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M70-30

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Math Expert
Joined: 02 Sep 2009
Posts: 52917
M70-30  [#permalink]

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04 Sep 2018, 01:06
00:00

Difficulty:

35% (medium)

Question Stats:

90% (01:40) correct 10% (00:14) wrong based on 10 sessions

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On the xy-plane, points (3,2) and $$(p,q)$$ are connected by line segment l. What is $$q$$?

(1) The slope of l is –2.

(2) l also passes through point (1,6).

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Math Expert
Joined: 02 Sep 2009
Posts: 52917
Re M70-30  [#permalink]

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04 Sep 2018, 01:06
Official Solution:

We’ll go for LOGICAL because that is our first choice in Data Sufficiency.

We are asked to find the y-coordinate of a specific point on the line segment.

(1) A line segment’s slope and a point on the line is all the information needed to find the line’s equation – but that’s not enough to identify a specific point on the segment! Insufficient. (A) & (D) are eliminated.

(2) The same is true: two points on a line segment are enough to find the segment’s equation, not a specific point on the line. (B) is eliminated.

Combining the statements is of no help, as they both give sufficient information to draw the line, but tell us nothing about the specific point $$(p,q)$$. (C) is eliminated.

Answer: E
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Joined: 15 Aug 2018
Posts: 1
Re: M70-30  [#permalink]

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08 Sep 2018, 04:42
Hi,

using just statement 2:
q-6/1-p=q-2/p-3=6-2/1-3

I get q=6,

So, statement 2 is sufficient. (B)
Please let me know if I am missing something.
Intern
Joined: 16 Oct 2017
Posts: 18
Re: M70-30  [#permalink]

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23 Nov 2018, 12:00
1
Answer should be C.
On combining we get
3-p/2-q = -2
simplifying p+q=7-------------(1)

1-p/6-q = -2
simplifying p+2q=13--------------(2)

Solving (1) and (2)
q=13

Hence C
Re: M70-30   [#permalink] 23 Nov 2018, 12:00
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