# tsa 2009 paper q 48

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The correct answer is C, but why ?? Thank you

Last edited by rogerdoger; 1 month ago

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#2

te key thing is to think about how B and C must be located if its necessary to go back to X after A.

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(Original post by

have you tried to sketch it?

te key thing is to think about how B and C must be located if its necessary to go back to X after A.

**mqb2766**)have you tried to sketch it?

te key thing is to think about how B and C must be located if its necessary to go back to X after A.

Last edited by rogerdoger; 1 month ago

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#4

(Original post by

c is the only choice that forms a triangle path, a loop. but i still don't understand.

**rogerdoger**)c is the only choice that forms a triangle path, a loop. but i still don't understand.

The key to thinking about it is whether ABC form a triangle or lie on a line.

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(Original post by

Did you sketch the other (correct) ones?

The key to thinking about it is whether ABC form a triangle or lie on a line.

**mqb2766**)Did you sketch the other (correct) ones?

The key to thinking about it is whether ABC form a triangle or lie on a line.

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#6

(Original post by

abc forms a triangle path or if i draw it in a line they can all be on a line but from c to x would go past ab on it's way to x. how does this help solve the problem?

**rogerdoger**)abc forms a triangle path or if i draw it in a line they can all be on a line but from c to x would go past ab on it's way to x. how does this help solve the problem?

B) is probably the easiest one to start with as thats obviously correct when ABC form a triangle? If you understand why A) is possible, you'll understand why C) is impossible.

I think you've got the germ of the answer in the previous post, but Im not sure if you fully understand. It helps if you upload the pictures corresponding to each relevant answer to be clear.

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B) is probably the easiest one to start with as thats obviously correct when ABC form a triangle? If you understand why A) is possible, you'll understand why C) is impossible.

I think you've got the germ of the answer in the previous post, but Im not sure if you fully understand. It helps if you upload the pictures corresponding to each relevant answer to be clear.

I think you've got the germ of the answer in the previous post, but Im not sure if you fully understand. It helps if you upload the pictures corresponding to each relevant answer to be clear.

i don't understand. can you illustrate?

why can't answer choice c be the shortest path?

all i know is having drawn out the paths for all 5 choices, only answer choice c forms a triangle path (a loop). all the other answer choices form a retraced "U" shape path (no loops in the path).

Last edited by rogerdoger; 1 month ago

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**mqb2766**)

have you tried to sketch it?

te key thing is to think about how B and C must be located if its necessary to go back to X after A.

i don't understand. can you illustrate?

why can't answer choice c be the shortest path?

all i know is having drawn out the paths for all 5 choices, only answer choice c forms a triangle path (a loop). all the other answer choices form a retraced "U" shape path. choice b forms a square loop.

Last edited by rogerdoger; 1 month ago

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#9

Only B) is a triangle. For the other choices, the ABC towns must lie on a line, because the shortest distance comes back through X in the middle of the trajectory or X is at the end of the line for E).

If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?

If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?

Last edited by mqb2766; 1 month ago

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(Original post by

Only B) is a triangle. For the other choices, the ABC towns must lie on a line, because the shortest distance comes back through X in the middle of the trajectory or X is at the end of the line for E).

If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?

**mqb2766**)Only B) is a triangle. For the other choices, the ABC towns must lie on a line, because the shortest distance comes back through X in the middle of the trajectory or X is at the end of the line for E).

If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?

choice B makes a square when i draw it out. not a triangle. i'm confused. i don't see the triangle you're talking about.

" For the other choices, the ABC towns must lie on a line, because the shortest distance comes back through X in the middle of the trajectory or X is at the end of the line for E)."

yes, i see that.

"If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?"

the end town could be either B or C at the end to X, couldn't it?

i still don't get why C couldn't be the shortest route compared to choice A. if you flatten the path into a line, choice A and C could travel the same distance.

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#11

(Original post by

"Only B) is a triangle. "

choice B makes a square when i draw it out. not a triangle. i'm confused. i don't see the triangle you're talking about.

" For the other choices, the ABC towns must lie on a line, because the shortest distance comes back through X in the middle of the trajectory or X is at the end of the line for E)."

yes, i see that.

"If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?"

the end town could be either B or C at the end to X, couldn't it?

i still don't get why C couldn't be the shortest route compared to choice A. if you flatten the path into a line, choice A and C could travel the same distance.

**rogerdoger**)"Only B) is a triangle. "

choice B makes a square when i draw it out. not a triangle. i'm confused. i don't see the triangle you're talking about.

" For the other choices, the ABC towns must lie on a line, because the shortest distance comes back through X in the middle of the trajectory or X is at the end of the line for E)."

yes, i see that.

"If C) was a shortest sequence, it would have to return through B at the end to X. Your diagram should make it clear, if not, upload it?"

the end town could be either B or C at the end to X, couldn't it?

i still don't get why C couldn't be the shortest route compared to choice A. if you flatten the path into a line, choice A and C could travel the same distance.

As for further explanation, pls upload your diagram / what you think. I've given the answer, if you think there could be a different scenario, upload the diagram.

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A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

best i could do. it won't do spacing.

now what?

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

best i could do. it won't do spacing.

now what?

Last edited by rogerdoger; 1 month ago

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#13

(Original post by

A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

best i could do. it won't do spacing.

now what?

**rogerdoger**)A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

best i could do. it won't do spacing.

now what?

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A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

now what?

"On the way from A-C, it passes through X and B which means theyre in a line."

yes, i see that.

"But on the way back to X, B is omitted,"

yes, i see that

"...hence they're not in a line."

ok, yes, i see that now.

Hence impossible."

this part i don't understand. couldn't the triangle be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

now what?

(Original post by

For C) can you see why the sequence wants them both to be in line, but also not be in a line? Hence its impossible. On the way from A-C, it passes through X and B which means theyre in a line. But on the way back to X, B is omitted, hence they're not in a line. Hence impossible.

**mqb2766**)For C) can you see why the sequence wants them both to be in line, but also not be in a line? Hence its impossible. On the way from A-C, it passes through X and B which means theyre in a line. But on the way back to X, B is omitted, hence they're not in a line. Hence impossible.

yes, i see that.

"But on the way back to X, B is omitted,"

yes, i see that

"...hence they're not in a line."

ok, yes, i see that now.

Hence impossible."

this part i don't understand. couldn't the triangle be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

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#15

(Original post by

A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

now what?

"On the way from A-C, it passes through X and B which means theyre in a line."

yes, i see that.

"But on the way back to X, B is omitted,"

yes, i see that

"...hence they're not in a line."

ok, yes, i see that now.

Hence impossible."

this part i don't understand. couldn't the triangle be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

**rogerdoger**)A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

now what?

"On the way from A-C, it passes through X and B which means theyre in a line."

yes, i see that.

"But on the way back to X, B is omitted,"

yes, i see that

"...hence they're not in a line."

ok, yes, i see that now.

Hence impossible."

this part i don't understand. couldn't the triangle be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

For C) you need C to be both inline with A, B and X (outward journey) and not inline with B, X (return journey). It can't be both?

B) is when A, B, C are in a triangle?

Last edited by mqb2766; 1 month ago

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A) A=X=B=C

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

now what?

(Original post by

For C) can you see why the sequence wants them both to be in line, but also not be in a line? Hence its impossible. On the way from A-C, it passes through X and B which means theyre in a line. But on the way back to X, B is omitted, hence they're not in a line. Hence impossible.
"On the way from A-C, it passes through X and B which means theyre in a line."

yes, i see that.

"But on the way back to X, B is omitted,"

yes, i see that

"...hence they're not in a line."

ok, yes, i see that now.

Hence impossible."

this part i don't understand. couldn't the triangle be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B be the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

"For C) you need C to be both inline with A, B and X (outward journey) and not inline with B, X (return journey). It can't be both?"

i don't understand. why do all 4 towns

"B) is when A, B, C are in a triangle?"

i don't understand. i don't see a triangle for choice b. when i drew the path out for choice b, i got square XABC. no where did i see a triangle ABC.

X to A, A to B, B to C, C to X. each leg of the trip makes up the 4 sides of a square.

B) X-A

| |

B-C

C) A=X-B

\ |

C

D) C=X=B=A

E) X=A=B=C

now what?

**mqb2766**)

For C) can you see why the sequence wants them both to be in line, but also not be in a line? Hence its impossible. On the way from A-C, it passes through X and B which means theyre in a line. But on the way back to X, B is omitted, hence they're not in a line. Hence impossible.

yes, i see that.

"But on the way back to X, B is omitted,"

yes, i see that

"...hence they're not in a line."

ok, yes, i see that now.

Hence impossible."

this part i don't understand. couldn't the triangle be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B be the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

(Original post by

Without being funny, it really would help for you to draw what you're suggesting and upload the image.

For C) you need C to be both inline with A, B and X (outward journey) and not inline with B, X (return journey). It can't be both?

B) is when A, B, C are in a triangle?

**mqb2766**)Without being funny, it really would help for you to draw what you're suggesting and upload the image.

For C) you need C to be both inline with A, B and X (outward journey) and not inline with B, X (return journey). It can't be both?

B) is when A, B, C are in a triangle?

i don't understand. why do all 4 towns

**have to be**inline? the instructions only said the paths between towns are straight lines. that implies the cities can be arranged in any geometry and not limited to a line?"B) is when A, B, C are in a triangle?"

i don't understand. i don't see a triangle for choice b. when i drew the path out for choice b, i got square XABC. no where did i see a triangle ABC.

X to A, A to B, B to C, C to X. each leg of the trip makes up the 4 sides of a square.

Last edited by rogerdoger; 1 month ago

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couldn't the triangle XBC be made infinitesimally smaller and smaller to make the route shorter and shorter?

why couldn't choice B be the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

why couldn't choice B be the answer? it makes a bigger loop of 4 cities where choice C makes a loop of 3 cities.

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#18

"For C) you need C to be both inline with A, B and X (outward journey) and not inline with B, X (return journey). It can't be both?"

i don't understand. why do all 4 towns

"B) is when A, B, C are in a triangle?"

i don't understand. i don't see a triangle for choice b. when i drew the path out for choice b, i got square XABC. no where did i see a triangle ABC.

X to A, A to B, B to C, C to X. each leg of the trip makes up the 4 sides of a square.

i don't understand. why do all 4 towns

**have to be**inline? the instructions only said the paths between towns are straight lines. that implies the cities can be arranged in any geometry and not limited to a line?**Not if the shortest path is a given. Pls draw the scenario youre describing and upload your diagram.**"B) is when A, B, C are in a triangle?"

i don't understand. i don't see a triangle for choice b. when i drew the path out for choice b, i got square XABC. no where did i see a triangle ABC.

X to A, A to B, B to C, C to X. each leg of the trip makes up the 4 sides of a square.

**Again, I was talking just about ABC for the triangle. The X could be in several places, one o which would produce a square. See #11.**
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"Not if the shortest path is a given. Pls draw the scenario youre describing and upload your diagram."

i did already. please see #12. here it is again:

A=X-B

\ |

C

"Again, I was talking just about ABC for the triangle. The X could be in several places, one o which would produce a square. See #11."

again see #12.

there is no triangle ABC for answer choice B. where were you seeing triangle ABC for answer choice B? i see a square XABC but i don't know where you are getting this triangle ABC. there is no triangle ABC for choice B. can you draw it out? i have no idea what triangle you're talking about for choice B.

i did already. please see #12. here it is again:

A=X-B

\ |

C

"Again, I was talking just about ABC for the triangle. The X could be in several places, one o which would produce a square. See #11."

again see #12.

there is no triangle ABC for answer choice B. where were you seeing triangle ABC for answer choice B? i see a square XABC but i don't know where you are getting this triangle ABC. there is no triangle ABC for choice B. can you draw it out? i have no idea what triangle you're talking about for choice B.

Last edited by rogerdoger; 1 month ago

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#20

(Original post by

"Not if the shortest path is a given. Pls draw the scenario youre describing and upload your diagram."

i did already. please see #12. here it is again:

A=X-B

\ |

C

**rogerdoger**)"Not if the shortest path is a given. Pls draw the scenario youre describing and upload your diagram."

i did already. please see #12. here it is again:

A=X-B

\ |

C

Last edited by mqb2766; 1 month ago

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