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What is the value of a - b ?

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What is the value of a - b ?  [#permalink]

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New post 15 Jan 2014, 01:50
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A
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D
E

Difficulty:

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Question Stats:

80% (00:32) correct 20% (00:42) wrong based on 651 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the value of a - b ?

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

Data Sufficiency
Question: 37
Category: Algebra First- and second- degree equations
Page: 155
Difficulty: 550


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Re: What is the value of a - b ?  [#permalink]

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New post 15 Jan 2014, 01:50
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Re: What is the value of a - b ?  [#permalink]

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New post 15 Jan 2014, 23:50
Hi Bunuel,

I think that the second statement is (a-b)² rather than (a-b).
Am I right?

Thanks.
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Re: What is the value of a - b ?  [#permalink]

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New post 16 Jan 2014, 00:52
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.

Answer: (A)
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Re: What is the value of a - b ?  [#permalink]

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Re: What is the value of a - b ?  [#permalink]

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New post 18 Jan 2014, 13:49
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.

Answer: A.


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 ?  [#permalink]

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New post 19 Jan 2014, 09:36
1
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.

Answer: A.


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 ?  [#permalink]

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New post 27 Nov 2014, 06:23
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.

Answer: A.


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 ?  [#permalink]

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New post 27 Nov 2014, 06:27
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?


The correct answer is A.

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: What is the value of a - b ?  [#permalink]

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New post 23 Mar 2017, 10:40
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 ? &nbs [#permalink] 23 Mar 2017, 10:40
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