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Math Expert V
Joined: 02 Sep 2009
Posts: 58335
The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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Difficulty:   5% (low)

Question Stats: 80% (01:19) correct 20% (01:45) wrong based on 187 sessions

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The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

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Retired Moderator G
Joined: 26 Nov 2012
Posts: 580
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

O / A = 3/4 => O = 3/4(A).

Now O/A-4 = 3/2 . Now sub O value in this...we get 3A / 4A-16 = 3/2 => A = 8 and O = 6.

IMO option C.
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Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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o a
3x 4x
3x 3
4x-4 2
=
6x = 12x-12
x = 2
3x = 6

C
CEO  V
Joined: 12 Sep 2015
Posts: 3990
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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2
Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

Let O = # of oranges originally in basket
Let A = # of apples originally in basket

The ratio of oranges to apples in a fruit basket is 3 to 4
So, O/A = 3/4
Cross multiply to get: 4O = 3A

After Mary and Alan eat four apples, the ratio changes to 3 to 2
NOTE: I'm assuming they eat a TOTAL of 4 apples, and not 4 apples each.
So, the number of apples is now A - 4
So, the oranges to apples ratio is as follows: O/(A-4) = 3/2
Cross multiply to get: 2O = 3(A - 4)
Expand: 2O = 3A - 12

We now have the following system:
4O = 3A
2O = 3A - 12

SUBTRACT the bottom equation from the top equation to get: 2O = 12
Solve: O= 6

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Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 833
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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1
1
Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

I vote for plugging in the answer choices on this one.

You can eliminate (A) immediately, since it's not a multiple of 3.

(B): if there are 3 oranges, there are 4 apples. After Mary and Alan eat 4 apples, there would be 0 apples. That's not a 3:2 ratio. Wrong.

(C): If there are 6 oranges, there are 8 apples. After Mary and Alan eat 4 apples, there would be 4 apples. That's 6:4, which is 3:2. Correct.
_________________ Chelsey Cooley | Manhattan Prep | Seattle and Online

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Current Student B
Joined: 24 Jul 2016
Posts: 75
Location: United States (MI)
GMAT 1: 730 Q51 V40 GPA: 3.6
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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I thought a decrease of 2 units mean 4 apples. So one unit means 2 apples. Hence, 3 units of oranges mean 6 oranges Sent from my iPhone using GMAT Club Forum mobile app
Current Student B
Status: DONE!
Joined: 05 Sep 2016
Posts: 358
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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1
orange/apple = 3x/(4x-4) = 3/2
6x=12x-12
12=6x
x=2

3(2) = 6 oranges
Intern  B
Joined: 27 Dec 2017
Posts: 26
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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Org:app::3:4;. Org:app-4::3:2
3/4APP: APP-4::3:2=3/2app=3(app-4)
12=3/2app=app is 8 org = 6

study mode
Intern  B
Joined: 31 May 2018
Posts: 22
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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GMATPrepNow wrote:
Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

Let O = # of oranges originally in basket
Let A = # of apples originally in basket

The ratio of oranges to apples in a fruit basket is 3 to 4
So, O/A = 3/4
Cross multiply to get: 4O = 3A

After Mary and Alan eat four apples, the ratio changes to 3 to 2
NOTE: I'm assuming they eat a TOTAL of 4 apples, and not 4 apples each.
So, the number of apples is now A - 4
So, the oranges to apples ratio is as follows: O/(A-4) = 3/2
Cross multiply to get: 2O = 3(A - 4)
Expand: 2O = 3A - 12

We now have the following system:
4O = 3A
2O = 3A - 12

SUBTRACT the bottom equation from the top equation to get: 2O = 12
Solve: O= 6

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I thought D, according to your below approach

3 4
6 8
9 12
12 16

Here 16-12=4; as 4 apple gone according to stem, so why not D?

Would you please explain this?

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CEO  V
Joined: 12 Sep 2015
Posts: 3990
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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Anupom wrote:
I thought D, according to your below approach

3 4
6 8
9 12
12 16

Here 16-12=4; as 4 apple gone according to stem, so why not D?

Would you please explain this?

I'm not entirely sure I follow your rationale.

Let's say the correct answer is D, which means there are 9 oranges and 12 apples in the bag ORIGINALLY.
AFTER 4 apples are eaten, there are now 9 oranges and 8 apples in the bag
However, the question tells us that the ratio of oranges to apples CHANGES to 3:2 (9:8)
So, the correct answer cannot be D
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Manager  B
Joined: 03 Aug 2017
Posts: 60
Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,  [#permalink]

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Bunuel wrote:
The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?

A. 2
B. 3
C. 6
D. 9
E. 12

This is how i solved.

The original ratio = 3/4 for Oranges / Apples

Lets form an equation 3x / 4x - 4 = 3/2

cross multiply to get x= 2

Now Original amount of Oranges = 3x ie 3*2 = 6 Oranges and choice C Re: The ratio of oranges to apples in a fruit basket is 3 to 4. However,   [#permalink] 03 Oct 2019, 01:39
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