If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?
(1) s is even
(2) p = 4t
If r, s, and t are all positive integers
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i would got for B for thisddm wrote:If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?
(1) s is even
(2) p = 4t
P= rst
statement 1. s is even .
thus from this we know rst will so will be even
but then
assume rst =4
2^4 /10 = 6 as remainder
2^6 /10 = 4 as remainder
hence insufficient
Statement B
p =4t
thus we know P is a factor of 4
2^ any factor of 4 divided by 10 will always leave a remainder of 6.
hence B is sufficient.
thus B.
hope that helps..

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I would go for 'B' too....nice explanation
sudhir3127 wrote:i would got for B for thisddm wrote:If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?
(1) s is even
(2) p = 4t
P= rst
statement 1. s is even .
thus from this we know rst will so will be even
but then
assume rst =4
2^4 /10 = 6 as remainder
2^6 /10 = 4 as remainder
hence insufficient
Statement B
p =4t
thus we know P is a factor of 4
2^ any factor of 4 divided by 10 will always leave a remainder of 6.
hence B is sufficient.
thus B.
hope that helps..
ddm wrote:If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?
(1) s is even
(2) p = 4t
IMO B. sinct p = 4t
(2^4t)/10 = (16^t)10. Since t is positive the last digit for 16 to the power of anything should be 6. Hence the remainder is going to be 6.
ddm wrote:If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst?
(1) s is even
(2) p = 4t
IMO B. sinct p = 4t
(2^4t)/10 = (16^t)10. Since t is positive the last digit for 16 to the power of anything should be 6. Hence the remainder is going to be 6.
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 ceilidh.erickson
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The key to understanding this problem is to think about units digits. Whenever a question asks "what is the remainder when divided by 10?", it's really asking "what is the units digit?"
In this problem, we're asking about the units digit of 2 raised to some power. The units digits of powers of 2 form the following pattern:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6 (only looking at the units digit here)
2^5 = 2
2^6 = 4
etc.
You can see that the units digit repeats every 4 powers. So, if we know that p is a multiple of 4, we'll know that the units digit is 6. Otherwise, we won't know. Statement (1) tells us that s (and therefore p) is a multiple of 2, but that's not enough. The units digit could be 4 or 6. Statement (2) tells us that p is a multiple of 4, though, so it's sufficient.
For more info, check out these posts on patterns of units digits:
https://www.beatthegmat.com/ifnandma ... tml#544266
https://www.beatthegmat.com/whatisthe ... tml#544267
In this problem, we're asking about the units digit of 2 raised to some power. The units digits of powers of 2 form the following pattern:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6 (only looking at the units digit here)
2^5 = 2
2^6 = 4
etc.
You can see that the units digit repeats every 4 powers. So, if we know that p is a multiple of 4, we'll know that the units digit is 6. Otherwise, we won't know. Statement (1) tells us that s (and therefore p) is a multiple of 2, but that's not enough. The units digit could be 4 or 6. Statement (2) tells us that p is a multiple of 4, though, so it's sufficient.
For more info, check out these posts on patterns of units digits:
https://www.beatthegmat.com/ifnandma ... tml#544266
https://www.beatthegmat.com/whatisthe ... tml#544267
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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 ceilidh.erickson
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No, 0 is not a positive integer  it's the only integer that's neither positive nor negative! Without that positive constraint, you're right, the answer here would have been E. But with it, statement (2) is sufficient.indiheats wrote:Why can T not be zero ? Making this 1/10  and therefore a different remainder ... ?
O is a positive integer, is it not ?
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education