If (y^2 - 1)^(1/2) = 4, what is the value of y?

Question

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

Bunuel · Accepted Answer

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

Luckisnoexcuse · Answer

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

Arsh4MBA · Answer

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

ravjai81 · Answer

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.

NeverGiveUp- Arpit · Answer

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)

ravjai81 · Answer

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 ...

atulindia · Answer

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

Bunuel · Answer

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?

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GMAT Data Sufficiency (DS) Questions

If (y^2 - 1)^(1/2) = 4, what is the value of y?

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