a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc
Which one of the following must be a factor of abcabc?
(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above
Nice Question...
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- ssmiles08
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abcabc = a*100000 + b*10000 + c*1000 + a*100 + b*10 + c
1000(a*100 + b*10 + c) + (a*100 + b*10 + c)
1001(a*100 + b*10 + c)
prime factors of 1001 are 7, 11, 13
7, and 11 are not options, so I think it is 13.
(B)
1000(a*100 + b*10 + c) + (a*100 + b*10 + c)
1001(a*100 + b*10 + c)
prime factors of 1001 are 7, 11, 13
7, and 11 are not options, so I think it is 13.
(B)
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The important thing in the question is the order , if you spot this then no need to expand
order is abcabc I can write it as-----abc~abc ( two groups) the group to the left is 1000 times the group to the right
let abc = p
in other words abcabc = 1000p +p = 1001p , so if you know the factors of 1001 you know the answer what are the factor of 1001 ?
we know 11 is a factor ( 11*91) so are 7 and 13 (91=7*13)
Hence the answer is 13
what I see is that when one gets a question similar to this one it should be answerable with in 1 min so there must be a catch to the question
just think why did the question say abcabc ---- because something is there
If you see this the question becomes very easy
order is abcabc I can write it as-----abc~abc ( two groups) the group to the left is 1000 times the group to the right
let abc = p
in other words abcabc = 1000p +p = 1001p , so if you know the factors of 1001 you know the answer what are the factor of 1001 ?
we know 11 is a factor ( 11*91) so are 7 and 13 (91=7*13)
Hence the answer is 13
what I see is that when one gets a question similar to this one it should be answerable with in 1 min so there must be a catch to the question
just think why did the question say abcabc ---- because something is there
If you see this the question becomes very easy
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If you see this the question becomes very easy
Agree.
Part of GMAT is about spotting patterns(i.e. if one exists). If one is successful in doing so under exam pressure/timing then it becomes really easy and if not then it becomes difficult
Good luck, All!