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# GMAT: Data sufficiency 6

28-32, pg. 280. Created by Sal Khan.

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• the value of x given in the second statement does tell us what Y is. based on statement one Y = x+3 so Y= 5, (PQ = 2, QR = 4 and PR = 5) • Although the second statement specifying the value of x is given, it is not required since it is useless without statement 1. I think Khan is right saying that the first statement suffices to answer the question.

We can argue that since we know the value of x and the equation of y (from the first statement), we can thus figure out the longer side; but how useful is finding the longer side with statement 2 (using the statement 1) when you already know the longer side?

Answer) A. Statement 1 ALONE is sufficient but statement 2 alone is not sufficient.

The other options do not have the image of the question and neither can we opt option C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
• is x equal to 5?
1)x>=5
2)x<=5 • For problem 32, how do we know the value of x is positive and not a negative value. Yes logically it doesnt make sense to have a value of -1 for a length, however this could be a case. • A side length of a triangle (or any other geometric figure) is `always` considered to be positive. Remember from geometry and algebra that to find distances along a number line, we take the absolute value of the difference in location. Absolute value results always in a positive distance.

Then if we are using locations of points (like the vertices of a triangle) on a coordinate plane, we take the positive square root of the difference in each dimension (the famous distance formula). ₂a₁
distance = √ [(x₂ - x₁)² + (y₂ - y₁)²]
That is the formula based on Pythagorean Theorem (c² = a² + b², so c = √ [a² + b²] ).

Because the square root bracket automatically informs us to take the principal (positive) square root we again end up with distance as a positive quantity.

It is possible to have a problem where the length of a side of a triangle is measured in an expression including x and that x is actually negative. Let's say that we know side AB of ΔABC is twice side CB (one side and hypotenuse of a 30-60-90 degree triangle),
and we know that
AB = 3x + 14, and CB = 2 - x
The question might ask us to find x and the lengths of the two sides, AB and CB
So we set up the equation
AB = 2CB
3x + 14 = 2(2 - x)
3x + 14 = 4 - 2x
5x = -10
x = -2
So, x was -2
The side lengths, however are both positive:
AB = 3x + 14 =-6 + 14 = 8 positive side length
CB = 2 - x = 2 + 2 = 4 positive side length

In the problem Sal just did, the smallest side length turned out to be x, which cannot be -1

Hope that helped
(1 vote)
• #28. I am confused about statement 1. I don't believe x/2 is enough prove x is an integer. Let's say x=5. 5/2 is not an integer. correct?
(1 vote) 