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

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New post 17 Jul 2015, 01:24
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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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Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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New post 17 Jul 2015, 02:05
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
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Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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New post 17 Jul 2015, 02:56
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
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Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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New post 17 Jul 2015, 11:25
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
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Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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New post 17 Jul 2015, 11:59
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
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Re: Let y = 2g + x^2 and g = 5x + 1. If g^2 = 256, then which of the  [#permalink]

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New post 19 Jul 2015, 12:57
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).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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

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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, 11:07
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