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23 Mar 2020, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:44) correct
35%
(01:57)
wrong
based on 165
sessions
History
Date
Time
Result
Not Attempted Yet
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
23 Mar 2020, 02:25
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A --> B North & then B --> C east.
So ABC forms a right angled triangle with right angled at B
--> \(AC^2 = AB^2 + BC^2\)
--> \(400 = AB^2 + BC^2\) ....... (1)
(1) The ratio of the distance going north to the distance going east is 4 to 3
--> Let AB = 4k & BC = 3k
--> \(400 = (4k)^2 + (3k)^2 = 25k^2\)
--> \(k^2 = 16\)
--> \(k = 4\)
Extra miles traveled due to detour = 4k + 3k - 20 = 7*4 - 20 = 8 miles --> Sufficient
(2) The distance traveled north going the direct route is 16
From (1), \(400 = AB^2 + BC^2\)
--> \(400 = 16^2 + BC^2 = 256 + BC^2\)
--> \(BC^2 = 144\)
--> \(BC = 12\)
Extra miles traveled due to detour = AB + BC - 20 = 28 - 20 = 8 miles --> Sufficient
Option D
So ABC forms a right angled triangle with right angled at B
--> \(AC^2 = AB^2 + BC^2\)
--> \(400 = AB^2 + BC^2\) ....... (1)
(1) The ratio of the distance going north to the distance going east is 4 to 3
--> Let AB = 4k & BC = 3k
--> \(400 = (4k)^2 + (3k)^2 = 25k^2\)
--> \(k^2 = 16\)
--> \(k = 4\)
Extra miles traveled due to detour = 4k + 3k - 20 = 7*4 - 20 = 8 miles --> Sufficient
(2) The distance traveled north going the direct route is 16
From (1), \(400 = AB^2 + BC^2\)
--> \(400 = 16^2 + BC^2 = 256 + BC^2\)
--> \(BC^2 = 144\)
--> \(BC = 12\)
Extra miles traveled due to detour = AB + BC - 20 = 28 - 20 = 8 miles --> Sufficient
Option D
Updated on: 24 Mar 2020, 01:08
Originally posted by freedom128 on 23 Mar 2020, 06:40.
Last edited by freedom128 on 24 Mar 2020, 01:08, edited 1 time in total.
Last edited by freedom128 on 24 Mar 2020, 01:08, edited 1 time in total.
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ABC is a right triangle with the hypotenuse (AC) length is 20 miles.
(1) From this statement, we can deduce that:
AB = 4*4 = 16 (going north)
BC = 4*3 = 12 (going east)
AC = 4*5 = 20 (going n.east)
As a result, we can calculate the miles John will travel due to the detour than if he had travel directly from A to C.
SUFFICIENT
(2) AB = 16 (going north) and AC = 20, so we can deduce value of BC.
NOT SUFFICIENT
FINAL ANSWER IS (A)
Posted from my mobile device
(1) From this statement, we can deduce that:
AB = 4*4 = 16 (going north)
BC = 4*3 = 12 (going east)
AC = 4*5 = 20 (going n.east)
As a result, we can calculate the miles John will travel due to the detour than if he had travel directly from A to C.
SUFFICIENT
(2) AB = 16 (going north) and AC = 20, so we can deduce value of BC.
NOT SUFFICIENT
FINAL ANSWER IS (A)
Posted from my mobile device
