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M21-08

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M21-08 [#permalink]

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New post 16 Sep 2014, 01:10
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Question Stats:

69% (01:13) correct 31% (01:40) wrong based on 51 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. 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?

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

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Re M21-08 [#permalink]

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New post 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. 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?

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.


Answer: C
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Re: M21-08 [#permalink]

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New post 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.

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Re: M21-08 [#permalink]

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New post 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

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Re: M21-08 [#permalink]

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New post 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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Re: M21-08 [#permalink]

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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?

Thanks in advance!

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Re: M21-08 [#permalink]

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New post 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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Re M21-08 [#permalink]

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New post 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)

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Re: M21-08 [#permalink]

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New post 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?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

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GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M21-08 [#permalink]

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New post 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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Re: M21-08   [#permalink] 25 Aug 2017, 17:44
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