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# What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16

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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
The Question 37, Page 155 in Data Sufficiency Sample Questions of Quant Review is as follows:

What is the value of a - b ?

(1) $$a = b + 4$$
(2) $$(a - b)^2 = 16$$

Solution:

Statement (1)

$$a= b+4$$
Or, $$a-b=4$$
As the value of a-b can be uniquely determined, statement (1) is sufficient.

Statement (2)

Solving the equation, $$(a - b)^2 = 16$$,
we have either $$a-b= 4$$ or $$a-b= -4$$.
As the value of $$a-b$$ can not be uniquely determined, statement (2) is not sufficient.

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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
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Bunuel wrote:
SOLUTION

What is the value of a - b ?

(1) a = b + 4 --> re-arrange: a-b=4. Sufficient.

(2) (a - b)^2 = 16 --> a-b=4 or a-b=-4. Not sufficient.

how is 1 sufficient when a & b can still be any combination of numbers i.e. (0,4), (1,5) (2,6).....and on and on
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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
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TroyfontaineMacon wrote:
Bunuel wrote:
SOLUTION

What is the value of a - b ?

(1) a = b + 4 --> re-arrange: a-b=4. Sufficient.

(2) (a - b)^2 = 16 --> a-b=4 or a-b=-4. Not sufficient.

how is 1 sufficient when a & b can still be any combination of numbers i.e. (0,4), (1,5) (2,6).....and on and on

Yes but we are asked to find the value of a-b, not the individual values of a and b.
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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
Bunuel wrote:
TroyfontaineMacon wrote:
Bunuel wrote:
SOLUTION

What is the value of a - b ?

(1) a = b + 4 --> re-arrange: a-b=4. Sufficient.

(2) (a - b)^2 = 16 --> a-b=4 or a-b=-4. Not sufficient.

how is 1 sufficient when a & b can still be any combination of numbers i.e. (0,4), (1,5) (2,6).....and on and on

Yes but we are asked to find the value of a-b, not the individual values of a and b.

Hi Bunuel,

I have learnt from GMATClub that the root of a positive number is always positive-so root of 16 should only be 4 right (for GMAT purposes). So-the answer should be D right?
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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
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KS15 wrote:
Bunuel wrote:
TroyfontaineMacon wrote:

how is 1 sufficient when a & b can still be any combination of numbers i.e. (0,4), (1,5) (2,6).....and on and on

Yes but we are asked to find the value of a-b, not the individual values of a and b.

Hi Bunuel,

I have learnt from GMATClub that the root of a positive number is always positive-so root of 16 should only be 4 right (for GMAT purposes). So-the answer should be D right?

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt[4]{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.
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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
Is this really a 550-level question?
Looks like 400-level one
Just kidding......;
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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
Bunuel wrote:
What is the value of a - b ?

(1) a = b + 4
(2) (a - b)^2 = 16

Solution:

Question Stem Analysis:

We need to determine the value of a - b.

Statement One Alone:

Since a = b + 4, we have a - b = (b + 4) - b = 4. Statement one alone is sufficient.

Statement Two Alone:

Taking the square root of both sides (and recall that √(x^2) = |x|), we have:

|a - b| = 4

This means a - b can be either 4 or -4. Statement two alone is not sufficient.

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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
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Re: What is the value of a - b ? (1) a = b + 4 (2) (a - b)^2 = 16 [#permalink]
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