Alone sufficient?
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Re: If a > b, how much greater than b is a ?  [#permalink]

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23 Feb 2017, 03:40
PROMPT ANALYSIS

a and b are real numbers with a greater than b

SUPER SET

The difference between b and a can be from zero to infinity

TRANSLATION

Since a and b are two variables, we need
The exact value of a and b
Two equation with only a and b s variable
Some characteristics of a and b that may narrow down the possible solution to only one.

STATEMENT ANALYSIS

St 1: a = 4b. Since b can take infinite possible values.NOT SUFFICIENT. Hence option a and d eliminated.
St 2: a+b = 100. A and b again can take infinite possible values. NOT SUFFICIENT. Hence option a, b and d is eliminated.

St1 & St 2: we have two equations and two variable. By solving, we get a =80, b = 20. Therefore, a - b = 60. SUFFICIENT. Option E eliminated.

Hence Option C is the answer.
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Re: If a > b, how much greater than b is a ? &nbs [#permalink] 23 Feb 2017, 03:40
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