Daniel rides to school each day on a path that takes him first to a

Question

Daniel rides to school each day on a path that takes him first to a point directly east of his house and then from there directly north to his school. How much shorter would his ride to school be if he could walk on a straight-line path directly to school from his home, instead of east and then north?

(1) The direct straight-line distance from home to school is 17 miles. 
(2) The distance he rides to the east is 7 miles less than the distance he rides going north.

CounterSniper · Answer

The answer is after combining both the statements : C

Kurtosis · Answer

Let the distance covered to the east = a
Let the distance covered to the north = b
Let the straight line distance = c = hypotenuse

Question: a + b - c = ?

St1: c = 17 --> Insufficient as we do not know the value of a and b

St2: a = b - 7 --> b = a + 7 --> Insufficient as we do not know the values of a, b and c

Combining St1 and St2: a + a + 7 - 17 = 2a - 10
We also know that c^2 = a^2 + b^2
289 = a^2 + (a + 7)^2
289 = a^2 + a^2 + 49 + 14a
2a^2 + 14a - 240 = 0
a^2 + 7a - 120 = 0
a = 7 or -15
Distance cannot be negative --> a = 7
2a - 10 = 4

Answer: C

tusharagarwal_02 · Answer

Hi there,

Since, we know that the arrangement is a right angle triangle and hypotenuse is 17 therefore, by default the remaining two sides would be 15 and 8.

I think the OA should be A.

Kindly guide me.

Bunuel · Answer

a^2 + b^2 = 17^2 has infinite number of solutions. Notice that we are not told that and b must be integers.

Daniel rides to school each day on a path that takes him first to a

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