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505-555 Level|   Algebra|                  
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ganand
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Is y = 6? (1) y^2 = 36 (2) y^2 - 7y + 6 = 0 08 Apr 2017, 03:10
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

76% (00:44) correct 24% (00:47) wrong based on 1041 sessions

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Is \(y = 6\) ?


(1) \(y^{2} = 36\)

(2) \(y^{2} - 7y + 6 = 0\)

Source: Quant Review 1st Edition
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C
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Bunuel
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Is y = 6? (1) y^2 = 36 (2) y^2 - 7y + 6 = 0 08 Apr 2017, 03:51
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Is \(y = 6\) ?

(1) \(y^{2} = 36\) --> \(y = 6\) or \(y = -6\). Not sufficient.

(2) \(y^{2} - 7y + 6 = 0\) --> \((y - 6)(y - 1) = 0\) --> \(y = 6\) or \(y = 1\). Not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(y = 6\). Sufficient.

Answer: C.
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Is y = 6? (1) y^2 = 36 (2) y^2 - 7y + 6 = 0 10 Apr 2017, 18:27
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1 is insufficient as y = - 6 or 6.
2 is insufficient as y is equal to 6 or 1

1 & 2 combined, y is 6.
Therefore, the answer is C
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Is y = 6? (1) y^2 = 36 (2) y^2 - 7y + 6 = 0 13 Mar 2020, 06:28
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ganand
Is \(y = 6\) ?


(1) \(y^{2} = 36\)

(2) \(y^{2} - 7y + 6 = 0\)

Source: Quant Review 1st Edition
Show more

Target question: Is y = 6 ?

Statement 1: y² = 36
If y² = 36, then EITHER y = 6 OR y = -6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y² - 7y + 6 = 0
Factor the equation to get: (y - 1)(y - 6) = 0
So, EITHER y - 1 = 0 OR y - 6 = 0
So, EITHER y = 1 OR y = 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER y = 6 OR y = -6
Statement 2 tells us that y = 1 OR y = 6
Since BOTH statements are TRUE, we can conclude that y = 6
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

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Brent
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Is y = 6? (1) y^2 = 36 (2) y^2 - 7y + 6 = 0 12 Jul 2025, 22:54
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The question is simple. But in many places it is said that sq rt of a number is always positive in GMAT. Yes, +6 or -6 if squared will give 36 but sq rt of 36 is always positive in GMAT? Bunuel
Bunuel
Is \(y = 6\) ?

(1) \(y^{2} = 36\) --> \(y = 6\) or \(y = -6\). Not sufficient.

(2) \(y^{2} - 7y + 6 = 0\) --> \((y - 6)(y - 1) = 0\) --> \(y = 6\) or \(y = 1\). Not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(y = 6\). Sufficient.

Answer: C.
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Is y = 6? (1) y^2 = 36 (2) y^2 - 7y + 6 = 0 12 Jul 2025, 23:22
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werty_123
The question is simple. But in many places it is said that sq rt of a number is always positive in GMAT. Yes, +6 or -6 if squared will give 36 but sq rt of 36 is always positive in GMAT? Bunuel
Bunuel
Is \(y = 6\) ?

(1) \(y^{2} = 36\) --> \(y = 6\) or \(y = -6\). Not sufficient.

(2) \(y^{2} - 7y + 6 = 0\) --> \((y - 6)(y - 1) = 0\) --> \(y = 6\) or \(y = 1\). Not sufficient.

(1)+(2) Intersection of values from (1) and (2) is \(y = 6\). Sufficient.

Answer: C.
Show more
Even roots cannot give negative result.

\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.


The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
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 \(x=\sqrt{9}=3\).
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