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# The units digit of J vs The units digit of K

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1410
Followers: 54

Kudos [?]: 1347 [1] , given: 8

The units digit of J vs The units digit of K [#permalink]  04 May 2017, 06:55
1
KUDOS
Expert's post
00:00

Question Stats:

94% (02:11) correct 5% (03:03) wrong based on 17 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.
_________________

Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 1410
Followers: 54

Kudos [?]: 1347 [2] , given: 8

Re: The units digit of J vs The units digit of K [#permalink]  06 May 2017, 05:39
2
KUDOS
Expert's post
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

[Reveal] Spoiler:
B

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Manager
Joined: 25 Nov 2017
Posts: 51
Followers: 0

Kudos [?]: 41 [1] , given: 5

Re: The units digit of J vs The units digit of K [#permalink]  13 Dec 2017, 21:13
1
KUDOS
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
GRE Instructor
Joined: 10 Apr 2015
Posts: 1410
Followers: 54

Kudos [?]: 1347 [1] , given: 8

Re: The units digit of J vs The units digit of K [#permalink]  14 Dec 2017, 10:12
1
KUDOS
Expert's post
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

Re: The units digit of J vs The units digit of K   [#permalink] 14 Dec 2017, 10:12
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