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# M21-08

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Math Expert
Joined: 02 Sep 2009
Posts: 44566

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16 Sep 2014, 01:10
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Difficulty:

45% (medium)

Question Stats:

60% (01:11) correct 40% (01:24) wrong based on 144 sessions

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In a fleet of a certain car-renting agency the ratio of the number of sedans to the number of hatchbacks was 9:8. After the addition of 3 sedans and 1 hatchback, this ratio rose to 6:5, how many more sedans than hatchbacks does the agency have after the addition ?

A. 2
B. 3
C. 5
D. 7
E. 9
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:10
Official Solution:

In a fleet of a certain car-renting agency the ratio of the number of sedans to the number of hatchbacks was 9:8. After the addition of 3 sedans and 1 hatchback, this ratio rose to 6:5, how many more sedans than hatchbacks does the agency have after the addition ?

A. 2
B. 3
C. 5
D. 7
E. 9

Denote $$H$$ and $$S$$ respectively as the number of hatchbacks and sedans in the fleet before the addition of new cars. We can compose a system of equations:

$$\frac{S}{H} = \frac{9}{8}$$

$$\frac{S + 3}{H + 1} = \frac{6}{5}$$

Solving this system, we get $$S = 27$$ and $$H = 24$$. Now the agency has 30 sedans and 25 hatchbacks. The answer to the question is 5.

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12 Sep 2016, 13:48
I overlooked the word "now" in the heat of the moment, which gave me the wrong answer as 3.
Here in the question stem it is written "If after addition" that makes the question an assumption as in a hypothetical situation where we are adding 3 Sedans and 1 Hatchback.
The question would be clear if it simply removes "if" and says after the addition.
Intern
Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
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16 Sep 2016, 06:47
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I always use this format when working with ratios: 9x/8x - the initial ratio. (9x+3)/(8x+1)=6/5 x=3
Manager
Joined: 28 Dec 2016
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17 Jan 2017, 19:35
Great question, but I too have problem understanding the question with complete clarity.
The question seems to ask about the the difference in number of cars before the addition of 3 sedans and 1 hatchback. ('now')
what is the difference 'now' should be worded refer to what is the difference 'after' the addition.
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Joined: 25 Jan 2016
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Location: United States (NJ)
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02 May 2017, 13:16
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I am not following the arithmetic on how we got x=3.

Can someone please show the details on how we got to x=3?

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Joined: 14 May 2015
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06 May 2017, 13:18
(9x+3)/(8x+1) = 6/5
x=3
difference= 9*3+3 - 8*3+1 =5
ans: c
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Joined: 26 Mar 2017
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18 Jun 2017, 07:38
I think this is a poor-quality question and I agree with explanation. I also believe that the question could be better written. I understood the question asked about the number before the addition, so I answered 3 (B)
Math Expert
Joined: 02 Sep 2009
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18 Jun 2017, 09:54
Pol DC wrote:
I think this is a poor-quality question and I agree with explanation. I also believe that the question could be better written. I understood the question asked about the number before the addition, so I answered 3 (B)

I don;t think the question is ambiguous:
In a fleet of a certain car-renting agency the ratio of the number of sedans to the number of hatchbacks was 9:8. If after the addition of 3 sedans and 1 hatchback, this ratio rose to 6:5, how many more sedans than hatchbacks does the agency have NOW?

What is confusing or unclear there?
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Joined: 16 May 2016
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Schools: Wharton '20 (II)
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25 Aug 2017, 17:44
Bunuel wrote:
Pol DC wrote:
I think this is a poor-quality question and I agree with explanation. I also believe that the question could be better written. I understood the question asked about the number before the addition, so I answered 3 (B)

I don;t think the question is ambiguous:
In a fleet of a certain car-renting agency the ratio of the number of sedans to the number of hatchbacks was 9:8. If after the addition of 3 sedans and 1 hatchback, this ratio rose to 6:5, how many more sedans than hatchbacks does the agency have NOW?

What is confusing or unclear there?

The addition of 3 sedans are hypothetical and in the future. Therefore now refers to 9:8, not 6:5; even though 6:5 helps us solve 9:8. For example, if you gave me three more apples and I now have seven, how many apples do I have now. Right now I have four, not seven.

I figured out the work for the question, but ended up following the grammar of the sentence, only to arrive at an incorrect result.
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14 Nov 2017, 05:00
There is a slight ambiguity as far as the wording is concerned. I think the use of "now" and "if" creates a lot of confusion. When we use "if", the meaning conveyed is that the situation described is hypothetical. "Now" then means that we are expected to give the ratio before the addition.
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14 Nov 2017, 06:29
spetznaz wrote:
There is a slight ambiguity as far as the wording is concerned. I think the use of "now" and "if" creates a lot of confusion. When we use "if", the meaning conveyed is that the situation described is hypothetical. "Now" then means that we are expected to give the ratio before the addition.

Edited as suggested. Hope now is clear.
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Re: M21-08   [#permalink] 14 Nov 2017, 06:29
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# M21-08

Moderators: chetan2u, Bunuel

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