John is trying to get from point A to point C, which is 20 miles away

Statement 1 - gives us a ratio of 3:4 for 2 sides and since we will have a right angled triangle (North; East; North-East) we will have a ratio of 3:4:5

Thus the other 2 sides will be 12:16:20 => 8 miles more than 20. - Sufficient

Statement 2 - One side is 16, other is 20 in a right angled triangle thus we would know the third side as well. and we will have the same answer
- Sufficient

Answer - D

upon plotting the points on paper we see that ∆ ABC is right angled
and longest distance which is A to C = 20
target find AB+BC-AC
find distance value AB, BC
#1
The ratio of the distance going north to the distance going east is 4 to 3
since its right angled
so value of AB, BC ; 16 & 12
sufficient
#2
The distance traveled north going the direct route is 16
again sufficient as given distance AB = 16 and AC = 20 ; and we know its right angled ∆ so BC = 12
sufficient
IMO D


John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

(1) The ratio of the distance going north to the distance going east is 4 to 3

(2) The distance traveled north going the direct route is 16

(1) sufic

A to C is the hypotenuse of a triangle, and ABC is a right-triangle;
If we know the ratio of the bases, we can find the unknown, by pythagoras;
(4x)^2+(3x)^2=(20)^2

(2) sufic

If we know two sides a right-triangle, we can find the missing side.

Ans (D)

John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

ABC is a right angled triangle right angled at B. AC = 20.

(1) The ratio of the distance going north to the distance going east is 4 to 3
By Pythagorean theorem: Let sides are 4x, 3x and 20
\(4x^2 + 3x^2 = 20^2\)
Solving, x = 4
Sides are 16, 12 and 20. Difference = 16 + 12 - 20 = 8.

SUFFICIENT.

(2) The distance traveled north going the direct route is 16
By Pythagorean theorem: Let sides are 16, x' and 20
\(16^2 + x'^2 = 20^2\)
Solving, x' = 12
Sides are 16, 12 and 20. Difference = 16 + 12 - 20 = 8.

SUFFICIENT.

Answer D.

John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

(1) The ratio of the distance going north to the distance going east is 4 to 3

(2) The distance traveled north going the direct route is 16

So, the detour route will make a right triangle where AC is the hypotenuse. From statement 1, we can write, (4x)^2 + (3x)^2 = (20)^2. So, x = 4. We can determine the distance of the detour route. Sufficient.

2) From this we get the two side of a right triangle and then using this the third side can also be find. Sufficient.
D is the CA.

John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

(1) The ratio of the distance going north to the distance going east is 4 to 3

(2) The distance traveled north going the direct route is 16

Question: The person has to travel in right angle and the hypotenuse being 20. If the road from A to C is blocked how much extra he will have to travel going from A to B and then C rather than directly C.

Statement 1:

The ratio is 4: 3 Therefore 4:3: 5 triplet can be used and if 5 corresponds to 20 what does other 4x and 3x correspond to

We can determine that 8 miles extra traveled.

Statement 2:

We know that for one side it is 16 and for other it is 20 using hypotenuse formula we can find the 3rd side as 12

we add 16 +12= 28 There fore 8 miles more than the hypotenuse.

IMO D

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