Gmat_mission wrote: ↑Fri Jan 08, 2021 4:20 am
DS06861_f001.png
In the figure above, \(PQR\) and \(STU\) are identical equilateral triangles, and \(PQ = 6.\) What is the perimeter of polygon \(PQWTUVR?\)
(1) Triangle \(SWV\) has perimeter \(9.\)
(2) \(VW\) has length \(3.5.\)
Answer:
A
Source: Official Guide
Target question: What is the perimeter of polygon PQWTUVR?
Let
x,
y and
z represent the lengths below.
Since each side of the equilateral triangle has lengths 6, we can label the sides as follows:
Finally, let's let QW have length
a and let VR have length
b
We know that
a +
z +
b = 6.
So, it follows that:
a +
b =
6 -
z
At this point we are ready to calculate the perimeter of PQWTUVR
The perimeter =
6 +
a + (
6 - x) +
6 + (
6 - y) +
b +
6
=
30 -
x -
y +
a +
b
Since
a +
b = 6 -
z, we can substitute to get:
Perimeter =
30 -
x -
y +
6 -
z
Simplify to get:
Perimeter =
36 - (
x +
y +
z)
In other words, to find the perimeter of PQWTUVR, we need to know the value of
x +
y +
z.
REPHRASED target question: What is the value of x + y + z?
Statement 1: Triangle SWV has perimeter 9.
In other words,
x +
y +
z = 9
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: VW has length 3.5
In other words,
z = 3.5
We still don't have enough information to find the value of
x +
y +
z.
Since we can’t answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
