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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  [#permalink]

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New post 03 Jul 2014, 00:30
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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.

(2) The second highest number of motorcycles sold on any one day was 59.
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In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 03 Jul 2014, 03:47
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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?

Notice that we are told that the dealership sold a different number of motorcycles each day.

(1) The smallest number of motorcycles sold on any one day was 3. The least number of motorcycles sold in June would be 3 + 5 + 6 + ... + 32 = (3 + 32)/2 *30 = 525. Sufficient.

(2) The second highest number of motorcycles sold on any one day was 59. The least number of motorcycles sold in June would be (1 + 2 + 3 + ... + 28) + 59 + 60 = (1 + 28)/2*28 + 119 = 525. Sufficient.

Answer: D.
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Re: In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 04 Jul 2014, 03:20
Bunuel wrote:
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?

Notice that we are told that the dealership sold a different number of motorcycles each day.

(1) The smallest number of motorcycles sold on any one day was 3. The least number of motorcycles sold in June would be 3 + 5 + 6 + ... + 32 = (3 + 32)/2 *30 = 525. Sufficient.

(2) The second highest number of motorcycles sold on any one day was 59. The least number of motorcycles sold in June would be (1 + 2 + 3 + ... + 28) + 59 + 60 = (1 + 28)/2*28 + 119 = 525. Sufficient.

Answer: D.


I am not very clear as to how did you solve this?
how did you take up (3 + 32)/2 * 30 and also how did you choose 3 + 5+6...

For 2nd point how did you split into 28 parts and did you randamply choose 60 as highest number because I chose 61 thinking that 59 + 61 = 120 would be a whole number which will help to divide the rest number motorcylces easily

Kindly explain.
Thanks in advance
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Re: In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 04 Jul 2014, 05:12
nehamodak wrote:
Bunuel wrote:
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?

Notice that we are told that the dealership sold a different number of motorcycles each day.

(1) The smallest number of motorcycles sold on any one day was 3. The least number of motorcycles sold in June would be 3 + 5 + 6 + ... + 32 = (3 + 32)/2 *30 = 525. Sufficient.

(2) The second highest number of motorcycles sold on any one day was 59. The least number of motorcycles sold in June would be (1 + 2 + 3 + ... + 28) + 59 + 60 = (1 + 28)/2*28 + 119 = 525. Sufficient.

Answer: D.


I am not very clear as to how did you solve this?
how did you take up (3 + 32)/2 * 30 and also how did you choose 3 + 5+6...

For 2nd point how did you split into 28 parts and did you randamply choose 60 as highest number because I chose 61 thinking that 59 + 61 = 120 would be a whole number which will help to divide the rest number motorcylces easily

Kindly explain.
Thanks in advance


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 .
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Re: In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 22 Oct 2014, 00:10
#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 !
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Re: In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 09 Nov 2014, 11:44
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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?
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Re: In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 09 Nov 2014, 12:31
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usre123 wrote:
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.
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Re: In the 30-day month of June, a motorcycle dealership sold a  [#permalink]

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New post 09 Nov 2014, 13:09
1
Raihanuddin wrote:
usre123 wrote:
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! :oops:
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Re: In the 30-day month of June, a motorcycle dealership sold a   [#permalink] 05 Mar 2019, 11:51
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