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

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Math Expert
Joined: 02 Sep 2009
Posts: 56277
If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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28 Aug 2017, 03:48
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54% (01:44) correct 46% (01:55) wrong based on 198 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

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Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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28 Aug 2017, 03:53
1
Bunuel wrote:

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

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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Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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28 Aug 2017, 05:48
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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Joined: 29 Jul 2012
Posts: 15
Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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28 Aug 2017, 12:16
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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Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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29 Aug 2017, 04:00
ravjai81 wrote:
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.

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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Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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29 Aug 2017, 11:28
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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Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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30 Aug 2017, 10:56
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 wrote:
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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Posts: 56277
Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?  [#permalink]

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24 Dec 2018, 04:09
Bunuel wrote:

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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Re: If (y^2 - 1)^(1/2) = 4, what is the value of y?   [#permalink] 24 Dec 2018, 04:09
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