The contents of a certain box consist of 14 apples and 23 or

Question

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

Bunuel · Accepted Answer

As only oranges must be removed then 14 apples which are now in the box must comprise 70% of total # of fruits after removal: 0.7*total=14 --> total=20, and as there are 37 fruits now 37-20=17 oranges must be removed.

Answer: D.

BrentGMATPrepNow · Answer

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

beyondgmatscore · Answer

The objective here is that 70% of the fruit in the box should be apples.

Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20

So we should have 20-14 = 6 oranges.

Right now, there are 23 oranges, so to get to 6 oranges, we should remove 23 - 6 = 17 oranges.

Answer D

heygirl · Answer

bunuel and beyondgmatscore, Thanks. i got it now. Geez, I feel like a fool to not have understood this :oops:

MHIKER · Answer

The content of a certain box consists 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

x= orange to be removed 
14=70%(37-x)
x= 17

ramprakash · Answer

Let x denotes the total no of fruits.

No of Apples remain the same.
Hence
14/x * 100 = 70
Solving we get x = 20

Apples = 14 Oranges = 6
Therfore, no of oranges to be removed = 17

Ans : D

Spidy001 · Answer

0.7(37-x) = 14 
=> x =17

Answer D

subhashghosh · Answer

(14)/(37-x) = 7/10

=> x = 17

Answer - D

menacel · Answer

\frac {14}{x}  =  \frac{70}{100}

Gives you twenty total pieces of fruit. 14 are apples, so 6 are oranges. 23-6=17 oranges that have to be removed

So

Imo D

Posted from my mobile device

venmic · Answer

14 apples and 23 oranges

70 percent of the pieces of fruit in the box will be apples

--> 70%(T) = 14
T = 20

remaining 
20-14 = 6

so 23-6 = 17

main point here is the apples remain the same no matter vvhat

Eulerelements · Answer

Ratio of apples to oranges is 7 to 3.
Since there are 14 apples there needs to be 6 oranges. 23-17=6 so 17 apples need to be removed.

Posted from my mobile device

mimajit · Answer

The content of a certain box consists 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

Testing ans choices 
If D = 17 no of oranges to be removed means there are 6 oranges left and 14 apples left a total of 20 fruits. 14 = 70% of 20 therefore D Is the correct ans

DhruvS · Answer

I did it like below:

Total Apples/(Total Fruits - Oranges to be removed) = 70%

Now assume Oranges to be removed = x

14/(14+23-x) = 70/100
Further solving will give :
20=37-x
x= 17

Hence D

Posted from my mobile device

KingAdam44 · Answer

A very simple and innocent approach of this problem is sufficient to solve this under 50 seconds:

14 Apples, 23 Oranges for 1 Box --> 14A + 23O = 1B, and we need to subtract enough Oranges to have 30% of oranges and 70% of apples left.

We know that the initial 14 Apples won't move, and that 2/3-->66% of 21 is 14! Just by understanding this, we can approximate the subtraction of 16 oranges to complete the equivalence, and the nearest number to this is 17: Answer D, it's done!

mathislife · Answer

The question stem tells us that we will not remove any apples and the desired end state is to have 70% of the box be apples. 
As a result we know that: 
.70(future total fruit)=14 apples
future total fruit = 20

This means future total fruit will be 14 apples and 6 oranges. Right now we have 23 oranges and we need to get to 6, which we can do by removing 17 oranges.

Ans D.

ScottTargetTestPrep · Answer

Solution:
 
If none of the apples are removed and only oranges are removed, then if there are 20 pieces of fruit, then the 14 apples will constitute 70 percent of all the pieces of fruit. Since now there are a total of 14 + 23 = 37 pieces of fruit, we see that 37 - 20 = 17 oranges must be removed.

Answer: D

ArnauG · Answer

Initially, the box contains 14 apples and 23 oranges, making a total of 14 + 23 = 37 pieces of fruit.

If x oranges are removed, the number of apples remains the same at 14, and the number of oranges becomes 23 - x.

To ensure that 70% of the pieces of fruit in the box are apples, we need to have:

Number of apples / Total number of fruit = 70% = 0.70

Substituting the values, we have:

14 / (37 - x) = 0.70

Multiplying both sides by (37 - x):

14 = 0.70 * (37 - x)

Dividing both sides by 0.70:

20 = 37 - x

Rearranging the equation:

x = 37 - 20 = 17

Therefore, 17 oranges must be removed from the box so that 70% of the pieces of fruit in the box will be apples.

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