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# Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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17 Jul 2015, 00:24
2
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Difficulty:

25% (medium)

Question Stats:

82% (02:18) correct 18% (03:09) wrong based on 102 sessions

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Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 256, then which of the following can be a value of 2y + 3g?

A. 100
B. 130
C. 141
D. 142
E. 160

Kudos for a correct solution.

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Joined: 28 Jan 2013
Posts: 31
Location: United States
GPA: 3.1
WE: Information Technology (Consulting)
Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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17 Jul 2015, 01:05
1
Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 256, then which of the following can be a value of 2y + 3g?

g^2 = 256
g= 16,-16

if g=16

16 = 5x + 1
x =3

y = 2g + x^2
y = 41

2y + 3g = 130

if g=-16

-16 = 5x +1
x = -17/5

y = 2g + x^2
y = 2(-16) + (-17/5)^2
y will be a negative value

2y + 3g will be a negative value

Since all the option are positive

Ans: B
CEO
Joined: 20 Mar 2014
Posts: 2636
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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17 Jul 2015, 01:56
Bunuel wrote:
Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 256, then which of the following can be a value of 2y + 3g?

A. 100
B. 130
C. 141
D. 142
E. 160

Kudos for a correct solution.

g^2 = 256 ---> g = 16 or -16 ----> g = 5x+1 ---> x =3 for g =16---> y =41

Thus 2y+3g = 82+48 = 130, B is the correct answer
Manager
Joined: 20 Jul 2011
Posts: 80
GMAT 1: 660 Q49 V31
Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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17 Jul 2015, 10:25
1
Bunuel wrote:
Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 256, then which of the following can be a value of 2y + 3g?

A. 100
B. 130
C. 141
D. 142
E. 160

Kudos for a correct solution.

Since g^2 = 256, g could be +16 or -16.

If g = 16, 5x + 1 = 16 => x = 3
If g = -16, 5x + 1 = -16 => x = -17/5

Solving for y,
if x = 3, y = 2g + x^2 => y = 2*16 + 3^2 => y = 41.
=> 2y + 3g => 2*41 + 3*16 => 130.

If x =-17/5, y = 2*-16 + (-17/5)^2 => -511/25, Since x is negative and g is also negative, 2y+3g is going to be negative. But all the options are positive. Hence can be ignored.

Hence Answer is 130. Option B
Intern
Joined: 01 Jul 2014
Posts: 26
Location: India
GMAT 1: 690 Q49 V34
GPA: 3.2
Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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17 Jul 2015, 10:59
1
g^2 = 256 ==> g=16 or -16

x = (g-1)/5 ==> x = 3 (for g = 16) or -17/5 ( g=-16)

y = 2g + x^2 ==> y = 41 ( g=16, x=3) or y = -ve value

2y+3g = 2*41 + 3*16 = 130

no option for any negative value
Math Expert
Joined: 02 Sep 2009
Posts: 52390
Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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19 Jul 2015, 11:57
Bunuel wrote:
Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 256, then which of the following can be a value of 2y + 3g?

A. 100
B. 130
C. 141
D. 142
E. 160

Kudos for a correct solution.

800score Official Solution:

First note that g can either be 16 or -16. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 16 and then g = -16. If g = 16, then x = 3. If g = -16, then x = -17/5. Since all of our solutions are whole numbers, we can dismiss -17/5. We use g = 16 and x = 3 to determine the value of y: y = 2(16) + 9 = 41. Finally, we substitute the values for y and g into the last expression to determine its value : 2(41) + 3(16) = 82 + 48 = 130; the correct answer is (B).
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Posts: 9464
Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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26 Mar 2017, 10:07
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Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the &nbs [#permalink] 26 Mar 2017, 10:07
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