BTGModeratorVI wrote: ↑

Thu Nov 26, 2020 1:09 pm

The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?

A. 3
B. 6
C. 14
D. 17
E. 20

Answer: D
Source: official guide

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