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Multiplying

by manelgirona » Sat Jan 30, 2010 8:03 am
If 4a8 and 6b are integers with unspecified digits a and b, which of the following could be the result of multiplying 4a8X6b?

a.) 20,574
b.) 23,816
c.) 30,686
d.) 32,507
e.) 36,728

OA: later
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by sars72 » Sat Jan 30, 2010 9:19 am
the product's unit digit is the unit digit of 8*b. Therefore, the units digit should be the units digito of a multiple of 8

8*1=8 -> 8
8*2=16 -> 6
8*3 =24 -> 4
8*4 = 32 -> 2
8*5 =40 - > 0
8*6 = 48 -> 8 ..and the cycle repeats

so, we have 0,2,4,6,7 as the possible units digits and thus answer choice D is eliminated

4a8 * 60 + 4a8 * b = x

let's find the upper bound value i.e. the value the answer should certainly be less than
--> 500*70 = 3500 -> ans choice E is eliminated

now let's find the lower bound value
400*60 = 24000 -> ans choices A & B are eliminated

So, now we only have answer choice C as a possible answer and thefore this is the answer.
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by manelgirona » Sat Jan 30, 2010 10:12 am
Correct.

thanks!
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by bigmonkey31 » Sat Jan 30, 2010 12:23 pm
Nice! So you just rounded up to 500 and 70 to get the upper bound and likewise (rounded down) for the lower bound, correct? Good strat
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by vibhusethi » Sun Jan 31, 2010 4:55 pm
Awesome solution! Thanks.
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