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The only types of vehicles sold at a certain dealership last month

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The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:26
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The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.
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The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:31
Sallyzodiac wrote:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.


ratio is 4:5:7, so if we have a common ratio as 'a', total becomes 4a+5a+7a = 16a..
so either we require any of the values of three or common ratio 'a'..


lets see the statements-


1) The number of vans sold at the dealership last month was between 10 and 20.
so 7a is between 10 and 20 , so ONLY value of 'a' can be 2..
total sedan = 32
suff

2) The number of sedans sold at the dealership last month was less than 10

now sedans are 4a, so it can have either 4 or 8 as its number and thus 'a' can be 1 or 2
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:36
My initial thought was that the range given in S1 and "the less than"-statement in S2 would result in several answers possible. However, looking closer at S1, we get that that the total number of vans sold is between 10 & 20. We know that the number of vans sold in total are 7/16, and since we can't sell half a van, the number of vans sold must be a multiple of 7. Between 10 and 20, there is only one multiple of 7 (14), thus the total number of vans sold must be 14. 14/(7/16) = 32 - i.e. the total amount of vehicles sold is 32.

Do people agree with this reasoning?

/S
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Re: The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:37
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The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

The ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively: s:t:v = 4x:5x:7x, for some positive integer x.

1) The number of vans sold at the dealership last month was between 10 and 20 --> 10 < v < 20 --> 10 < 7x < 20. There is only one multiple of 7 in this range - 14, therefore v = 14, x = 2. We can find all the unknowns. Sufficient.

2) The number of sedans sold at the dealership last month was less than 10 --> s < 10 --> 4x < 10. x can e 1 or 2. Not sufficient.

Answer: A.

Hope it's clear.
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Re: The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:40
Bunuel wrote:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

The ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively: s:t:v = 4x:5x:7x, for some positive integer x.

1) The number of vans sold at the dealership last month was between 10 and 20 --> 10 < v < 20 --> 10 < 7x < 20. There is only one multiple of 7 in this range - 14, therefore v = 14, x = 2. We can find all the unknowns. Sufficient.

2) The number of sedans sold at the dealership last month was less than 10 --> s < 10 --> 4x < 10. x can e 1 or 2. Not sufficient.

Answer: A.

Hope it's clear.


Great, thanks Bunuel, then my reasoning was correct! :)
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Re: The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:41
chetan2u wrote:
Sallyzodiac wrote:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.


ratio is 4:5:7, so if we have a common ratio as 'a', total becomes 4a+5a+7a = 16a..
so either we require any of the values of three or common ratio 'a'..


lets see the statements-


1) The number of vans sold at the dealership last month was between 10 and 20.
so 16a is between 10 and 20 , so ONLY value of 'a' can be 1..
total sedan = 16
suff

2) The number of sedans sold at the dealership last month was less than 10

now sedans are 4a, so it can have either 4 or 8 as its number and thus 'a' can be 1 or 2
insuff

A


Chetan2u; do you mean 16a?
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Re: The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:42
1
chetan2u wrote:
Sallyzodiac wrote:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.


ratio is 4:5:7, so if we have a common ratio as 'a', total becomes 4a+5a+7a = 16a..
so either we require any of the values of three or common ratio 'a'..


lets see the statements-


1) The number of vans sold at the dealership last month was between 10 and 20.
so 16a is between 10 and 20 , so ONLY value of 'a' can be 1..
total sedan = 16
suff


2) The number of sedans sold at the dealership last month was less than 10

now sedans are 4a, so it can have either 4 or 8 as its number and thus 'a' can be 1 or 2
insuff

A


For (1) we are told that "The number of vans...", not the number of total vehicles.
_________________

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!!!

Resources:
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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: The only types of vehicles sold at a certain dealership last month  [#permalink]

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New post 03 May 2016, 05:47
Bunuel wrote:
chetan2u wrote:
Sallyzodiac wrote:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.


ratio is 4:5:7, so if we have a common ratio as 'a', total becomes 4a+5a+7a = 16a..
so either we require any of the values of three or common ratio 'a'..


lets see the statements-


1) The number of vans sold at the dealership last month was between 10 and 20.
so 16a is between 10 and 20 , so ONLY value of 'a' can be 1..
total sedan = 16
suff


2) The number of sedans sold at the dealership last month was less than 10

now sedans are 4a, so it can have either 4 or 8 as its number and thus 'a' can be 1 or 2
insuff

A


For (1) we are told that "The number of vans...", not the number of total vehicles.


thanks .. misread it , but coincidentally even if it said all vehicles, Statement I would be suff
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The only types of vehicles sold at a certain dealership last month  [#permalink]

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