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The units digit of J vs The units digit of K

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The units digit of J vs The units digit of K [#permalink] New post 04 May 2017, 06:55
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Question Stats:

93% (02:07) correct 6% (03:03) wrong based on 15 sessions
\(J = (2^{43})(3^{44})(5^{45})\)
\(K = (7^{46})(11^{47})(13^{48})\)

Quantity A
Quantity B
The units digit of J
The units digit of K


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: The units digit of J vs The units digit of K [#permalink] New post 06 May 2017, 05:39
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GreenlightTestPrep wrote:
\(J = (2^{43})(3^{44})(5^{45})\)
\(K = (7^{46})(11^{47})(13^{48})\)

Quantity A
Quantity B
The units digit of J
The units digit of K


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


J = (2)(2)(2)...(2)(2)(3)(3)(3)...(3)(3)(5)(5)(5)...(5)(5)
= (2)(2)(2)...(2)(2)(3)(3)(3)...(3)(3)(5)(5)(5)...(5)(5)
= 10(2)(2)...(2)(2)(3)(3)(3)...(3)(3)(5)(5)...(5)(5)
Since J = some multiple of 10, the units digit of J is 0

K = (7)(7)(7)(7)...(7)(7)(11)(11)(11)...(11)(11)(13)(13)(13)....(13)(13)
Since there are no 2's or 5's hiding in the prime factorization of K, we can conclude that K is not a multiple of 10, which means the units digit of K is NOT 0

So, we get:
Quantity A: 0
Quantity B: a positive integer that is NOT equal to 0


Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
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Re: The units digit of J vs The units digit of K [#permalink] New post 13 Dec 2017, 21:13
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Can we not simply multiply the pattern of all numbers?

QA
We know that 2 has the 4 following patterns: 2,4,8,6 so (2^43) must have an ending of 8
3 has the following pattern 3,9,7,1 so 3^44 must be 1
5 has always the same pattern 5.
QB
7: 7,9,3,1 so 7^46 is 9
11 is like 5. The same pattern so always 1.
13: 3,9,7,1 so 7^48 so the ending is 1.

QA : (....8)(....1)(....5) = end with 0
QB: (....9)(....1)(....1) = end with 9

So B is greater
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Re: The units digit of J vs The units digit of K [#permalink] New post 14 Dec 2017, 10:12
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Popo wrote:
Can we not simply multiply the pattern of all numbers?

QA
We know that 2 has the 4 following patterns: 2,4,8,6 so (2^43) must have an ending of 8
3 has the following pattern 3,9,7,1 so 3^44 must be 1
5 has always the same pattern 5.
QB
7: 7,9,3,1 so 7^46 is 9
11 is like 5. The same pattern so always 1.
13: 3,9,7,1 so 7^48 so the ending is 1.

QA : (....8)(....1)(....5) = end with 0
QB: (....9)(....1)(....1) = end with 9

So B is greater


That works too.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
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Re: The units digit of J vs The units digit of K   [#permalink] 14 Dec 2017, 10:12
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