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

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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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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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

Great, thanks Bunuel, then my reasoning was correct!

Chetan2u; do you mean 16a?

For (1) we are told that "The number of vans...", not the number of total vehicles.
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thanks .. misread it , but coincidentally even if it said all vehicles, Statement I would be suff
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Bunuel, this one is asked in Official Mock, please tag it under GMAT Prep

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Added the tag. Thank you!
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Given:
The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans.
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

Let the number of sedans, number of trucks and number of vans be 4k , 5k & 7k respectively, where k is a positive integer.

Asked: 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.
Number of vans = 7k = 14 ; k = 2; since 14 is the only multiple of 7 between 10 and 20.
Total number of vehicles sold at the dealership last month = 4k + 5k + 7k = 16k = 32
SUFFICIENT

2) The number of sedans sold at the dealership last month was less than 10.
Number of sedans = 4k = 4 or 8;
Since the number of sedans may be 4 or 8, the value of k can not be determined uniquely.
Total number of vehicles sold at the dealership last month = 4k + 5k + 7k = 16k = 16 or 32
NOT SUFFICIENT

IMO A

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