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If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of
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22 Mar 2021, 10:18
22 Mar 2021, 10:18
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75% (00:56) correct
25% (01:20) wrong based on 20 sessions
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If \((x + 2)^2 = 9\) and \((y + 3)^2 = 25\), then what is the maximum value of \(\frac{x}{y}\)?
(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of
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22 Mar 2021, 10:58
22 Mar 2021, 10:58
1
Carcass wrote:
If \((x + 2)^2 = 9\) and \((y + 3)^2 = 25\), then what is the maximum value of \(\frac{x}{y}\)?
(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(x + 2)² = 9
We have (something)² = 9
So, EITHER something = 3 OR something = -3
In other words, EITHER x + 2= 3 OR x + 2 = -3
If x + 2= 3. then x = 1
If x + 2= -3. then x = -5
(y + 3)² = 25
We have (something)² = 25
So, EITHER something = 5 OR something = -5
In other words, EITHER y + 3= 5 OR y + 3 = -5
If y + 3= 5, then y = 2
If y + 3= -5, then y = -8
We want to MAXIMIZE the value of x/y
If the x-value and y-value have OPPOSITE signs, x/y will be NEGATIVE
If the x-value and y-value have the SAME sign, x/y will be POSITIVE
So, need the x-value and y-value have the SAME sign
Try #1
x/y = 1/2
Try #2
x/y = (-5)/(-8) = 5/8
Since 5/8 is greater than 1/2, the correct answer is C
Re: If (x + 2)^2 = 9 and (y + 3)^2 = 25, then what is the maximum value of
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24 Mar 2021, 00:51
24 Mar 2021, 00:51
The questions involves taking a square root, hence we need to be careful to consider even the negative values.
x+2 = +3 or -3
y+3 = +5 or -5
Considering all possible cases,
x can be 1 or -5
y can be 2 or -8
4 possibilities of x/y are 1/2, 1/(-8), (-5)/2,(-5)(-8)
Out of these, 5/8 is the greatest, hence option C is correct
x+2 = +3 or -3
y+3 = +5 or -5
Considering all possible cases,
x can be 1 or -5
y can be 2 or -8
4 possibilities of x/y are 1/2, 1/(-8), (-5)/2,(-5)(-8)
Out of these, 5/8 is the greatest, hence option C is correct
