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In the 30-day month of June, a motorcycle dealership sold a

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In the 30-day month of June, a motorcycle dealership sold a

by BTGmoderatorLU » Wed Jan 02, 2019 1:57 pm

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Source: Veritas Prep

In the 30-day month of June, a motorcycle dealership sold a different number of motorcycles each day. If it recorded at least one sale each day, did the dealership sell at least 525 motorcycles during June?

1) The smallest number of motorcycles sold on any one day was 3.
2) The second highest number of motorcycles sold on any one day was 59.

The OA is D
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Source: — Data Sufficiency |
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by Manasa3190 » Wed Jan 02, 2019 8:57 pm

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In the 30-day month of June, a motorcycle dealership sold a different number of motorcycles each day. If it recorded at least one sale each day, did the dealership sell at least 525 motorcycles during June?

1) The smallest number of motorcycles sold on any one day was 3.
Since number of cycles sold are different on each day, June has 30 days
Least number of cycles sold is 30
Let us consider the least case possible,
3,4,.........33(in 30 days, all consecutive numbers)
n(n+1)/2 => (33(34)/2) -3 = 525
So, in least case it is 525
Sufficient

2) The second highest number of motorcycles sold on any one day was 59.
Since number of cycles sold are different on each day, June has 30 days
Least number of cycles sold is 30
Let us consider the least case possible,
1,2,3,4,.........30(in 30 days, all consecutive numbers)
n(n+1)/2 => (30*(31)/2) = 465
But given second highest is 59 , and Least case highest would be 60
Lets replace 29, 30 we considered as second highest and highest with 59 and 60
465 - 29-30+59+60 = 525
So, in least case it is 525
Sufficient

Option D is correct
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by deloitte247 » Wed Jan 09, 2019 12:58 am

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Statement 1--> The smallest number of motorcycles sold in any one day was 3.
Motorcycle dealership sold a different number of motorcycle each day for 30 days.
There was a day the motorcycle dealer sold just 3 =least no. of motorcycle sold remaining 29 days.
Highest no. of motorcycle sold = 29+3= 32
$$Average=\frac{\left(32+3\right)}{2}=17.5$$
$$Sum=\ average\ \cdot\ \frac{\left(no.\ of\ item\right)}{days}\ =\ 17.5\cdot30=525$$
Statement 1 is SUFFICIENT

Statement 2--> The second highest value of motorcycles sold on any one day was 59.
For at least one sale per day,
Day 1 = 1
Day 29 = 59 (second highest)
Day 30 = 60 (highest)
Day 28 = 28

$$Average\ of\ 28\ days=\frac{\left(1+28\right)}{2}=\frac{29}{2}=14.5$$
$$Sum=average\ \cdot\ no.\ of\ days\ =\ 14.5\cdot28\ =406$$
$$406+remaining\ 2\ days\ =\ 406+\left(59+60\right)=525$$
STATEMENT 2 is also SUFFICIENT

Option D is the answer as BOTH STATEMENT ALONE ARE SUFFICIENT.
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