APPROACH #1: Algebra
14 + 23 = 37
So, there are presently 37 pieces of fruit in the box

Let x = the number of oranges REMOVED
So, 37 - x = the number of pieces of fruit AFTER x oranges are removed

Since we are not removing any apples, we will always have 14 apples in the box.

Since we want 70% of the fruit to be apples we can write: 14/(37 - x) = 70/100 (aka 70%)
Simplify: 14/(37 - x) = 7/10
Cross multiply: (7)(37 - x) = (14)(10)
Expand and simplify: 259 - 7x = 140
Subtract 259 from both sides: -7x = -119
Solve: x = 17

Answer: D

APPROACH #2: Number sense
There are presently 37 pieces of fruit in the box, and 14 pieces are APPLES
If we remove 3 oranges (answer choice A), then there are 34 pieces of fruit remaining.
So, 14/34 = the fraction of apples in the box
We want that fraction to be equivalent to 70% (aka 7/10)
In order for the fraction to be equivalent to 7/10, the denominator must be a multiple of 10.
Since removing 3 oranges results in a denominator of 34, we can immediately eliminate answer choice A

When we scan the answer choices, we see that only answer choice D (17) will result in a denominator which is a multiple of 10.

Answer: D

Cheers,
Brent