Question:

In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?

1. 5
2. 5.5
3. 6
4. 6.5
5. 7

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
As the area of square region PRTV is 81 then RT^2= 81--> RT= 9;
The area of square region
PQXW= QX^2= RS^2 and the area of square region XSTU= ST^2= (9−RS)^2
Given:
(9−RS)^2/RS^2= 1/4--> 9−RS/RS= 1/2--> RS= 6

Approach Solution 2:
RT=9 since area of square is 81
Let RS=x and ST=9-x
Ratio of the area of squares is 1:4
Hence x^2 = 4 (9-x)^2
Hence x = 2(9-x)
3x = 18 ... x=6

Approach Solution 3:
PRTV is a square, with area of 81 => RT = 9
RT = RS + ST = 9
RS^2 = 4ST ^ 2
=> RS = 2ST
=>3ST = 9
=> ST = 3
=> RS = 6

“In the figure above, the area of square region PRTV is 81, and the”- is a topic of the   Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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