Triangle construction : Quant Question Archive [LOCKED]
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# Triangle construction

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Director
Joined: 20 Apr 2005
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23 May 2005, 15:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

GMAT question No. 394

Right triangle PQR is to be constructed in the ey-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y <= 16. How many different triangles with these properties could be construected ?

A. 110
B. 1,100
C. 9,900
D. 10,000
E. 12,100
Director
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23 May 2005, 16:08
2*2*45*55 = 9,900

45 = sum 1 to 9 for x
55 = sum 1 to 10 for y
Senior Manager
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23 May 2005, 16:16
Looks a straightforward C, unless I am goofing it up.

Two basic conditions for the above figure to materialize are
P(y) = R(y) ..... (1)
AND
P(x) = Q(x) ..... (2)

Since Range(x) = 10 and Range(y) = 11,
P(y) = R(y) can have 11 values, and Q(y) can take remaining 10 values.
P(x) = Q(x) can have 10 values, and R(x) can take the remaining 9 values.

Therefore, total = 11x10x10x9 = 9900.
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Re: Triangle construction   [#permalink] 23 May 2005, 16:16
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