If 20x + 30y = 280, what is the value of x?

Question

(1) 4x = 56 – 6y
(2) y^2 = 16

Kudos for a correct  solution .

Skywalker18 · Answer

1.
4x = 56 - 6y
=>4x + 6y =56
This equation is same as 20 x +30 y =280
Not sufficient .

2. y^2=16
=> y= +4 or -4

Substituting the values of y in the original equation will give us 2 different values for X.
Not sufficient .

Answer E .

GMATinsight · Answer

Given : 20x + 30y = 280

i.e. 2x + 3y = 28

Question  : x = ?

Statement 1 : 4x = 56 – 6y 
i.e. 4x + 6y = 28
i.e. 2x + 3y = 28
NOT SUFFICIENT

Statement 2 : y^2 = 16 
i.e. y =  + 4
@y =+4, x = 8
@y =-4, x = 20
NOT SUFFICIENT

Combining the two statement   
Combining the statement is of no use as first statement is of no use because it's reproduction of the information available in question stem. Hence
NOT SUFFICIENT

Answer: Option E

sunita123 · Answer

If 20x + 30y = 280, what is the value of x?

Statement 1
4x = 56 – 6y---This equation is same (in reduced form) as the question stem
2 variables, one equation 
So not sufficient

Statement 2
y^2 = 16
y=+4 , -4

for 2 values of y , 20x + 30y = 280 will give 2 values of x
So not sufficient

Combine statement 1 & Statement 2
No new result as statement 1 is the same as the question stem
So not sufficient
Hence Answer is E

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value?  This question asks for the value of x.

Given information in the question stem or diagram: 20x + 30y = 280. This should be simplified before you move to the statements. Divide all terms by 10 to see that this equation is really 2x + 3y = 28. Note: On the GMAT, you should always simplify algebraically whenever you are given information that is not in simplified form.

Statement 1: 4x = 56 – 6y. This statement appears to give you a second linear equation, which would be sufficient to solve for x when combined with the given information. However, before you do anything with this equation you should simplify it as you did with the question. If you add 6y to both sides of the equation and divide by 2, you see that this equation is really the same as the given equation: 2x + 3y = 28. These are not two distinct linear equations so this information is not sufficient. Eliminate choices A and D. Note: Be ready for this set-up in Data Sufficiency algebra questions: the “disguised” second equation that is really the same as the first.

Statement 2: y^2 = 16 or y = 4 or -4. The equation gives two different values for y, but it is important to glance at the original equation to make sure that the different values for y will actually result in different values for x. In this case they do as the original equation is a linear equation. Since this information gives you two different values for x it is not sufficient.

Together: Given that the equation from Statement 1 is the same as in the given information, the analysis of the two statements together is the same as for Statement 2. Statement 1 is no help and since Statement 2 is not sufficient alone,  the answer is E .

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If 20x + 30y = 280, what is the value of x?

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GMAT Data Sufficiency (DS) Questions

If 20x + 30y = 280, what is the value of x?

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