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n consecutive integers

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri May 29, 2015 9:09 am
j_shreyans wrote:The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9
For any set of evenly spaced integers:
Median = sum/number.

Let the statements guide you.
Test EVEN VALUES LESS THAN 9.

If n=2, then the median = 45/2 = 22.5
The two integers would be 22 and 23.

If n=4, then the median = 45/4 = 11.25.
Not possible: Since the median of two consecutive integers must be halfway between them, the median must be a multiple of 1/2.

If n=6, then the median = 45/6 = 7.5
The six integers would be 5, 6, 7, 8, 9, 10.

Since it's possible that n=2 or that n=6, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by DavidG@VeritasPrep » Fri May 29, 2015 9:13 am
The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even

Let's do some simple algebra. If n = 2, our consecutive numbers will be x and x + 1.
So we have x + x + 1 = 45 --> 2x = 44; x = 22. This works. So n could be 2.

If n = 6, our consecutive numbers will be: x, x + 1, x + 2, x + 3, x + 4, x + 5
This gives x + x + 1 + x +2 + x + 3 + x + 4 + x + 5 = 45 --> 6x + 15 = 45. 6x = 30. x = 5. This also works. So n could be 6.

Not Sufficient.

(2) n < 9

We already know that n could be 2 or n could be 6, so this statement doesn't help. Alone it's no good. And together, they are still not sufficient. Answer is E
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by Brent@GMATPrepNow » Fri May 29, 2015 9:18 am
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9
Target question: What is the value of n?

Given: The sum of n consecutive positive integers is 45.
Let's see what this given information tells us.
Some possible scenarios:
- the numbers are 1,2,3,4,5,6,7,8,9
- the numbers are 5,6,7,8,9,10
- the numbers are 7,8,9,10,11
- the numbers are 14,15,16
- the numbers are 22,23
At this point, we might already see that the answer is E.
To see why, let's go straight to . . .

Statements 1 and 2 combined
There are two sets of consecutive numbers that meet the two given conditions:
Case a: the numbers are {5,6,7,8,9,10} in which case n = 6
Case b: the numbers are {22,23} in which case n = 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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