In the figure above, PQRT is a rectangle. What is the length

[AbeNeedsAnswers]

In the figure above, PQRT is a rectangle. What is the length of segment PQ ?

(1) The area of region PQRS is 39 and TS = 6.
(2) The area of region PQRT is 30 and QR = 10.

B

Source: Official Guide 2020

[Brent@GMATPrepNow]

In the figure above, PQRT is a rectangle. What is the length of segment PQ ?

(1) The area of region PQRS is 39 and TS = 6.
(2) The area of region PQRT is 30 and QR = 10.

B

Source: Official Guide 2020

Let's assign some variables to some of the lengths...


Target question: What is the value of x?

Statement 1: The area of region PQRS is 39 and TS = 6.
Region PQRS is a TRAPEZOID
Area of trapezoid = (height)(base1 + base2)/2
So, we get: (x)(y + z)/2 = 39
Replace z (aka TS) with 6 to get: (x)(y + 6)/2 = 39
Multiply both sides by 2 to get: (x)(y + 6) = 78
At this point, we can see that there's no way to definitively solve this equation for x (aka PQ)
Statement 1 is NOT SUFFICIENT

Statement 2: The area of region PQRT is 30 and QR = 10
PQRT is a rectangle, so the area = (base)(height)
We can write: xy = 30
Replace y (aka QR) with 10 to get: (x)(10) = 30
Solve: x = 3 (i.e., PQ = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

[[email protected]]

Hi All,

We're told that PQRT is a rectangle. We're asked fo the length of segment PQ. This question can be solved with a mix of Geometry rules and TESTing VALUES. To start, when dealing with complex shapes, it helps to break the shape down into 'pieces': here, we're dealing with a rectangle and a right triangle.

(1) The area of region PQRS is 39 and TS = 6.

TS is the 'base' of the triangle, but we don't know anything about either the height/width of the triangle/rectangle or the length of the rectangle. Thus, there are lots of possible values for PQ. Here are two examples:
IF....
PQ = 1, then the area of the triangle is (1/2)(6)(1) = 3 and the area of the rectangle is 39 - 3 = 36. This makes the length 36 and the answer is 1.
PQ = 2, then the area of the triangle is (1/2)(6)(2) = 6 and the area of the rectangle is 39 - 6 = 33. This makes the length 16.5 and the answer is 2.
Fact 1 is INSUFFICIENT

(2) The area of region PQRT is 30 and QR = 10.

The information in Fact 2 gives us the length of the rectangle and the area of the rectangle, so we can solve for the width:
Area = (Base)(Height)
30 = (10)(Height)
3 = Height
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

In the figure above, PQRT is a rectangle. What is the length of segment PQ ?

(1) The area of region PQRS is 39 and TS = 6.
(2) The area of region PQRT is 30 and QR = 10.

B

Source: Official Guide 2020

Solution:

Question Stem Analysis:

We need to determine the length of segment PQ. Notice that it’s the height of trapezoid PQRS.

Statement One Alone:

Since we don’t know the length of PT or QR (except that they are equal in length), we can’t determine PQ. For example, if PT = QR = 2, then the lower base PS of trapezoid PQRS is 8. So PQ = 39/[½(2 + 8)] = 39/5 = 7.8. However, if PT = QR = 3, then the lower base PS of trapezoid PQRS is 9. So PQ = 39/[½(3 + 9)] = 39/6 = 6.5. Statement one alone is not sufficient.

Statement Two Alone:

Since PQRT is a rectangle and QR (the length of rectangle PQRT) is 10, then the width of rectangle PQRT is PQ, and PQ = 30/10 = 3. Statement two alone is sufficient.

Answer: B