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

Hi NehaModak,

I am happy to help you with this .

STMT1:

We are initially told that "The smallest number of motorcycles sold on any one day was 3" .
We are also told that "motorcycle dealership sold a different number of motorcycles each day".
In a 30 day month of June we are still left with 29 days . (one day with least no [3] motor cycles sold).

therefore it will be 3+4+5+6+7+ ...................32 .
To find if the motor cycle dealer sold atleast 525 motorcycles , we need to find the sum of all motorcycles sold during the given period.

Sum = average * no of terms .

In a consecutive set , mean(average) = median . Therefore average = 17.5.
no of terms between 3 to 32 inclusive is 30 .
Sum = 17.5 * 30 = 525 (Sufficient) .

STMT2:

The second highest number of motorcycles sold on any one day was 59.

From the above stmt we can infer that both last 2 values of the june month are fixed .

As we are asked about the least number of motor cycles sold , we need to assume that the least number of motorcycles sold on 1st day will be 1 and 2nd day will be 2 and so on till day 28 . [Note : 29th and 30th day are fixed]
Therefore, the least number of motorcycles sold in June would be

(1+2+ ........28) + (29+30)

Therefore sum of motor cycles sold from 1 to 28 days will be .

14.5 (average) * 28(no of days) + [59+60]

525. (Sufficient).

Hope this helps .

#nehamodak

just incase the sum=avg*mean doesn't strike you during the test...
always remember the sum of the integers formula

sum of n integers - n(n+1)/2

hence from 3-32 is the least 30 numbers
1 to 32 is
32(32+1)/2=528

528-3=525

3 is the 1+2...that we considered in the above formula and will be deducted.

all the best !

sorry, but for n(n+1), shouldn't we have 30(31), since number of days=30?

or if you use the sum formula:
(a+l)/2 *n
you have (3+ 32)/2 *30....

Obviously, I don't know how to apply formula one. Can anyone pls explain?

In formula 1. Poster considered number from 1 to 32.
Formula-
1. Sum of first n positive consecutive integers = (n(n+1))/2
2. Sum of first n positive even integers = n(n+1)
3. Sum of first odd integers = n^2

Now In this question if we consider consecutive integers from 1 to 32, we are actually taking 1 and 2 also. So from sum we have to subtract 1+2=3

528-3 =525

Another way

a) We are sure that 3 is the least number and other least possible different numbers are next 29 consecutive numbers.

So sum of consecutive numbers = Mean*total no.
Now, In consecutive numbers Mean = (3+32)/2
Therefore, Sum= 17.5*30 = 525.

Here we are considering consecutive numbers as least possibility. Say total has been given in question 526. Then answer would be E.

sorry. stupid question!

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