Hello,
Can you please assist with this?
If p is a prime number, what is the value of p?
(1) The sum of any p consecutive positive integers is a multiple of p.
(2) 2p - 1 is the square of an integer.
OA: E
My approach was as follows:
1) Here p could be 3 or p could be 5. Hence, in-suff.
2) Here I plugged in values till 5 and thought that this was suff. But I was wrong since p = 13 also works here. I was wondering if there is a different way to solve this problem or if for these kinds of problems we have to test at least a few values?
Thanks a lot,
Sri
To find prime p given 2p - 1 is the square of an integer
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For any set of CONSECUTIVE INTEGERS with an ODD NUMBER OF TERMS:gmattesttaker2 wrote:Hello,
Can you please assist with this?
If p is a prime number, what is the value of p?
(1) The sum of any p consecutive positive integers is a multiple of p.
(2) 2p - 1 is the square of an integer.
The SUM is always equal to a MULTIPLE OF THE NUMBER OF TERMS.
Examples:
The sum of any 3 consecutive integers is equal to a MULTIPLE OF 3.
The sum of any 5 consecutive integers is equal to a MULTIPLE OF 5.
The sum of any 13 consecutive integers is equal to a MULTIPLE OF 13.
Statement 1: The sum of any p consecutive positive integers is a multiple of p.
According to the property discussed above, p can be ANY ODD PRIME NUMBER.
INSUFFICIENT.
Statement 2: 2p - 1 is the square of an integer
Make a list of the perfect squares up to 100:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Set 2p-1 equal to this list and simplify:
2p-1 = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
2p = 2, 5, 10, 17, 26, 37, 50, 65, 82, 101.
Since 2p must be equal to an EVEN integer, the list of options can be narrowed as follows:
2p = 2, 10, 26, 50, 82
p = 1, 5, 13, 25, 41.
In the resulting list, the following options are prime:
p=5, p=13, p=41.
Since p can be different values, INSUFFICIENT.
Statements combined:
Since p=5, p=13 and p=41 satisfy both statements, the value of p cannot be determined.
INSUFFICIENT.
The correct answer is E.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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