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Points A, B, C, and D lie on number line, not necessarily in that

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Points A, B, C, and D lie on number line, not necessarily in that  [#permalink]

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New post 30 Dec 2018, 06:43
1
1
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (02:25) correct 47% (01:51) wrong based on 21 sessions

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Points A, B, C, and D lie on number line, not necessarily in that order. If AC=20, CD=7, and AB=3, which of the following could be the value of BD?

I. 30

II. 24

III. 10

A) I only

B) II only

C) III only

D) I and II only

E) I, II, and III

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Re: Points A, B, C, and D lie on number line, not necessarily in that  [#permalink]

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New post 30 Dec 2018, 08:59
rohan2345 wrote:
Points A, B, C, and D lie on number line, not necessary in the order. If AC= 20, CD= 7, AB=3, which of the following could be the value of BD?

I. 30
II. 24
III. 10

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III


Let the order of points be as follows:
I. B-A-C-D => BD= 3+20+7 = 30
II. A-B-C-D => BD = AC+CD-AB = 20+7-3 = 24
III. A-B-D-C => BD = AC-AB-CD = 20-3-7 = 10

Hence, answer: E. I, II, and III
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Re: Points A, B, C, and D lie on number line, not necessarily in that  [#permalink]

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New post 01 Jan 2019, 18:39
1
rohan2345 wrote:
Points A, B, C, and D lie on number line, not necessarily in that order. If AC=20, CD=7, and AB=3, which of the following could be the value of BD?

I. 30

II. 24

III. 10

A) I only

B) II only

C) III only

D) I and II only

E) I, II, and III

Attachment:
2019.1.1.numberline.jpg
2019.1.1.numberline.jpg [ 118.56 KiB | Viewed 247 times ]

Trial and error works.
Describing that trial and error is not so easy.

1) Draw each defined line segment. Note length.

2) For each option I, II, and III:

-- manipulate arithmetically to see whether we can achieve the required length
with the numbers given. If we can do so, almost certainly,
we can arrange the letters to place the BD segment in a way that matches the arithmetic.

-- Length of the line with letters in order? AC + CD = 20 + 7 = 27

Because the Roman numerals do not ask for 27, we know that IF the length of BD is possible,
will have to switch the order of letters.

Given: AC=20, CD=7, and AB=3

I) 30
3 + 20 + 7 = 30
BA + AC + CD
B__A______________C_____D
BD = 30
See diagram for letters' order with segment lengths and numeric value of letter.

II) 24
(20 + 7) - 3 = 24
AC = 20
A__________________C = 20

CD = 7

A__________________C_____D = 27

AC + CD = 27
We need to subtract 3 from this line segment.
Place B inside.

A___B____________C______D

AB = 3
BD = 10

2) A___B___________C______D
See diagram for letters' values.

III) 10
20 (- 7 - 3) = 10
20 - 10 = 10
20 = AC
10 = 3 + 7, and AB = 3, CD = 7

A_________________________________C = 20

We need 3 and 7 to be subtracted from this length.
AB = 3
CD = 7

A___B__________D__________C

BD = 10

All three values are possible.

Answer E
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Re: Points A, B, C, and D lie on number line, not necessarily in that   [#permalink] 01 Jan 2019, 18:39
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