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03 May 2016, 09:51
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (02:36) correct
44%
(01:34)
wrong
based on 9
sessions
History
Date
Time
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Not Attempted Yet
What is the units digit of the product of m and n?
(1) w=7/5*n!, where w is an integer.
(2) y=3/4*m!, where y is an integer.
(1) w=7/5*n!, where w is an integer.
(2) y=3/4*m!, where y is an integer.
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03 May 2016, 11:13
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We need to find units digit of the product mn
(1) w=7/5*n!, where w is an integer.
Since w is an integer , the minimum value of n! should be 5!
n can be any integer greater than or equal to 5
But we have no information about m.
Not sufficient
(2) y=3/4*m!, where y is an integer.
Since y is an integer , the minimum value of m! should be 4!
m can be any integer greater than or equal to 4
But we have no information about n
Not sufficient
Combining 1 and 2 , we get
Not sufficient
Answer E
(1) w=7/5*n!, where w is an integer.
Since w is an integer , the minimum value of n! should be 5!
n can be any integer greater than or equal to 5
But we have no information about m.
Not sufficient
(2) y=3/4*m!, where y is an integer.
Since y is an integer , the minimum value of m! should be 4!
m can be any integer greater than or equal to 4
But we have no information about n
Not sufficient
Combining 1 and 2 , we get
Not sufficient
Answer E
03 May 2016, 16:10
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Statement(1) : w=7/5*n!, where w is an integer.
Here, since w is an integer, the denominator can completely divide n!
Which means that n has to necessarily be 5 or greater
But no information given on m
Not Sufficient
Statement (2): y=3/4*m!, where y is an integer.
Similarly, here, since y is an integer, the denominator can completely divide m!
Which means that m has to necessarily be 4 or greater
But no information given on n
Not Sufficient
Using both statements, we can say that the minimum value of product of m and n
= m x n
= 5! x 4!
Regardless of how big the values of m and n will be , the product will contain the digits 5 and 2 through n and m
This means that the units digit will always be 0
Correct Option : C
Here, since w is an integer, the denominator can completely divide n!
Which means that n has to necessarily be 5 or greater
But no information given on m
Not Sufficient
Statement (2): y=3/4*m!, where y is an integer.
Similarly, here, since y is an integer, the denominator can completely divide m!
Which means that m has to necessarily be 4 or greater
But no information given on n
Not Sufficient
Using both statements, we can say that the minimum value of product of m and n
= m x n
= 5! x 4!
Regardless of how big the values of m and n will be , the product will contain the digits 5 and 2 through n and m
This means that the units digit will always be 0
Correct Option : C
