If n is an integer between 3 and 9, what is the value of n ?

[Anaira Mitch]

If n is an integer between 3 and 9, what is the value of n ?
(1) On the number line, the distance from 3 to n is 2/3 of the distance from 3 to 9.
(2) On the number line, n is 10 units to the right of -3

[Jay@ManhattanReview]

If n is an integer between 3 and 9, what is the value of n ?

(1) On the number line, the distance from 3 to n is 2/3 of the distance from 3 to 9.
(2) On the number line, n is 10 units to the right of -3

Let us take each statement one by one.

S1: On the number line, the distance from 3 to n is 2/3 of the distance from 3 to 9.

The statement means that (n-3) = (2/3)*(9-3)

=> n-3 = (2/3)*(6)

=> n = 7. Sufficient.

S2: On the number line, n is 10 units to the right of -3.

On a number line, a number on the right of a number X would be greater than number X.

Thus, n = (-3) + 10

=> n = 7. Sufficient.

The correct answer: D

Hope this helps!

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-Jay
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[Matt@VeritasPrep]

Slightly more compact:

S1:

|3 - n| = (2/3) * |9 - 3|

|3 - n| = (2/3) * 6 = 4

so n = -1 or n = 7. Since we're told that 3 < n < 9, we must have n = 7. SUFFICIENT

S2:

n = -3 + 10 = 7, hey, also SUFFICIENT!

[Brent@GMATPrepNow]

If n is an integer between 3 and 9, what is the value of n ?
(1) On the number line, the distance from 3 to n is 2/3 of the distance from 3 to 9.
(2) On the number line, n is 10 units to the right of -3

Given: n is an integer between 3 and 9
In other words, the number line looks like This: <------3-----n------9------>

Target question: What is the value of n ?

Statement 1: On the number line, the distance from 3 to n is 2/3 of the distance from 3 to 9.
We can write: (n - 3) = (2/3)(9 - 3)
Since this is a linear equation with only one variable, we COULD to find the value of n (but we would never waste precious time on test day doing so)
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Aside: If we solve the equation we get n = 7

Statement 2: On the number line, n is 10 units to the right of -3
In other words, n = -3 + 10
In other words, n = 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent