Nups1324 wrote:
GMATinsight wrote:
Bunuel wrote:
A frog located at (x,y), with both x and y integers, makes successive jumps of length 5 and always lands on points with integer coordinates. Suppose that the frog starts at (0,0) and ends at (1,0). What is the smallest possible number of jumps the frog makes?
A. 2
B. 3
C. 4
D. 5
E. 6
There will three jumps needed as shown in figure
First Jump: (0,0) to (3,4) Pink oneSecond Jump (3,4) to (6,0) Green oneThird Jump (6,0) to (1,0) Orange oneAnswer: Option B
Hi
GMATinsightIt would be really helpful if you could show us how did you shortlist the point (3,4)
See if the frog needs to be at (1,0) in the end, then it has to be at point (6,0) or (-4,0). Then only can a jump of 5 units will land it on (1,0). But how did you find (3,4)?
I saw your attachment and I used this.
Let our desirable coordinates be (x,y) then
Distance between (0,0) & (x,y) = Distance between (6,0) & (x,y) = 5
Right.? Then by solving we get x as 3.
Then Distance between (6,0) & (3,y) = 5 [In order to find y]
We get y as 2.
Tagging others just in case
Bunuel chetan2u yashikaaggarwal IanStewart ScottTargetTestPrep VeritasKarishma fskilnikThank you
Posted from my mobile device Solution:
Notice that the distance between (0, 0) and (3, 4) is 5. You can either apply the distance formula (which is √[(3 - 0)^2 + (4 - 0)^2]), or you can observe that the horizontal distance between (0, 0) and (3, 4) is 3 and the vertical distance between the two points is 4. Thus, the distance between the two points is equal to the hypotenuse of a right triangle where the legs have lengths 3 and 4; i.e. 5.
To understand the reason why (3, 4) was selected as the first point, notice that the frog can jump only to points (±5, 0), (0, ±5), (±3, ±4) and (±4, ±3). These are the only points with integer coordinates that have a distance of 5 from the origin.
Notice that (0, 0) -> (3, 4) -> (6, 0) -> (1, 0) is not the only three-step solution to this problem. Here are some alternate solutions:
(0, 0) -> (-5, 0) -> (-2, 4) -> (1, 0)
(0, 0) -> (-5, 0) -> (-2, -4) -> (1, 0)
(0, 0) -> (3, -4) -> (6, 0) -> (1, 0)
etc.
Finally, the distance between (6, 0) and (3, 2) is not 5. The distance between these two points is √[(6 - 3)^2 + (0 - 2)^2]) = √[3^2 + (-2)^2]) = √(9 + 4) = √13.
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