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# M20-27

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Math Expert
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135978 [0], given: 12719

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16 Sep 2014, 00:09
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68% (01:19) correct 32% (01:18) wrong based on 118 sessions

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If 8 apples and 10 oranges cost as much as 22 apples and 4 oranges, how much does a combination of 7 oranges and 3 apples cost?

(1) An orange costs $0.01 more than an apple (2) The ratio of the price of an orange to the price of an apple is 7:3 [Reveal] Spoiler: OA _________________ Kudos [?]: 135978 [0], given: 12719 Math Expert Joined: 02 Sep 2009 Posts: 42652 Kudos [?]: 135978 [0], given: 12719 Re M20-27 [#permalink] ### Show Tags 16 Sep 2014, 00:09 Official Solution: Let $$o$$ denote the price of an orange and $$a$$ the price of an apple. We know from the stem that $$8a + 10o = 22a + 4o$$ or$$14a = 6o$$ or $$o:a = \frac{7}{3}$$. Statement (1) by itself is sufficient. S1 provides another equation: $$o = a + 0.01$$. After solving the system of two linear equations for $$a$$ and $$o$$ we will be able to answer the question. Statement (2) by itself is insufficient. S2 adds no new information. Answer: A _________________ Kudos [?]: 135978 [0], given: 12719 Senior Manager Joined: 15 Sep 2011 Posts: 358 Kudos [?]: 431 [0], given: 45 Location: United States WE: Corporate Finance (Manufacturing) M20-27 [#permalink] ### Show Tags 04 Aug 2015, 19:54 Bunuel wrote: If 8 apples and 10 oranges cost as much as 22 apples and 4 oranges, how much does a combination of 7 oranges and 3 apples cost? (1) An orange costs$0.01 more than an apple

(2) The ratio of the price of an orange to the price of an apple is 7:3

Hello Bunuel,

In the math book, it states, under the subtitle, following cases, order is important: "If a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'" <http://gmatclub.com/forum/word-problems-made-easy-87346.html>

So, by the definition the second statement backwards. I mean, the ratio of the price of an orange to the price of an apple is $$3:7$$, not $$7:3$$
$$a =$$ apples
$$o =$$ oranges
$$8a + 10o = 22a + 4o$$
$$6o = 14a$$
If $$3o = 7a$$, then the ratio is $$3:7$$

I'm sure most people understand what the statement intends to mean, but I thought the problem could be less confusing for others who are working on ratio problems (like myself ). After all, it's not the first time I've seen two values be set up to equal $$0$$, especially after the section on moduli. Let me know your thoughts. Thanks

Kudos [?]: 431 [0], given: 45

Math Expert
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135978 [0], given: 12719

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20 Aug 2015, 08:07
mejia401 wrote:
Bunuel wrote:
If 8 apples and 10 oranges cost as much as 22 apples and 4 oranges, how much does a combination of 7 oranges and 3 apples cost?

(1) An orange costs \$0.01 more than an apple

(2) The ratio of the price of an orange to the price of an apple is 7:3

Hello Bunuel,

In the math book, it states, under the subtitle, following cases, order is important: "If a problems says ‘the ratio of x and y’, it means ‘x divided by y’ NOT 'y divided by x'" <http://gmatclub.com/forum/word-problems-made-easy-87346.html>

So, by the definition the second statement backwards. I mean, the ratio of the price of an orange to the price of an apple is $$3:7$$, not $$7:3$$
$$a =$$ apples
$$o =$$ oranges
$$8a + 10o = 22a + 4o$$
$$6o = 14a$$
If $$3o = 7a$$, then the ratio is 3:7

I'm sure most people understand what the statement intends to mean, but I thought the problem could be less confusing for others who are working on ratio problems (like myself ). After all, it's not the first time I've seen two values be set up to equal $$0$$, especially after the section on moduli. Let me know your thoughts. Thanks

$$3o = 7a$$

$$o:a=7:3$$.

No?
_________________

Kudos [?]: 135978 [0], given: 12719

Senior Manager
Joined: 18 Aug 2014
Posts: 278

Kudos [?]: 76 [0], given: 78

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20 May 2016, 16:04
Bunuel wrote:
Official Solution:

Let $$o$$ denote the price of an orange and $$a$$ the price of an apple. We know from the stem that $$8a + 10o = 22a + 4o$$ or$$14a = 6o$$ or $$o:a = \frac{7}{3}$$.

I'm sorry but how do we get to $$o:a = \frac{7}{3}$$ from 14a = 6o? Should it not be a = $$\frac{3}{7}$$o after dividing 14 from both sides?
_________________

Kudos [?]: 76 [0], given: 78

Math Expert
Joined: 02 Aug 2009
Posts: 5365

Kudos [?]: 6157 [0], given: 121

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20 May 2016, 19:04
redfield wrote:
Bunuel wrote:
Official Solution:

Let $$o$$ denote the price of an orange and $$a$$ the price of an apple. We know from the stem that $$8a + 10o = 22a + 4o$$ or$$14a = 6o$$ or $$o:a = \frac{7}{3}$$.

I'm sorry but how do we get to $$o:a = \frac{7}{3}$$ from 14a = 6o? Should it not be a = $$\frac{3}{7}$$o after dividing 14 from both sides?

Hi,
yes a = $$\frac{3}{7}$$o ....
If I divide both sides by o... $$\frac{a}{o}=\frac{3}{7}$$...... so a:o = 3/7, which is same as the opposite $$o:a = \frac{7}{3}$$ ..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6157 [0], given: 121

Senior Manager
Joined: 18 Aug 2014
Posts: 278

Kudos [?]: 76 [0], given: 78

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20 May 2016, 19:31
chetan2u wrote:
redfield wrote:
Bunuel wrote:
Official Solution:

Let $$o$$ denote the price of an orange and $$a$$ the price of an apple. We know from the stem that $$8a + 10o = 22a + 4o$$ or$$14a = 6o$$ or $$o:a = \frac{7}{3}$$.

I'm sorry but how do we get to $$o:a = \frac{7}{3}$$ from 14a = 6o? Should it not be a = $$\frac{3}{7}$$o after dividing 14 from both sides?

Hi,
yes a = $$\frac{3}{7}$$o ....
If I divide both sides by o... $$\frac{a}{o}=\frac{3}{7}$$...... so a:o = 3/7, which is same as the opposite $$o:a = \frac{7}{3}$$ ..

Woops I think I was overlooking the ratio that prefaced the fraction (o:a), thanks for breaking it down.
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Kudos [?]: 76 [0], given: 78

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Location: India
GMAT 1: 640 Q48 V29

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19 Oct 2017, 22:48
The ratio of price of apples to price of oranges is 3:7. To find 7O+3A , we need to find A and O. Option B does not give us any new input. Option A does help us find A and O. Hence the answer is option A.
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" The few , the fearless "

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Re: M20-27   [#permalink] 19 Oct 2017, 22:48
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# M20-27

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