Ship X and ship Y are 5 miles apart and are on a collision course. Shi

Question

Ship X and ship Y are 5 miles apart and are on a collision course. Ship X is sailing directly north, and ship Y is sailing directly east. If the point of impact is 1 mile closer to the current position of ship X than to the current position of ship Y, how many miles away from the point of impact is ship Y at this time?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Nova GMAT
Difficulty Level: 600

Show Answer

Official Answer

D

(A) 1 
(B) 2 
(C) 3 
(D) 4 
(E) 5

Source:   Nova GMAT  
Difficulty Level:   600

GMATinsight · Answer

It's the construction of the right triangle 3-4-5

Hence Y is 4 miles from point of impact and x is 3 miles away from point of impact

Answer option D

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kolodits · Answer

We can draw a right triangle that its hyp is 5 and the sides are x and y, while y=x+1.
Thus 5^2 = x^2 + (x+1)^2.
This matches answer (D) y=4.
Verify: 5^2=3^2+4^2.

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generis · Answer

ships.jpg Method I - test answers If you draw a quick sketch, see figure, there is a right triangle with hypotenuse of 5. Think: 3-4-5 right triangle? Test values, start with C, where Y = 3. If distance to collision point for Y = 3, then, per Pythagorean theorem, X = 4. INCORRECT. The collision point is closer to X. But we have the numbers -- we need 3 and 4. Just need them switched. Option D has Y = 4. If Y = 4 then X = 3, collision point is one mile closer to X than Y, and we have the answer. Y = 4 Method II Algebra (I'm putting this method in because a similar question might not be a neat 3-4-5 right triangle) Again, quick sketch. Let distance from ship X to collision point = d, so Distance from ship Y to collision point = (d + 1) d ^2 + (d + 1) ^2 = 5 ^2 d ^2 + d ^2 + 2d + 1 = 25 2d ^2 + 2d - 24 = 0 d ^2 + d - 12 = 0 (d - 3) (d +4) = 0 d = 3, -4. Distance can't be negative. d = 3 = SHIP X Ship Y is d + 1 = 4. Answer D

MathRevolution · Answer

X is due North and Y are due East which forms a right-angled triangle with 5 miles being the hypotenuse.

The point of impact is 1 mile closer to X than Y hence X = 3 and Y = 4.

Answer D

Ship X and ship Y are 5 miles apart and are on a collision course. Shi

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Ship X and ship Y are 5 miles apart and are on a collision course. Shi

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