GMAT Quantitative Reasoning Practice Test 6

Question : 22 of 100

Marks: +1, -0

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.

Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.
Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.
The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).
The problem can be solved using EITHER statement (1) only or statement (2) only.
The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

Validate

Solution:

To solve this problem, you need to find the distance east and north that he travels. Since he goes directly east and then directly north, his path forms a right angle, which in turn is part of a right triangle. His straight-line distance to school is the hypotenuse of the right triangle formed by his paths. Although statement (1) gives you the hypotenuse, you do not know enough information to solve for the other sides. Statement (2) gives the relationship between the two legs of the right triangle, but again this is not enough information. Using the information from both statements, you can write an equation using the Pythagorean theorem:

a^2+b^2=c^2

. Let

x=

the distance he travels east and

x+7=

the distance he travels north.

x^2+(x+7)^2=17^2

. This equation can now be solved for the missing legs and therefore the solution to the problem.

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