If a > b, How much Greater than b is a?

Question: 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.

1. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
2. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If a is greater than b How much Greater than b is a”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

It is given in the question that a > b
It is asked in the question to find out how much a is greater than b.
We are given two statements and we are asked to find out if the statements are sufficient to get the answer.
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 says:
b = a/4
Hence, a - b = a - a/4 = 3a/4
But this does not give us the values of both variables.
This statement is not sufficient to get the answer.

Statement 2 says:
a+b = 100
This statement is not sufficient to get the answer.
Combining both the statements:
We can find the value of a and b separately by combining the following equations:
b = a/4 and a+b = 100
Hence we can find the value of a-b.
This statement is sufficient to get the answer.

Thus the answer is C.

Approach Solution 2:

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.

Approach Solution 3:

It is given in the question that a > b

It is asked in the question to find out how much a is greater than b.

1. B = A/ 4 is not sufficient
2. A+B = 100 is not sufficient
3. Combining both A + A/4 = 100

A = 80 B = 20
So the answer will be C.

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