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m09 32

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Re: m09 32 [#permalink] New post 03 Sep 2010, 05:10
The OA is NOT B, but D. See Bunuel's explanation closely:
m09-74730.html#p685866
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Re: m09 32 [#permalink] New post 05 Sep 2010, 08:23
obvious D. No need to debate on answer. A quick press of the calculator reviewed 7625597484987. Last digit is 7.
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Re: m09 32 [#permalink] New post 07 Sep 2010, 21:24
Its D.

3 to the power 3 to the power 3 translates into 3 to the power 27. Cyclicity is 3, 9, 7, 1 and to degree 4. So 3 to the power 27 goes for 3rd value in the cycle -7.
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Re: m09 32 [#permalink] New post 08 Sep 2011, 04:48
alexgmd wrote:
easy "B"


ans is D not B.

look for above explanation.
if still you have any doubt, i can try to clarify them.
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Re: m09 32 [#permalink] New post 17 Sep 2011, 08:00
Nice question. Thanks.
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Re: m09 32 [#permalink] New post 07 Sep 2012, 04:54
gijoedude wrote:
Answer is 7.

Step 1: 3^3= 27.

Step 2: Therefore 3^(3^3)=3^27. = 3*3*3*.......3 (27 3s).

Step 3: We know 3*3*3 = 27

Step 4: Hence step 2 can be simplified as 27*27*...27 (9 27s)

Step 5: We know 27*27*27 ends in 3 (multiply it out. No need to do the entire multiplication. Only the last digits matter).

Step 6: Hence we end up abc3*abc3*abc3 = a number ending with 7 (again only the last digits matter)

Step 7: Voila!


This is way too complicated !
Every digit has a pattern that repeats. See the chart given below. Some repeat in multiples of 4, others repeat in multiples of 1 and 2.
Key takeaway is that EVERY POWER REPEATS !

Powers of 2 - 2,4,8,6,,2,4,8,6
Powers of 3- 3,9,7,1,3,9,7,1
Powers of 4 - 4,6,4,6,4,6
Powers of 5 - 5,5,5,5,5,5,5,
Powers of 6 - 6,6,6,6,6,6,6,
Powers of 7 - 7,9,3,1,7,..
Powers of 8 - 8,4,2,6,8
Powers of 9 - 9,1,9,1

They key is to find the pattern for reptition. A units digit for a power of 3 repeats every 4 terms.
The units digit for 3 ^ 27 ==> Hence the term that corresponds to Remainder of (27 divided by 4) = 3rd term = 7 is the answer

To stretch this a lil bit more
2 ^ 100 = Remainder of (100 divided by 4) = Remainder = 0 , ie 4th term

A word of caution - Focus on the word remainder.
The division only tells us the POSITION of the term in the sequence and NOT the repeating term itself.
2^50 =-> REMAINDER OF (50 divided by 4) = 2ND TERM in the sequence, hence 4
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Re: m09 32 [#permalink] New post 10 Sep 2012, 00:58
Exponentiation is not associative. Addition and multiplication are. For example, (2 + 3) + 4 = 2 + (3 + 4) = 9 and (2·3)·4 = 2·(3·4) = 24, but 23 to the 4 is 84 or 4,096, whereas 2 to the 34 is 281 or 2,417,851,639,229,258,349,412,352. Without parentheses to modify the order of calculation, by convention the order is top-down, not bottom-up:

b^{p^q} = b^{(p^q)} != (b^p)^q = b^{(p \c*q)} = b^{p \c*q}
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Re: m09 32 [#permalink] New post 07 Sep 2013, 04:22
this works for units digit only.
for any integer a
a ^ (4n+x) = a^x...

3^27 = 3^(4*6+3) = 3^3 =27...

so units digit is 7....
Re: m09 32   [#permalink] 07 Sep 2013, 04:22
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