Dan and Karen, who live 10 miles apart meet at a cafe that is directly north of Dan’s house and directly east of Karen’s house. If the cafe is 2 miles closer to Dan’s house than to Karen’s house, how many miles is the cafe from Karen’s house?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Ans C
its C
Can anyone explain the answer please?
A
suppose Karen is x distance from Cafe then Dan is x-2 distance from cafe. Cafe is lieing at the right angle to Karen’s house and Dan’s house thus forming right angle triangle where distance between Dan’s and Karen’s house is 10 which is stisfying pathagorous theorem.
there 10^2=x^2+(x-2)^2
Thus x=6
Let distance of the cafe from Dan’s house be x
then the distance from Karen’s house is x+2
Dan’s house, Karen’s house and the cafe make a right triangle with hypotenuse 10
Therefore,
100 = x^2 + (x+2)^2
Solve this and you will get x = 6
The question asks for the distance of the cafe from Karen’s house which is x+2
Therefore, the answer is 8, i.e. C
After opening the parentheses the sign should be change
like as follws:
x – (0.10x – 300) = 12000
x-.10x+300=12000
‘D’ is not amibigous since… government council is singular and requires an ‘it’..The ministers would require the plural form so there is no ambiguity as it could only be the council
C.
x= Karen’s to Cafe
x^2+(x-2)^2=10^2
(x-8)(x+6)
x=8
Its simple eq of right angle
10^2 = x^2 + (x+2)^2
100 = x ^2 + x^2 + 4 +4x
100 = 2x^2 +4x + 4
50 = x^2 +2x +2
48 = x^2 +2x
48 = x(x+2)
x = 24
x+2=48
x=46
can anyone solve equqtion for me
Hi All.
Thankd a lot for your solutions…i posted this from ETS guide and the correct answer is 8..
Answer is E.
Sum of first 100 integers = 5050
Sum of first 200 integers would be (5050 *2) +(100 * 100) = 20100
Considering the plot … we have a right triangle with Karens House , Dans House being the points at the end of the hypotenue which is 10 miles in length.
Let the distance of the cafe from Dan’s House be x miles, the the distance of the cafe from Karen’s house will be (x+2) miles
Thus
– 6(x + 
= 0
10^2 = x^2 + (x +2 )^2
100 = x^2 + (x +2 )^2
100 = 2x^2 + 4 + 4x
50 = x^2 + 2 + 2x
This gives us
x^2 + 2x – 48 = 0
which solves as
x(x +
(x-6)(x+8)= 0
Thus since x is a distance it has to be positive::
x = 6
Thus Karen’s house is x + 2 ==> 6 +2 ==> 8 miles from the cafe
Ans is C
The ans for the above q is 8.
Ans is C
x=6