Gmat_mission wrote: ↑

Wed Mar 24, 2021 7:42 am

A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?

(A) 4
(B) 5
(C) 8
(D) 9
(E) 15

Answer: C

Source: GMAT Paper Tests

A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall.
We have something like this:

Since the wall is perpendicular to the ground, we have a right triangle, which means we can apply the Pythagorean Theorem to write: x² + 7² = 25²
Simplify to get: x² + 49 = 625
Subtract 49 from both sides: x² = 576
Solve: x = 24

ASIDE: We could have avoided all of the calculations above had we recognized that 7 and 25 are two of the three values in the Pythagorean triple 7-24-25, which means the missing side must have length 24

So, the ladder, in its ORIGINAL position, extends to a height of 24 feet.

If the top of the ladder slips down 4 feet . . .
If the ladder slips down 4 feet, then the ladder's NEW height = 24 - 4 = 20
So, we have something like this:


Once again, we COULD apply the Pythagorean Theorem to find the value of y (I'll let you do that on your own)
However, we can save time by recognizing that 25 and 20 are two of the three values in the magnified version of the Pythagorean triple 3-4-5
That is, if we take the Pythagorean triple 3-4-5 and multiply each side length by 5, we get the equivalent Pythagorean triple 15-20-25
This means the missing side must have length 15
In other words, y = 15

. . . how many feet will the bottom of the ladder slip?
Originally, the bottom of the ladder was 7 feet from the wall.
Afterwards, the bottom of the ladder was 15 feet from the wall
So, the bottom slipped 8 feet

Answer: C

Gmat_mission wrote: ↑

Wed Mar 24, 2021 7:42 am

A ladder 25 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?

(A) 4
(B) 5
(C) 8
(D) 9
(E) 15

Answer: C

Source: GMAT Paper Tests

Solution:

When the bottom of the 25-foot ladder is 7 feet from the base of the wall, the top of the ladder is 24 feet above the ground (notice that 7^2 + 24^2 = 25^2). Therefore, when the top of the ladder slips down 4 feet, it’s now 20 feet above the ground, and the bottom of the ladder is 15 feet from the wall (notice that 15^2 + 20^2 = 25^2). Recall that the bottom of the ladder was originally 7 feet from the wall; therefore, it must have slid 8 feet so that it is now 15 feet from the wall.

Answer: C