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/if-n-and-m-a ... tml#544266
https://www.beatthegmat.com/what-is-the- ... 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/if-n-and-m-a ... tml#544266
https://www.beatthegmat.com/what-is-the- ... 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