The patterns in remainder problems will always emerge fairly early when you plug in numbers. therefore, if you don't IMMEDIATELY realize a good theoretical way to do a remainder problem, you should get on the number plugging RIGHT AWAY.
I would IMMEDIATELY start plugging in numbers and using PATTERN RECOGNITION on a problem like this one. remainder problems usually show patterns after a very, very small number of plug-ins.Statement (1):
it's easy to generate t's that do this: 6, 13, 20, 27,
... (note that 6 is a member of this list, and an awfully valuable one at that; it's quite easy to plug in)
try 6: 36 + 30 + 6 = 72; divide by 7 --> remainder 2
try 13: 169 + 65 + 6 = 240; divide by 7 --> remainder 2
try 20: 400 + 100 + 6 = 506; divide by 7 --> remainder 2
by this point i'd be convinced.
Note that 3 plug-ins is NOT good enough for a great many problems, esp. number properties problems.however, as i said above,
remainder problems don't keep secrets for long. sufficient.
Statement (2):
it's harder to find t's that do this.
however, the gmat is nice to you. if examples are harder to find, then the results will usually come VERY quickly once you find those examples. just take perfect squares, examine them, and see whether they give the requisite remainder upon division by 7. the first two perfect squares that do so are 1^2 = 1 and 6^2 = 36.
if you don't recognize that (1^2)/7 gives remainder 1, then you'll have to dig up 6^2 = 36 and 8^2 = 64. that's not that much more work.
in any case, you'll have:
For 1 & 6:1 + 5 + 6 = 12 --> divide by 7; remainder = 5
36 + 30 + 6 = 72 --> divide by 7, remainder = 2 (the work for this was already done above; you should NOT do it twice. i'm reproducing it here only for the sake of quick understanding.)
or
For 6 & 8:36 + 30 + 6 = 72 --> divide by 7, remainder = 2 (the work for this was already done above; you should NOT do it twice. i'm reproducing it here only for the sake of quick understanding.)
64 +40 + 6 = 110 --> divide by 7, remainder = 5 either way, insufficient within the first two plug-ins!
answer (a)
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