SOLUTION


The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between City R and City U is 62 kilometers. What is the value of x ?

(1) By the most direct route, the distance between S and T is twice the distance between S and R. We can find the value of \(y\), which will be \(ST=56=2y\) --> \(y=28\). But we have no information about \(x\). Not sufficient.

(2) By the most direct route, the distance between T and U is 1.5 times the distance between R and T. \(TU=69=1.5x\) --> \(x=46\). Sufficient.

Answer: B.
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1) from graph the distance between S and T gives the value of y, hence not sufficient
2) this gives value of x, hence sufficient.

Hence B
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X=?

(1) interpreting the chart plus the statement: 56 = 2 (y)
INSUFFICIENT bec we don't know anything about x and it's relationship to y.
(2) 69 = 1.5x, SUFFICIENT

Answer: B

The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between City R and City U is 62 kilometers. What is the value of x ?


R S T U
R 0 28 x 62

S 28 0 56 75

T x 56 0 69

U 62 75 69 0

(1) By the most direct route, the distance between S and T is twice the distance between S and R.
y = 28
This tells us nothing about x.
INSUFFICIENT

(2) By the most direct route, the distance between T and U is 1.5 times the distance between R and T.
tu distance = 69
tu = 1.5(rt)
69 = 1.5(rt)
46=rt
The distance between r and t on the graph = x, therefore, x=46.
SUFFICIENT

(B)

for statement 1 - if you know that RS is 28 and ST is 56, why is it incorrect to assume that RT is 28+56?

It would be the distance through S, but there might be a shorter direct route.
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gotcha that makes sense, thanks for the reply bunuel

We need to determine the value of x.

Statement One Alone:

By the most direct route, the distance between S and T is twice the distance between S and R.

The distance between S and R is y, and the distance between S and T is 56 kilometers.

Since the distance between S and T is twice the distance between S and R, we can say:

2y = 56

y = 56/2 = 28 kilometers

However, we still do not have a value for x. Statement one is not sufficient to answer the question.

Statement Two Alone:

By the most direct route, the value of the distance between T and U is 1.5 times the distance between R and T.

The distance between T and U is 69 kilometers, and the distance between R and T is x. Since the distance between T and U is 1.5 times the distance between R and T, we can say:

1.5x = 69

x = 69/1.5 = 46 kilometers

Thus, the value of x is 46. Statement two is sufficient to answer the question.

Answer: B
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Hi Bunuel
What if people mistakenly think that the highlighted part is something like the "black circle" in the screenshot (attached) NOT the "red circle"?
Thanks__
PS-it is better if the underlined part is edited with "R and T" in statement 2 (a space is needed between 'R' and 'and' for better understanding).

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Dear TheUltimateWinner
I presume it is almost impossible if you take into consideration the question stem:

The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between City R and City U is 62 kilometers

In your case it is not the Distance between TWO cities.