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Jerry and Silvia wanted to go from the southwest corner of a square

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Jerry and Silvia wanted to go from the southwest corner of a square  [#permalink]

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New post 13 Mar 2019, 08:41
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Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia’s trip was, compared to Jerry’s trip?

(A) 30%

(B) 40%

(C) 50%

(D) 60%

(E) 70%
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Re: Jerry and Silvia wanted to go from the southwest corner of a square  [#permalink]

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New post 13 Mar 2019, 08:51
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TyrionLannister wrote:
Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia’s trip was, compared to Jerry’s trip?

(A) 30%

(B) 40%

(C) 50%

(D) 60%

(E) 70%


So, Jerry travels travels along sides of a square = 2x
Silvia travels along hypotenuse = y= 1.4x (\sqrt{2}=1.4)

Difference of the distance travelled = 2-1.4=0.6, So silvia travelled 0.6 units less for ever 2 units Jerry traveled (remember jerry has travelled 2 x units).
So for every 1 unit jerry travels, silvia travel 0.3 units less. or 30%

Answer A
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Re: Jerry and Silvia wanted to go from the southwest corner of a square  [#permalink]

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New post 13 Mar 2019, 09:04
TyrionLannister wrote:
Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia’s trip was, compared to Jerry’s trip?

(A) 30%

(B) 40%

(C) 50%

(D) 60%

(E) 70%



We are talking about right triangle............So e can take any example such as" 3-4-5

Jerry walked 7 units & Silvia walked 5 units

Percentage shorter = (7-5)/7 = 2/7 = 0.286 ...........(it is useful to memorize 1/7 = 0.143..)

The closest answer is 30%

Answer: A
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Re: Jerry and Silvia wanted to go from the southwest corner of a square  [#permalink]

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New post 15 Mar 2019, 06:41
TyrionLannister wrote:
Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia’s trip was, compared to Jerry’s trip?

(A) 30%

(B) 40%

(C) 50%

(D) 60%

(E) 70%


Let’s let the side of the square = 10. Jerry walked on two sides of the field, and Silvia walked on the diagonal of the field. Thus, Jerry’s trip was 20 and Silvia’s was 10√2, which is about 10 x 1.4 = 14.

So Silvia’s trip is approximately 6 units shorter than Jerry’s, or approximately 6/20 = 3/10 = 30% shorter.

Answer: A
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Re: Jerry and Silvia wanted to go from the southwest corner of a square  [#permalink]

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New post 18 Mar 2019, 05:08
Noshad wrote:
Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia’s trip was, compared to Jerry’s trip?

(A) 30%

(B) 40%

(C) 50%

(D) 60%

(E) 70%


let each side = 2

Jerry walked = 4
Silva walked= 2√2
so difference = 4-2√2 = 2*(2-1.4 ) = 1.2
1.2/4= 30 %
IMO A
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Re: Jerry and Silvia wanted to go from the southwest corner of a square  [#permalink]

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New post 18 Mar 2019, 19:26
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Distance travelled by Jerry is 2S and distance travelled by Silvia is \(\sqrt{2}S\) ~ \(1.4S\)

The difference is 0.6S.

\(\frac{0.6S}{2S}*100\)

30%

OPTION: A
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Re: Jerry and Silvia wanted to go from the southwest corner of a square   [#permalink] 18 Mar 2019, 19:26
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