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Bunuel
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i think the correct answer shd be 28<x<35 and not 28<x<=35
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pujjwal
i think the correct answer shd be 28<x<35 and not 28<x<=35

Just look at the option trend and you will understand why is it given <=35. Anyhow both the options wont change the answer.
Hope this helps. :)
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I do not understand how we are able to discern that 29 was the smallest without checking if there were any numbers lower than 29. How are we sure that the only two prime factors were 29 and 31? Could someone point me to the theory behind this?
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saifsaif
I do not understand how we are able to discern that 29 was the smallest without checking if there were any numbers lower than 29. How are we sure that the only two prime factors were 29 and 31? Could someone point me to the theory behind this?

Factorise 899: 899 = 29*31. As you can see 899 does not have nay other primes but 29 and 31.
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Hey Bunuel can you post similar questions to practice
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Hello,
Could you advise, how to apply this approach for 901?
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Hello,
Could you advise, how to apply this approach for 901?
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In order to apply this approach you need a number to be equal to a difference of two squares. 899 equals 900 - 1. 900 is 30 squared while 1 is one squared. Therefore we could apply the identity [x^2-y^2]
901 is not a a difference of two squares, rather it is a sum of two squares so this identity does not apply. 901 is a composite number because we can see that 17 can evenly divide into it. 17 x 53 =901
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Mich18
Hello,
Could you advise, how to apply this approach for 901?
899 = 900-1
\(=30^2-1^2\)
=(30+1)(30-1)
=31*29, both are primes.
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This is a tough one, i took some time doing prime factorization to get the answer and i thought its not feasible to solving under 2 minutes until i saw official solution. The shortcut is very useful and this goes into my error log. It would be helpful if we have similar questions to practice.

Bunuel - Can you please point me in the direction of similar questions to practice ?
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I think this is a poor-quality question and I don't agree with the explanation. smallest prime factor of 899 is 7 and prime factorisation is 1*7*127
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BhavyaMehta1
I think this is a poor-quality question and I don't agree with the explanation. smallest prime factor of 899 is 7 and prime factorisation is 1*7*127

HOW did you get this??? 899 is NOT divisible by 7 or by 127.

899 = 29*31.
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