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# Which of the following numbers has a zero in its units digit?

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
Which of the following numbers has a zero in its units digit?  [#permalink]

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20 Apr 2016, 23:37
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:05) correct 21% (01:07) wrong based on 89 sessions

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Which of the following numbers has a zero in its units digit?

I. $$(4!)×(4!)×(3!)×(11)×(17)×(31)$$

II. $$(2!)×(3!)×(3!)×(5)×(17)×(31)$$

III. $$(2!)^5×(3!)^5×(4!)^5$$

A. I only
B. II only
C. III only
D. I, II and III
E. II and III

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Posts: 1882
Re: Which of the following numbers has a zero in its units digit?  [#permalink]

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21 Apr 2016, 01:19
1
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Bunuel wrote:
Which of the following numbers has a zero in its units digit?

I. (4!)×(4!)×(3!)×(11)×(17)×(31)
II. (2!)×(3!)×(3!)×(5)×(17)×(31)
III. (2!)^5×(3!)^5×(4!)^5

A. I only
B. II only
C. III only
D. I, II and III
E. II and III

10 = 5*2
Hence to have a 0, we need to have atleast one power of 5 in the multiplication.

I. (4!)×(4!)×(3!)×(11)×(17)×(31)
This does not have a power of 5. Hence no 0

II. (2!)×(3!)×(3!)×(5)×(17)×(31)
This will have a 0 as there is one power of 5

III. (2!)^5×(3!)^5×(4!)^5
This will again not have a 0 as there are no powers of 5

Correct Option: B
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Re: Which of the following numbers has a zero in its units digit?  [#permalink]

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21 Apr 2016, 10:09
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Status: QA & VA Forum Moderator
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Re: Which of the following numbers has a zero in its units digit?  [#permalink]

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22 Apr 2016, 10:27
1
Bunuel wrote:
Which of the following numbers has a zero in its units digit?

I. (4!)×(4!)×(3!)×(11)×(17)×(31)
II. (2!)×(3!)×(3!)×(5)×(17)×(31)
III. (2!)^5×(3!)^5×(4!)^5

A. I only
B. II only
C. III only
D. I, II and III
E. II and III

At a glance solution

0 in the units place will come only when you have at least a multiple of 2 and 5

Check clearly none of the given option is both a multiple of 2 and 5 except option (II)

Hence (B) is the correct answer.
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Re: Which of the following numbers has a zero in its units digit?  [#permalink]

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23 Jan 2017, 15:56
Bunuel wrote:
Which of the following numbers has a zero in its units digit?

I. (4!)×(4!)×(3!)×(11)×(17)×(31)
II. (2!)×(3!)×(3!)×(5)×(17)×(31)
III. (2!)^5×(3!)^5×(4!)^5

A. I only
B. II only
C. III only
D. I, II and III
E. II and III

oh what a trap here...
I noticed that II must have 0 in units digit. A, C are out right away.
I - doesn't have a factor of 5, therefore, no where to make zero in units digit. D is out
III - again no 5...E is out too...
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Posts: 8870
Re: Which of the following numbers has a zero in its units digit?  [#permalink]

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17 Mar 2018, 06:39
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Re: Which of the following numbers has a zero in its units digit? &nbs [#permalink] 17 Mar 2018, 06:39
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