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kevincan
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BG
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Agree with (C)

My brain is smoking from these number property questions...
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BG
think it is C
If one of the primes is raised to power 2 then the resulting number will have 12 factors. The number is 105 with 8 factors 1,3,5,7,15,21,35,105
Jaynayak, 525=5^2*3*7 and has 12 factors so it fiolates B


Excellent reasoningn.. Agree wiht (C)
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C

St1: Infinite possiblities : SUFF
St2: Multiple possibilities: SUFF

Combined: Let number = 3^x * 5^y * 7^z, where x, y and z are intergers greater than zero.

Then the total number of factors will be (x+1) * (y+1) * (z+1)

So the minimum factors will be when x = 1, y = 1 and z = 1 i.e 8 factors
If we increase any of x,y,z by 1 then the total number of factors exceeds 10. So we can guarantee that x = 1 and y = 1 and z= 1. i.e number = 105
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BG
think it is C
If one of the primes is raised to power 2 then the resulting number will have 12 factors. The number is 105 with 8 factors 1,3,5,7,15,21,35,105
Jaynayak, 525=5^2*3*7 and has 12 factors so it fiolates B


Thanks a lot .......

Had the right thought but didnot carry it through..... So close yet so far.....
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Excellent work, BG and ps_dahiya. ps_dahiya's work is especially instructive for similar questions! You can use this on test day, I'm sure!
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rbcola
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WOw. Where are you getting these problems from Kevin? I would put them in the 700+ bin. What do you guys think ?

C for this one. Since the number is a multiple of 105. 105 has 8 factors. Multiplying it by another number (say another 3) will give 12 factors. So 105 is the only solution.
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I'm making them up for a book- I'm a Kaplan trainer- I hope you find them useful, and I certainly find your solutions very helpful. Thanks to everybody who tries them out!



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