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If (y^2 - 1)^(1/2) = 4, what is the value of y? 28 Aug 2017, 03:48
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A
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53% (01:46) correct 47% (01:58) wrong based on 451 sessions

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Fresh GMAT Club Tests' Challenge Question:



If \(\sqrt{y^2-1}=4\), what is the value of y?

(1) \(y < -\pi\)
(2) The greatest integer less than y is NOT a prime number


M35-116

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If (y^2 - 1)^(1/2) = 4, what is the value of y? 15 Nov 2021, 09:17
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Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(\sqrt{y^2-1}=4\), what is the value of y?

(1) \(y < -\pi\)
(2) The greatest integer less than y is NOT a prime number


M35-116
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Official Solution:


If \(\sqrt{y^2-1}=4\), what is the value of \(y\)?

Square \(\sqrt{y^2-1}=4\);

\(y^2-1=16\);

\(y=\sqrt{17}=4.somehting\) or \(y=-\sqrt{17}=-4.somehting\).

(1) \(y < -\pi\)

\(-\pi \approx -3.14\), so the above tells us that \(y < -3.14\), thus \(y=-\sqrt{17}\). Sufficient.

(2) The greatest integer less than \(y\) is NOT a prime number

Both \(y=\sqrt{17}=4.somehting\) and \(y=-\sqrt{17}=-4.somehting\) satisfy this statement.

If \(y=\sqrt{17}=4.somehting\), then the greatest integer less than \(y\) is 4, which is not a prime.

If \(y=-\sqrt{17}=-4.somehting\), then the greatest integer less than \(y\) is -5, which is not a prime.

Not sufficient.


Answer: A
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 28 Aug 2017, 03:53
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Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(\sqrt{y^2-1}=4\), what is the value of y?

(1) \(y < -\pi\)
(2) The greatest integer less than y is NOT a prime number
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y^2-1 = 16
y^2 = 17
y = +4.something & -4.something

(1) if y<-pi then y = -4.something
Sufficient

(2) greatest integer less than y is not a prime number
if y = 4.something then 4 is not a prime number
if y=-4.something then -5 is not a prime number
not sufficient

A
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 28 Aug 2017, 05:48
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From Q y^2=17;

S1: explicitly mentions y=-4.2.. as it is les than -3.14.

No sufficient info from 2
Hence A
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 28 Aug 2017, 12:16
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Answer to this should be D i.e. both statements are independently are sufficient
y^2-1 = 16
y^2 = 17
y = +4.something & -4.something

a) says y<−pi or y<-3.something, since -4.something is less than -3.something; we have one unique answer, hence A is sufficient.
b) says greatest integer less than y is NOT a prime number, now prime numbers are not negative so greatest integer less than +4.something is 4 which is not prime; we have one unique answer, hence B is sufficient.

Therefore, both statements can answer the Q and therefore answer choice is D.
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 29 Aug 2017, 04:00
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Answer to this should be D i.e. both statements are independently are sufficient
y^2-1 = 16
y^2 = 17
y = +4.something & -4.something

a) says y<−pi or y<-3.something, since -4.something is less than -3.something; we have one unique answer, hence A is sufficient.
b) says greatest integer less than y is NOT a prime number, now prime numbers are not negative so greatest integer less than +4.something is 4 which is not prime; we have one unique answer, hence B is sufficient.

Therefore, both statements can answer the Q and therefore answer choice is D.
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One common thing i have seen in GMAT DS question is that if D is sufficient then A and B both will give same answer. in your case you have A as -ve value and B as +ve value for the same equation which may not be possible.

As you mentioned prime cannot be negative then we can have -5 as well the answer for this option (-5 is not prime). So we have two different answer for B so answer should be A (IMO)
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 29 Aug 2017, 11:28
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Thanks Arpit .....

After having mentioned that -ve numbers are not prime, I missed to consider -5 as the other option.

Got it, Ans is A indeed.

Good luck for GMAT ...
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 30 Aug 2017, 10:56
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Hi,

Answer is D only but you have stated answer as +4. something from statement 2.

answer from second statement is also -4. something since greatest integer less than Y is not a prime number then it should bey has to be negative 4.something

ravjai81
Answer to this should be D i.e. both statements are independently are sufficient
y^2-1 = 16
y^2 = 17
y = +4.something & -4.something

a) says y<−pi or y<-3.something, since -4.something is less than -3.something; we have one unique answer, hence A is sufficient.
b) says greatest integer less than y is NOT a prime number, now prime numbers are not negative so greatest integer less than +4.something is 4 which is not prime; we have one unique answer, hence B is sufficient.

Therefore, both statements can answer the Q and therefore answer choice is D.
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If (y^2 - 1)^(1/2) = 4, what is the value of y? 24 Dec 2018, 04:09
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Bunuel

Fresh GMAT Club Tests' Challenge Question:



If \(\sqrt{y^2-1}=4\), what is the value of y?

(1) \(y < -\pi\)
(2) The greatest integer less than y is NOT a prime number
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Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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If (y^2 - 1)^(1/2) = 4, what is the value of y? 19 Jan 2023, 05:30
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