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Amys school is 10 miles from her home. She travels 4 miles from schoo
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02 May 2023, 07:26
02 May 2023, 07:26
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Question Stats:
46% (01:11) correct
53% (01:57) wrong based on 15 sessions
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Amy’s school is 10 miles from her home. She travels 4 miles from school to tennis practice. If she is then X miles from her home, what could be the possible value of X?
Indicate all the apply
4
6
8
10
12
14
16
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Indicate all the apply
4
6
8
10
12
14
16
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
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Official Answer
B,C,D,E,F
Amys school is 10 miles from her home. She travels 4 miles from schoo
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28 May 2023, 00:10
28 May 2023, 00:10
3
Expert Reply
OE
She travels 4 miles further from school to tennis practice,
CASE I:
GRe case I.jpg [ 21.75 KiB | Viewed 1023 times ]
Now, x = 14
GRE case II.jpg [ 24.41 KiB | Viewed 1018 times ]
Now, x = 10 – 4 = 6
CASE III: It is not necessary that she travels in a straight line.
GRE case III.jpg [ 48.01 KiB | Viewed 1013 times ]
We can observe, if she goes on any other path, we get a triangle and we need to find the
third side, that is, x.
We know, in a triangle,
Difference of other 2 sides < Any side of the triangle < Sum of other 2 sides
that is, (10- 4) < x < (10+ 4)
that is, 6 < x < 14
As maximum possible distance is 14 and the minimum possible is 6.
6 ≤ X ≤ 14
Hence, the possible values are B, C, D E and F.
Ans. (B, C, D, E, F)
She travels 4 miles further from school to tennis practice,
CASE I:
Attachment:
GRe case I.jpg [ 21.75 KiB | Viewed 1023 times ]
Now, x = 14
Attachment:
GRE case II.jpg [ 24.41 KiB | Viewed 1018 times ]
Now, x = 10 – 4 = 6
CASE III: It is not necessary that she travels in a straight line.
Attachment:
GRE case III.jpg [ 48.01 KiB | Viewed 1013 times ]
We can observe, if she goes on any other path, we get a triangle and we need to find the
third side, that is, x.
We know, in a triangle,
Difference of other 2 sides < Any side of the triangle < Sum of other 2 sides
that is, (10- 4) < x < (10+ 4)
that is, 6 < x < 14
As maximum possible distance is 14 and the minimum possible is 6.
6 ≤ X ≤ 14
Hence, the possible values are B, C, D E and F.
Ans. (B, C, D, E, F)
Re: Amys school is 10 miles from her home. She travels 4 miles from schoo
[#permalink]
11 Oct 2023, 09:35
11 Oct 2023, 09:35
Carcass wrote:
OE
She travels 4 miles further from school to tennis practice,
CASE I:
Now, x = 14
Now, x = 10 – 4 = 6
CASE III: It is not necessary that she travels in a straight line.
We can observe, if she goes on any other path, we get a triangle and we need to find the
third side, that is, x.
We know, in a triangle,
Difference of other 2 sides < Any side of the triangle < Sun of other 2 sides
that is, (10- 4) < x < (10+ 4)
that is, 6 < x < 14
As maximum possible distance is 14 and the minimum possible is 6.
6 ≤ X ≤ 14
Hence, the possible values are B, C, D E and F.
Ans. (B, C, D, E, F)
She travels 4 miles further from school to tennis practice,
CASE I:
Attachment:
GRe case I.jpg
Now, x = 14
Attachment:
GRE case II.jpg
Now, x = 10 – 4 = 6
CASE III: It is not necessary that she travels in a straight line.
Attachment:
GRE case III.jpg
We can observe, if she goes on any other path, we get a triangle and we need to find the
third side, that is, x.
We know, in a triangle,
Difference of other 2 sides < Any side of the triangle < Sun of other 2 sides
that is, (10- 4) < x < (10+ 4)
that is, 6 < x < 14
As maximum possible distance is 14 and the minimum possible is 6.
6 ≤ X ≤ 14
Hence, the possible values are B, C, D E and F.
Ans. (B, C, D, E, F)
Oh! Thank you. Just a quick question -- when we are applying the triangle inequality, it's a strict inequality and then in the next line it's not. In another sum, too, the correct answers did not include the strict ineq values (like here it's 6 and 14). So, how do we know when to apply strict inequality and when not to?
