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If n is the sum of the first 50 positive integers, what is t

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by Max@Math Revolution » Sun Jun 10, 2018 11:47 pm
[GMAT math practice question]

If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?

A. 3
B. 5
C. 7
D. 17
E. 51
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by Brent@GMATPrepNow » Mon Jun 11, 2018 4:51 am
Max@Math Revolution wrote: If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?

A. 3
B. 5
C. 7
D. 17
E. 51
n = 1 + 2 + 3 + 4 + ...... + 47 + 48 + 49 + 50

Let's add the values in pairs, starting from the outside and work towards the middle
n = (1 + 50) + (2 + 49) + (3 + 48) + . . ..
= 51 + 51 + 51 + .....

Since we are adding 50 values (from 1 to 50), we will get 25 PAIRS of values
So, n = (25)(51)

Factor: n = (5)(5)(3)(17)

Answer: 17

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by Brent@GMATPrepNow » Mon Jun 11, 2018 4:54 am
Max@Math Revolution wrote:[GMAT math practice question]

If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?

A. 3
B. 5
C. 7
D. 17
E. 51
Alternatively, we can use the following formula:
Sum of the first k positive integers = (k)(k+1)/2
For example, the sum of the first 10 positive integers = (10)(10 + 1)/2 = 55

So, the sum of the first 50 positive integers = (50)(50 + 1)/2
= (50)(51)/2
= (25)(51)
= (5)(5)(3)(17)

Answer: D

Cheers,
Brent
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by Max@Math Revolution » Wed Jun 13, 2018 1:42 am
=>

1 + 2 + 3 + ... + 50 = 50*(50 + 1)/2 = 25*51 = 52*3*17
17 is the greatest prime factor of n.

Therefore, the answer is D.
Answer: D
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by Jeff@TargetTestPrep » Wed Jun 13, 2018 3:37 pm
Max@Math Revolution wrote:[GMAT math practice question]

If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?

A. 3
B. 5
C. 7
D. 17
E. 51

The average of consecutive positive integers is: (largest plus smallest)/2. Thus, the sum of the first 50 positive integers is:

(50 + 1)/2 x 50 = 51 x 25 = 17 x 3 x 5^2

So the largest prime factor is 17.

Answer: D

Jeffrey Miller
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[email protected]

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