I saw the following question posted on the website but, for some reason, I could not find the method used to solve the problem. I have the following concerns with this question:
- Please let me know if what I have stated below is correct.
- If so, is there a faster way to understand this problem? This definitely took me more than 2 minutes, and I am not sure if what I have is the right method.
The numbers a, b, and c are all positive. If b^2 + c^2 = 17, what is the value of a^2 + c^2?
(1) a-b=3
(2) (a+b)/(a-b)=7
- First, the question is asking for a value. Therefore, either statement must result in ONE value in order to be sufficient.
- Second, I need the numerical value of c^2 AND a^2 to obtain sufficiency.
(1) a-b=3 -> b=a-3 -> b^2=a^2-6a+9.
b^2+c^2=17 -> a^2-6a+9+c^2=17 -> a^2+c^2=17+6a-9 -> a^2+c^2=8+6a
Insufficient. Values of c^2 & a^2 are not given. Also, 2 variables & 1 equation = no good. A&D are eliminated, BCE remain.
(2) (a+b)/(a-b) = 7 -> a+b=7(a-b) -> a+b=7a-7b -> -6a=-8b -> b=(3a)/4
b^2+c^2=17 -> (((3a)^2)/(4^2))+c^2=17 -> ((9a^2)/16)+c^2=17.
Insufficient. Values of c^2 & a^2 are not given. Also, 2 variables & 1 equation = no good. B is eliminated. C&E remain.
(1)&(2)
From (1): a^2+c^2=8+6a. From (2): ((9a^2)/16)+c^2=17.
Together: 8+6a-a^2=17-((9a^2)/16). 1 equation, 1 variable = good. We can solve for a and we can solve for a^2. Plug in a^2 to get c^2. c^2 AND a^2 are determined. Sufficient. Answer is C.
- Please let me know if what I have stated below is correct.
- If so, is there a faster way to understand this problem? This definitely took me more than 2 minutes, and I am not sure if what I have is the right method.
The numbers a, b, and c are all positive. If b^2 + c^2 = 17, what is the value of a^2 + c^2?
(1) a-b=3
(2) (a+b)/(a-b)=7
- First, the question is asking for a value. Therefore, either statement must result in ONE value in order to be sufficient.
- Second, I need the numerical value of c^2 AND a^2 to obtain sufficiency.
(1) a-b=3 -> b=a-3 -> b^2=a^2-6a+9.
b^2+c^2=17 -> a^2-6a+9+c^2=17 -> a^2+c^2=17+6a-9 -> a^2+c^2=8+6a
Insufficient. Values of c^2 & a^2 are not given. Also, 2 variables & 1 equation = no good. A&D are eliminated, BCE remain.
(2) (a+b)/(a-b) = 7 -> a+b=7(a-b) -> a+b=7a-7b -> -6a=-8b -> b=(3a)/4
b^2+c^2=17 -> (((3a)^2)/(4^2))+c^2=17 -> ((9a^2)/16)+c^2=17.
Insufficient. Values of c^2 & a^2 are not given. Also, 2 variables & 1 equation = no good. B is eliminated. C&E remain.
(1)&(2)
From (1): a^2+c^2=8+6a. From (2): ((9a^2)/16)+c^2=17.
Together: 8+6a-a^2=17-((9a^2)/16). 1 equation, 1 variable = good. We can solve for a and we can solve for a^2. Plug in a^2 to get c^2. c^2 AND a^2 are determined. Sufficient. Answer is C.
