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26 Apr 2019, 03:15
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B
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Difficulty:
5%
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Question Stats:
89% (01:33) correct
11%
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wrong
based on 1606
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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.
DS75602.01
OG2020 NEW QUESTION
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Updated on: 14 Apr 2022, 12:26
Originally posted by BrentGMATPrepNow on 09 May 2019, 06:26.
Last edited by BrentGMATPrepNow on 14 Apr 2022, 12:26, edited 2 times in total.
Last edited by BrentGMATPrepNow on 14 Apr 2022, 12:26, edited 2 times in total.
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Bunuel
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 + (y + z)]/2 = 39
Replace z (aka TS) with 6 to get: (x)(y + y + 6)/2 = 39
Simplify to get: (x)(2y + 6)/2 = 39
Multiply both sides by 2 to get: (x)(2y + 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
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General Discussion
26 Apr 2019, 06:32
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We can do everything algebraically: If we use W and L to represent the width and length of the rectangle, so W is the length of PQ (which we want to find), and if we use B to represent the line TS, which is the base of the triangle, then the area of the rectangle is LW, and the area of the triangle is BW/2.
Statement 1 tells us that if we add the rectangle's area and the triangle's area, we get 39. It also tells us that B = 6. So
LW + (BW/2) = 39
LW + (6W/2) = 39
LW + 3W = 39
W(L+3) = 39
So we might have W = 1 and L = 36, say, or W = 3 and L = 10, among other possibilities.
But there's a much faster way to see that Statement 1 is not sufficient. If you just draw the triangle's base TS of length 6, and draw some height RT that isn't too long (so the area of the triangle alone is less than 39), if we then start extending a rectangle to the left by drawing PT and QR, the area of the entire shape will get larger and larger the longer we make the rectangle's length. For exactly one length of the rectangle, the area of the entire shape will be exactly 39. But that length will be different for any height we choose - the length will need to be big if the height is small, and will need to be small if the height is big, so we can't possibly find the dimensions of the figure.
Statement 2 tells us LW = 30 and L = 10, so W = 3 and Statement 2 is sufficient. The answer is B.
Statement 1 tells us that if we add the rectangle's area and the triangle's area, we get 39. It also tells us that B = 6. So
LW + (BW/2) = 39
LW + (6W/2) = 39
LW + 3W = 39
W(L+3) = 39
So we might have W = 1 and L = 36, say, or W = 3 and L = 10, among other possibilities.
But there's a much faster way to see that Statement 1 is not sufficient. If you just draw the triangle's base TS of length 6, and draw some height RT that isn't too long (so the area of the triangle alone is less than 39), if we then start extending a rectangle to the left by drawing PT and QR, the area of the entire shape will get larger and larger the longer we make the rectangle's length. For exactly one length of the rectangle, the area of the entire shape will be exactly 39. But that length will be different for any height we choose - the length will need to be big if the height is small, and will need to be small if the height is big, so we can't possibly find the dimensions of the figure.
Statement 2 tells us LW = 30 and L = 10, so W = 3 and Statement 2 is sufficient. The answer is B.
