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John’s home is at the same distance from his two friends Brian’s home

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John’s home is at the same distance from his two friends Brian’s home  [#permalink]

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New post 04 Oct 2018, 02:04
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:56) correct 31% (01:50) wrong based on 55 sessions

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John’s home is at the same distance from his two friends Brian’s home and Andy’s home. The distance between Brian’s home and Andy’s home is 8 miles, which of the following could be the distance between the John’s home and either of his friend’s home?

I. 3 miles
II. 10 miles
III. 12 miles

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

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Re: John’s home is at the same distance from his two friends Brian’s home  [#permalink]

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New post 04 Oct 2018, 07:11
Bunuel wrote:
John’s home is at the same distance from his two friends Brian’s home and Andy’s home. The distance between Brian’s home and Andy’s home is 8 miles, which of the following could be the distance between the John’s home and either of his friend’s home?

I. 3 miles
II. 10 miles
III. 12 miles

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III


the three houses make an isosceles triangle with sides x, x and 8
The rule that can be used here is..
The third side will be greater than the difference of other two sides and lesser than the sum of two sides..

I. x+x>8........2x>8.....so x>4
II. x-x<8.... So there is no upper limit to x

Out of 3, 10 and 12..... 3 does not fit in
So II and III
E
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Re: John’s home is at the same distance from his two friends Brian’s home  [#permalink]

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New post 07 Oct 2018, 19:27
Bunuel wrote:
John’s home is at the same distance from his two friends Brian’s home and Andy’s home. The distance between Brian’s home and Andy’s home is 8 miles, which of the following could be the distance between the John’s home and either of his friend’s home?

I. 3 miles
II. 10 miles
III. 12 miles

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III


Let d = the distance between the John’s home and either of his friend’s homes. If John’s home is exactly midway between Brian’s home and Andy’s home on a straight line, then d = 4. If John’s home is not on a straight line with his friends’ homes, then d > 4. Therefore, d ≥ 4. We can see that only 10 and 12 are greater than 4.

Answer: E
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Re: John’s home is at the same distance from his two friends Brian’s home  [#permalink]

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New post 07 Oct 2018, 23:50
Think of it as an isosceles triangle with unequal side 8 and two equal side x.
x+x > 8
x>4
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Re: John’s home is at the same distance from his two friends Brian’s home   [#permalink] 07 Oct 2018, 23:50
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