Which of the following is NOT prime?
1,556,551
2,442,113
3,893,257
3,999,991
9,999,991
Number properties
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x² - y² = (x + y)(x - y).sud21 wrote:Which of the following is NOT prime?
1,556,551
2,442,113
3,893,257
3,999,991
9,999,991
Some integers can be expressed as the DIFFERENCE OF TWO SQUARES:
99 = 100 - 1 = 10² - 2² = (10 + 1)(10 - 1) = (11)(99).
9991 = 10000 - 9 = 100² - 3² = (100 + 3)(100 - 3) = (103)(97).
Test this line of reasoning in the answer choices.
Note the following:
If the question stem includes the phrase which of the following, the correct answer is likely to be D or E.
E: 9,999,991 = 10,000,000 - 9.
Doesn't work:
10,000,000 is not a perfect square
D: 3,999,991 = 4,000,000 - 9 = 2000² - 3² = (2000 + 3)(2000 - 3) = (2003)(1997).
Since 3,999,991 is divisible by 2003 and 1997, D is NOT prime.
The correct answer is D.
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Hi Mitch,
I am unable to apply this kind of approach in exam. Do we have any other approach?
I was thinking of doing a Divisibility rule test of 2,3,5,7 for all these options.
apart from div by 77 I am able to do every div test i.e. of 2,3,5 in mind
will this approach work?
Thanks & Regards,
Vishal
I am unable to apply this kind of approach in exam. Do we have any other approach?
I was thinking of doing a Divisibility rule test of 2,3,5,7 for all these options.
apart from div by 77 I am able to do every div test i.e. of 2,3,5 in mind
will this approach work?
Thanks & Regards,
Vishal
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When a question stem asks whether a large integer is prime, the easiest approach -- in most cases -- is to test for divisibility by small factors such as 2, 3, 5 and 9.vishalwin wrote:Hi Mitch,
I am unable to apply this kind of approach in exam. Do we have any other approach?
I was thinking of doing a Divisibility rule test of 2,3,5,7 for all these options.
apart from div by 77 I am able to do every div test i.e. of 2,3,5 in mind
will this approach work?
Thanks & Regards,
Vishal
Here, the correct answer choice is not divisible by any of these small factors, so this approach is not viable.
3,999,991 has only 4 factors: 1, 1997, 2003, and 3,999,991.
The approach used in my solution above seems the fastest way to determine that 3,999,991 is not prime.
Official problems that test the same concept:
https://www.beatthegmat.com/og-ps-query-t276099.html
https://www.beatthegmat.com/another-toug ... 67922.html
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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.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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