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Bruce, John, Linda, and Mark stand, in that order, in a straight line. If Linda stands 7 feet away from Mark, what is the distance from Bruce to John?
(1) Bruce stands 7 feet away from Linda.
(2) John stands 11 feet away from Mark.
(1) Bruce stands 7 feet away from Linda.
(2) John stands 11 feet away from Mark.
15 Mar 2017, 16:04
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SajjadAhmad
Bruce, John, Linda, and Mark stand, in that order, in a straight line. If Linda stands 7 feet away from Mark, what is the distance from Bruce to John?
(1) Bruce stands 7 feet away from Linda.
(2) John stands 11 feet away from Mark.
Dear SajjadAhmad, (1) Bruce stands 7 feet away from Linda.
(2) John stands 11 feet away from Mark.
This is a great question! I'm happy to respond. Consider this diagram:
Attachment:
BJLM segment.png [ 6.5 KiB | Viewed 1962 times ]
Call the distance BJ = x and the distance JL = y. The question is asking for x.
Statement #1: Bruce stands 7 feet away from Linda.
In our symbols, x + y = 7.
With this equation alone, we cannot solve for x. This statement, alone and by itself, is not sufficient.
Forget statement #1 now.
Statement #2: John stands 11 feet away from Mark.
In our symbols,
y + 7 = 11, so y = 4.
With this statement alone, we can't solve for x. This statement, alone and by itself, is not sufficient.
We can see, though, where this is going. When we combine the statements, we get y = 4 from #2, and then we plug that into the #1 equation:
x + y = 7
x + 4 = 7
x = 3
This allows us to calculate a unique numerical answer to the prompt. Combined, the statements are sufficient.
OA = (C)
A great math problem!
Let me know if there are any questions.
Mike
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