Is the area of the top of a rectangular pool larger than 1000 square f

Question

Tough and Tricky questions: Geometry.

Is the area of the top of a rectangular pool larger than 1000 square feet?

(1) The pool’s top measures 50 feet diagonally.
(2) One side of the pool’s top measures 25 feet.

Kudos for a correct  solution .

minwoswoh · Answer

Question Stem: "Is ab > 1,000?"

Statement 1 
a^2 + b^2 = 50^2
Insufficient

Statement 2 
a = 25
Insufficient

Statement 1 + 2 
a^2 + b^2 = 50^2
25^2 + b^2 = 50^2

Sufficient. Correct Answer = C

Bonus Track 
You will yield b^2 = 1,875
This actually has 2 solutions: one positive and one negative. You can discard the negative one since this is a Geometry problem and you are dealing with lengths.

qw1981 · Answer

S1: Diagnol=50 units. We cannot find the length of sides from this alone. Hence Not Suff.

S2: length of one side is 25 units. Not suff as we do not know what is the length of the 2nd side. HEnce Not suff.

Combining: We will get the length of second side. and then we can calculate the area.

HEnce answer is C.

Temurkhon · Answer

Question asks whether A*B>1000. Yes/No St 1. a^2+b^2=50^2. Can have 30,40,50 in this case Area>1000 (answer Yes) and sqrt100,sqrt2400, 50 in this case Area<1000 (anwer No). INSUFFICIENT St 2. 25*50=1250>1000 (answer Yes) and 25*4=100<1000 (answer No). INSUFFUCIENT St 1+2= 25^2+b^2=50^2. No need calculating, after finding other side we are able answer question definitely C

Bunuel · Answer

The correct answer is C.

Bunuel · Answer

OFFICIAL SOLUTION:

Statement (1) tells us the diagonal measure, but we don't know the dimensions. The pool’s top might be very long and narrow, measuring less than a foot on one side. In this case its area would be well under 1000 square feet. The pool could also be 30 by 40 feet, with a diagonal of 50 feet and an area of 1200 square feet. So we can't answer whether the area of the pool is greater than 1000 square feet.

Statement (2) tells us the length of one side, but we need the length and the width of the pool to determine its area.

Combining the two statements, we could use the Pythagorean theorem to determine the missing dimension of the pool. We could then determine whether the area is larger than 1000 square feet. Since this is a Data Sufficiency question, you should not waste time with the calculation.Since combining the statements gives us sufficiency, the correct answer is choice (C).

Note:  If you want to determine the actual area of the pool, you can use the properties of triangles to quickly calculate the area. Since the length of one side of the pool is half the length of the diagonal, we know that the triangle formed by the two sides of the pool and the diagonal is a 30-60-90 triangle. The side that is 25 feet must be the short side, and the longer side will be √3 times the length of the short side, or 25√3 feet.

The area is thus 25 × 25√3 = 625√3, which is larger than 1000 square feet.

CCMBA · Answer

We need to know the length and width of the rectangle.

(1) We only know the diagonal. This diagonal creates 2 right triangles. We know the hypotenuse but not the measures of the legs, which correspond to the length and width of the rectangle. NOT sufficient.

Strike A/D.

(2) We only know length, but not width. NOT sufficient.

Strike B.

(1/2) We can use pythagorean theorem (or recognize that we have ratios corresponding to 30-60-90) to determine the width as 25*rad3. We can solve for the area to determine whether it is greater than 1000. Sufficient.

The answer is C.

bumpbot · Answer

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Is the area of the top of a rectangular pool larger than 1000 square f

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Is the area of the top of a rectangular pool larger than 1000 square f

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