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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

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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

3

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OE

She travels 4 miles further from school to tennis practice,

CASE I:

GRe case I.jpg [ 21.75 KiB | Viewed 1263 times ]

Now, x = 14

GRE case II.jpg [ 24.41 KiB | Viewed 1258 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 1254 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 1263 times ]

Now, x = 14

Attachment:

GRE case II.jpg [ 24.41 KiB | Viewed 1258 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 1254 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

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?

Re: Amys school is 10 miles from her home. She travels 4 miles from schoo
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11 Oct 2023, 10:20

Expert Reply

What are you pointing out is a rule.

when to apply it depends on the question but the rules of the third side is a rule. It is always the same

when to apply it depends on the question but the rules of the third side is a rule. It is always the same

gmatclubot

Re: Amys school is 10 miles from her home. She travels 4 miles from schoo [#permalink]

11 Oct 2023, 10:20
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