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06 Aug 2003, 05:33
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What is the units place of (A)^2A
1. A is not divisible by 5
2. Ais an even no.
1. A is not divisible by 5
2. Ais an even no.
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06 Aug 2003, 08:38
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My answer is 6. Crude method but still took me a minute.
From condition (1), A is not divisible by 5
for A=1, A^2A=1
for A=3, A^2A=3^6=3^3 * 3^3=27 * 27 => Unit's digit is 9
Hence, cond. (1) is not sufficient
From condition (1), A is even
for A=2, A^2A=2^4=16 => Unit's digit is 6
for A=4, A^2A=4^8= (4^2)^4=16^4 => Unit's digit is 6
for A=6, A^2A=6^12= (6^2)^6=36^6 => Unit's digit is 6
for A=8, A^2A=8^16= (8^2)^8=16^8 => Unit's digit is 6
Because the units digit is 6 before applying the power is 6 and the power is even, it has to give a 6 as the unit's digit in the final answer.
My answer is 6. Crude method but still took me a minute.
From condition (1), A is not divisible by 5
for A=1, A^2A=1
for A=3, A^2A=3^6=3^3 * 3^3=27 * 27 => Unit's digit is 9
Hence, cond. (1) is not sufficient
From condition (1), A is even
for A=2, A^2A=2^4=16 => Unit's digit is 6
for A=4, A^2A=4^8= (4^2)^4=16^4 => Unit's digit is 6
for A=6, A^2A=6^12= (6^2)^6=36^6 => Unit's digit is 6
for A=8, A^2A=8^16= (8^2)^8=16^8 => Unit's digit is 6
Because the units digit is 6 before applying the power is 6 and the power is even, it has to give a 6 as the unit's digit in the final answer.
06 Aug 2003, 08:51
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(1) A is not divisible by 5
2^4=16, so the unit digit is 6
1^2=1; the units digit is 1, not suff
(2) A is even
2^4=16 --- 6
-2^-4=1/16 not even an integer
10^20 --- 0
not suff
Combine: 2^4=16, but -2^4 is not an integer, So it is E for the given verbiage.
If (2) were to be that A is positive and even, then the answer would be C.
Any even= 2N
(2N)^4N= (16*N^4)^N it will always have 6 as its last digits, save that N is a multiple of 5. 0^0 has no sense.
N^4
1^4=1 last digit is 1, does not affect 6
2^4=16, does not affect 6
3^4=81, does not affect 6
4^4=256, does not affect 6
5^4=625 DOES AFFECT 6
6^4 never affect 6
7^4=2401 does not affect 6
8^4=4096 does not affect 6
9^4=6561 does not affect 6
and so on
2^4=16, so the unit digit is 6
1^2=1; the units digit is 1, not suff
(2) A is even
2^4=16 --- 6
-2^-4=1/16 not even an integer
10^20 --- 0
not suff
Combine: 2^4=16, but -2^4 is not an integer, So it is E for the given verbiage.
If (2) were to be that A is positive and even, then the answer would be C.
Any even= 2N
(2N)^4N= (16*N^4)^N it will always have 6 as its last digits, save that N is a multiple of 5. 0^0 has no sense.
N^4
1^4=1 last digit is 1, does not affect 6
2^4=16, does not affect 6
3^4=81, does not affect 6
4^4=256, does not affect 6
5^4=625 DOES AFFECT 6
6^4 never affect 6
7^4=2401 does not affect 6
8^4=4096 does not affect 6
9^4=6561 does not affect 6
and so on
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
