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555-605 (Medium)|   Algebra|      
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Carcass
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What is the value of a + b ? (1) (a + b) 2 = 4 (2) a = 2 b 30 Sep 2022, 00:53
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Difficulty:

25% (medium)

Question Stats:

68% (00:34) correct 32% (00:45) wrong based on 68 sessions

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What is the value of a + b ?

(1) (a + b)^2 = 4
(2) a = 2 − b


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B
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divyadna
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What is the value of a + b ? (1) (a + b) 2 = 4 (2) a = 2 b 09 Oct 2022, 08:28
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Statement 1: (a+b)^2=4
a+b=2 or a+b=-2
Statement 1 is insufficient.
Statement 2: a=2-b
a+b=2
Statement 2 is alone sufficient.
B is the correct answer

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Singhalatul87
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What is the value of a + b ? (1) (a + b) 2 = 4 (2) a = 2 b 09 Oct 2022, 11:10
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We need value of "a + b"

Let's screen the options
1. (a + b)^2 = 4 => a^2 + b^2 + 2ab = 4

All these variables are unknown, hence Insufficient

Eliminate A, D

2. a = 2 - b => can be restructured as, a + b = 2

Sufficient.

B is answer
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What is the value of a + b ? (1) (a + b) 2 = 4 (2) a = 2 b 01 Feb 2023, 08:51
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gmatphobia ,
Bunuel
If we solve Statement 1 in the following way , then we get only one value.

STATEMENT 1 .

(a+b)^2 = 4 .
Taking square root both sides.

a+b = \sqrt{4}
In GMAT square root has just the positive value.

Hence,
a+b = 2

So answer choice C is the answer.

Regards
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What is the value of a + b ? (1) (a + b) 2 = 4 (2) a = 2 b 02 Feb 2023, 09:38
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GMATTarget720plus
gmatphobia ,
Bunuel
If we solve Statement 1 in the following way , then we get only one value.

STATEMENT 1 .

(a+b)^2 = 4 .
Taking square root both sides.

a+b = \sqrt{4}
In GMAT square root has just the positive value.

Hence,
a+b = 2

So answer choice C is the answer.

Regards
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When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative 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 \(x=\sqrt{9}=3\).

Hope it helps.
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