Quadratic equations on Algebra strat guide 2

[jannek.fahrenholz]

In PROBLEM SET chapter 5 there is number 10 the following problem:

Data sufficiency: What is x?

(1) x = 4y - 4
(2) xy = 8

Answer as stated in solutions shall be E, both are not sufficient. I did everything like in solutions and I do have the same values such as y=-1 and 2 as well as x = -8 and 4.

Why is this not sufficient. My answer would be D, both together are sufficient?

Thanks for your help and best regs.

[jnelson0612]

In PROBLEM SET chapter 5 there is number 10 the following problem:

Data sufficiency: What is x?

(1) x = 4y - 4
(2) xy = 8

Answer as stated in solutions shall be E, both are not sufficient. I did everything like in solutions and I do have the same values such as y=-1 and 2 as well as x = -8 and 4.

Why is this not sufficient. My answer would be D, both together are sufficient?

Thanks for your help and best regs.

Hi Jannek,
Let's first review the answer choices, because I'm a little concerned about your description of answer D.
A=statement 1 only is sufficient
B=statement 2 only is not sufficient
C=1 and 2 must be used together to be sufficient
D=either 1 or 2 is sufficient
E=neither is sufficient and you just can't answer the question

Now, let's work the problem:

What is x?

(1) x = 4y - 4
(2) xy = 8

The question is asking us for one and only one value of x. If I can use a statement and obtain more than one value of x that statement is not sufficient. A good way to handle this would be to test numbers that fit the statement. Let's start with statement 1:

1) x = 4y - 4
If y=1 then x=0
If y=2 then x=4
Not sufficient. I already have two values for x. Cross out answer choices A and D.

2) xy=8
If x=1 then y=8
If x=2 then y=4
Not sufficient. I already have two values for x. Cross out answer choice B.

Now, I should try to combine then. I know that xy=8 from statement 2. If I divide both sides by x I get y=8/x. Let's take 8/x and sub it in for y on the first equation:

x=4(8/x) - 4
thus
x=32/x - 4

I want to get the x out of the denominator. Let me multiply both sides by x. I get:
x^2 = 32 - 4x

Subtract 32 from both sides. Add 4x to both sides to create a quadratic. We get:
x^2 + 4x - 32 = 0
Factor:
(x+8)(x-4) = 0

Set (x+8)=0 and (x-4)=0. x can be -8 or 4. I still don't know what x is; two values is not good enough. I need one and only one value. Cross off answer choice C. Choose E.

[jannek.fahrenholz]

In PROBLEM SET chapter 5 there is number 10 the following problem:

Data sufficiency: What is x?

(1) x = 4y - 4
(2) xy = 8

Answer as stated in solutions shall be E, both are not sufficient. I did everything like in solutions and I do have the same values such as y=-1 and 2 as well as x = -8 and 4.

Why is this not sufficient. My answer would be D, both together are sufficient?

Thanks for your help and best regs.

Hi Jannek,
Let's first review the answer choices, because I'm a little concerned about your description of answer D.
A=statement 1 only is sufficient
B=statement 2 only is not sufficient
C=1 and 2 must be used together to be sufficient
D=either 1 or 2 is sufficient
E=neither is sufficient and you just can't answer the question

Now, let's work the problem:

What is x?

(1) x = 4y - 4
(2) xy = 8

The question is asking us for one and only one value of x. If I can use a statement and obtain more than one value of x that statement is not sufficient. A good way to handle this would be to test numbers that fit the statement. Let's start with statement 1:

1) x = 4y - 4
If y=1 then x=0
If y=2 then x=4
Not sufficient. I already have two values for x. Cross out answer choices A and D.

2) xy=8
If x=1 then y=8
If x=2 then y=4
Not sufficient. I already have two values for x. Cross out answer choice B.

Now, I should try to combine then. I know that xy=8 from statement 2. If I divide both sides by x I get y=8/x. Let's take 8/x and sub it in for y on the first equation:

x=4(8/x) - 4
thus
x=32/x - 4

I want to get the x out of the denominator. Let me multiply both sides by x. I get:
x^2 = 32 - 4x

Subtract 32 from both sides. Add 4x to both sides to create a quadratic. We get:
x^2 + 4x - 32 = 0
Factor:
(x+8)(x-4) = 0

Set (x+8)=0 and (x-4)=0. x can be -8 or 4. I still don't know what x is; two values is not good enough. I need one and only one value. Cross off answer choice C. Choose E.

Ok. Thank you Jamie. Now I now that only one value is enough. That helped.

[tim]

:)