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If the vertices of a triangle have coordinates (x, 1),

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If the vertices of a triangle have coordinates (x, 1),

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Source: Official Guide

If the set S consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in S, but 10 is not in S.
(2) The sum of the even integers in S is 26

The OA is D.



Last edited by BTGmoderatorLU on Thu Aug 09, 2018 3:06 pm; edited 1 time in total

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BTGmoderatorLU wrote:
Source: GMAT Club Tests

If the vertices of a triangle have coordinates (x, 1), (5, 1), and (5, y) where x < 5 and y > 1, what is the area of the triangle?

(1) x = y.
(2) The angle at the vertex (x, 1) is equal to the angle at the vertex (5, y).

The OA is C.
On a coordinate plane, put the point (5, 1). Since we cannot fix the other two points (x, 1) and (5, y), we can draw the straight line passing through the vertex (5, 1).

Somewhere on the line parallel to X-axis the vertex (x, 1) would lie and somewhere on the line parallel to Y-axis the vertex (5, y) would lie. This implies that it is a right-angled triangle.

Thus, the area of the triangle = 1/2*(5 - x)*(y - 1)

Let's take each statement one by one.

(1) x = y.

Can't get the value of 1/2*(5 - x)*(y - 1). Insufficient.

(2) The angle at the vertex (x, 1) is equal to the angle at the vertex (5, y).

=> This implies that it is an isosceles right-angled triangle.

=> (5 - x) = (y - 1)

Can't get the value of 1/2*(5 - x)*(y - 1). Insufficient.

(1) and (2) together

From x = y and (5 - x) = (y - 1), we get that x = y = 2

Thus, the area of the triangle = 1/2*(5 - x)*(y - 1) = 1/2*(5 - 2)*(2 - 1) = 3 unit

Sufficient.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote:
Source: Official Guide

If the set S consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in S, but 10 is not in S.
(2) The sum of the even integers in S is 26

The OA is D.
This seems to be a different question than the one Jay has quoted. Did you accidentally change it when editing?

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