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In two similar triangles (or rectangles), the ratio of their areas is the square of the ratio of their sides.

Given: ratio of diagonals \(= \frac{18}{15}=1.2\) (note that diagonals are the hypotenuses in right triangles made by width and length).

(1) The ratio of width to length is the same for both screens. This implies that the rectangles are similar, hence right triangles made by diagonals are similar as well, which means that the ratio of areas of triangles = ratio of areas of rectangles \(= ( \frac{18}{15} )^2 = 1.44\). Sufficient.

(2) The width of the 18''-screen is 20% greater than that of the 15''-screen. Given: the ratio of widths = 1.2 = ratio of diagonals (hypotenuse), so right triangles made by width and length are similar, (in right triangles if 2 corresponding sides are in the same ratio, in our case \(\frac{W}{w}=\frac{D}{d}=1.2\), then these right triangles are similar). Therefore the rectangles are similar too, which means that the ratio of areas of triangles = the ratio of areas of rectangles \(= ( \frac{18}{15} )^2=1.44\). Sufficient.

In two similar triangles (or rectangles), the ratio of their areas is the square of the ratio of their sides.

Given: ratio of diagonals \(= \frac{18}{15}=1.2\) (note that diagonals are the hypotenuses in right triangles made by width and length).

(1) The ratio of width to length is the same for both screens. This implies that the rectangles are similar, hence right triangles made by diagonals are similar as well, which means that the ratio of areas of triangles = ratio of areas of rectangles \(= ( \frac{18}{15} )^2 = 1.44\). Sufficient.

(2) The width of the 18''-screen is 20% greater than that of the 15''-screen. Given: the ratio of widths = 1.2 = ratio of diagonals (hypotenuse), so right triangles made by width and length are similar, (in right triangles if 2 corresponding sides are in the same ratio, in our case \(\frac{W}{w}=\frac{D}{d}=1.2\), then these right triangles are similar). Therefore the rectangles are similar too, which means that the ratio of areas of triangles = the ratio of areas of rectangles \(= ( \frac{18}{15} )^2=1.44\). Sufficient.

Answer: D

I did not follow the highlighted part. Ratio of widths is same as ratio of hypotenuse.

In two similar triangles (or rectangles), the ratio of their areas is the square of the ratio of their sides.

Given: ratio of diagonals \(= \frac{18}{15}=1.2\) (note that diagonals are the hypotenuses in right triangles made by width and length).

(1) The ratio of width to length is the same for both screens. This implies that the rectangles are similar, hence right triangles made by diagonals are similar as well, which means that the ratio of areas of triangles = ratio of areas of rectangles \(= ( \frac{18}{15} )^2 = 1.44\). Sufficient.

(2) The width of the 18''-screen is 20% greater than that of the 15''-screen. Given: the ratio of widths = 1.2 = ratio of diagonals (hypotenuse), so right triangles made by width and length are similar, (in right triangles if 2 corresponding sides are in the same ratio, in our case \(\frac{W}{w}=\frac{D}{d}=1.2\), then these right triangles are similar). Therefore the rectangles are similar too, which means that the ratio of areas of triangles = the ratio of areas of rectangles \(= ( \frac{18}{15} )^2=1.44\). Sufficient.

Answer: D

I did not follow the highlighted part. Ratio of widths is same as ratio of hypotenuse.

Stem says that the ratio of the diagonals is 18/15 = 1.2 and (2) says that the ration of widths is also 1.2. So, the ratio of widths = 1.2 = ratio of diagonals (hypotenuse).
_________________

I got this question right doing educated guess... I was sure about (a) BUT was short on time and I decided to guess on (d) because I identified that 20 % more combined with the known lenghts of the diagonal (15 and 18) was enough to know de ratio of the areas; but in the explanation it says that this is concluded because 18/15 = 1.2 and 20 % more is also 1.2... then I doubt If my thought was roght, for instance if instead of 20 % more would be 30 % more then what would be the answer? The same or it would change something?

I got this question right doing educated guess... I was sure about (a) BUT was short on time and I decided to guess on (d) because I identified that 20 % more combined with the known lenghts of the diagonal (15 and 18) was enough to know de ratio of the areas; but in the explanation it says that this is concluded because 18/15 = 1.2 and 20 % more is also 1.2... then I doubt If my thought was roght, for instance if instead of 20 % more would be 30 % more then what would be the answer? The same or it would change something?

Thanks

Best regards

Luis Navarro Looking for 700

No, in this case (30%) the statement wouldn't be sufficient.

Ratio of the areas of the triangles with sides \(18, \ 13, \ \sqrt{18^2-13^2}\) and \(15, \ 10, \ \sqrt{15^2-10^2}\) is NOT the same as the ratio of the areas of the triangles with sides \(18, \ 6.5, \ \sqrt{18^2-6.5^2}\) and \(15, \ 5, \ \sqrt{15^2-5^2}\).
_________________

I got this question right doing educated guess... I was sure about (a) BUT was short on time and I decided to guess on (d) because I identified that 20 % more combined with the known lenghts of the diagonal (15 and 18) was enough to know de ratio of the areas; but in the explanation it says that this is concluded because 18/15 = 1.2 and 20 % more is also 1.2... then I doubt If my thought was roght, for instance if instead of 20 % more would be 30 % more then what would be the answer? The same or it would change something?

Thanks

Best regards

Luis Navarro Looking for 700

No, in this case (30%) the statement wouldn't be sufficient.

Ratio of the areas of the triangles with sides \(18, \ 13, \ \sqrt{18^2-13^2}\) and \(15, \ 10, \ \sqrt{15^2-10^2}\) is NOT the same as the ratio of the areas of the triangles with sides \(18, \ 6.5, \ \sqrt{18^2-6.5^2}\) and \(15, \ 5, \ \sqrt{15^2-5^2}\).

I think this is a high-quality question and I agree with explanation. Can we solve this prob by doing this :

Let's assume 2x=18, then we know that in a rectangle triangle we have the legs given by x and xsqrt(3) same with 2x=15 We found that the stem is sufficient to solve the problem. the ratio is (9*9*sqrt(3))/(15/2*15/2*sqrt(3))=1.44

(2) The width of the 18''-screen is 20% greater than that of the 15''-screen. Given: the ratio of widths = 1.2 = ratio of diagonals (hypotenuse), so right triangles made by width and length are similar

How can u say the ratio of widths= ratio of diagonals?

(2) The width of the 18''-screen is 20% greater than that of the 15''-screen. Given: the ratio of widths = 1.2 = ratio of diagonals (hypotenuse), so right triangles made by width and length are similar

How can u say the ratio of widths= ratio of diagonals?

Ratio of lengths should also be given right!!

Stem says that the ratio of the diagonals is 18/15 = 1.2 and (2) says that the ration of widths is also 1.2. So, the ratio of widths = 1.2 = ratio of diagonals (hypotenuse).
_________________

explanation is clear, however although concluded it as sufficient as well, I wasn't thinking of the logic you presented for S2 (pressed for time). So I want to clear up whether, in this case, doesn't the very fact that S1 proves sufficient (i.e. similar rectangles thus similar ratio of areas) necessarily mean that if S2 provides measurements of the rectangles' sides, such measurements must also be in a 1.2 ratio? For instance, could S2 have been 30% instead of 20% or wouldn't that be a flawed question where the statements provide incongruent answers (no pun intended)? Thx

explanation is clear, however although concluded it as sufficient as well, I wasn't thinking of the logic you presented for S2 (pressed for time). So I want to clear up whether, in this case, doesn't the very fact that S1 proves sufficient (i.e. similar rectangles thus similar ratio of areas) necessarily mean that if S2 provides measurements of the rectangles' sides, such measurements must also be in a 1.2 ratio? For instance, could S2 have been 30% instead of 20% or wouldn't that be a flawed question where the statements provide incongruent answers (no pun intended)? Thx

On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.
_________________

explanation is clear, however although concluded it as sufficient as well, I wasn't thinking of the logic you presented for S2 (pressed for time). So I want to clear up whether, in this case, doesn't the very fact that S1 proves sufficient (i.e. similar rectangles thus similar ratio of areas) necessarily mean that if S2 provides measurements of the rectangles' sides, such measurements must also be in a 1.2 ratio? For instance, could S2 have been 30% instead of 20% or wouldn't that be a flawed question where the statements provide incongruent answers (no pun intended)? Thx

On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.

Thus, S2 could not possibly have been 30%, correct? (I'm implicitly referring to an earlier reply you made to luisnavarro which said if S2 was 30%, then it would be insufficient)

explanation is clear, however although concluded it as sufficient as well, I wasn't thinking of the logic you presented for S2 (pressed for time). So I want to clear up whether, in this case, doesn't the very fact that S1 proves sufficient (i.e. similar rectangles thus similar ratio of areas) necessarily mean that if S2 provides measurements of the rectangles' sides, such measurements must also be in a 1.2 ratio? For instance, could S2 have been 30% instead of 20% or wouldn't that be a flawed question where the statements provide incongruent answers (no pun intended)? Thx

On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.

Thus, S2 could not possibly have been 30%, correct? (I'm implicitly referring to an earlier reply you made to luisnavarro which said if S2 was 30%, then it would be insufficient)