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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)!
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42%
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If m is a positive integer, then m^3 has how many digits?
(1) m has 3 digits.
(2) m^2 has 5 digits.
(1) m has 3 digits.
(2) m^2 has 5 digits.
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20 Feb 2014, 01:17
Kudos
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SOLUTION
If m is a positive integer, then m^3 has how many digits?
Pick some easy numbers.
(1) m has 3 digits --> if \(m=100=10^2\) then \(m^3=10^6\) so it will have 7 digits but if \(m=300=3*10^2\) then \(m^3=27*10^6\) so it will have 8 digits. Not sufficient.
(2) m^2 has 5 digits --> the same values of \(m\) (100 and 300) satisfy this statement too (because if \(m=10^2\) then \(m^2=10^4\) and has 5 digits and if \(m=3*10^2\) then \(m^2=9*10^4\) also has 5 digits), so \(m^3\) may still have 7 or 8 digits. Not sufficient.
(1)+(2) The same example worked for both statements so even taken together statements are not sufficient.
Answer: E.
If m is a positive integer, then m^3 has how many digits?
Pick some easy numbers.
(1) m has 3 digits --> if \(m=100=10^2\) then \(m^3=10^6\) so it will have 7 digits but if \(m=300=3*10^2\) then \(m^3=27*10^6\) so it will have 8 digits. Not sufficient.
(2) m^2 has 5 digits --> the same values of \(m\) (100 and 300) satisfy this statement too (because if \(m=10^2\) then \(m^2=10^4\) and has 5 digits and if \(m=3*10^2\) then \(m^2=9*10^4\) also has 5 digits), so \(m^3\) may still have 7 or 8 digits. Not sufficient.
(1)+(2) The same example worked for both statements so even taken together statements are not sufficient.
Answer: E.
Runirish
as we know,
the minimum value of a 3 digit integer is 100 = \(10^2\)
the maximum value of a 3 digit integer is 999 = \(10^4 - 1\)
the minimum value of a 5 digit integer is 10000 = \(10^4\)
the maximum value of a 5 digit integer is 99999 = \(10^6 - 1\)
.
.
hence,
.
the minimum value of a \(n\) digit integer is \(10^(n-1)\)
the maximum value of a \(n\) digit integer is \(10^(n+1) - 1\)
Back to original qtn:
If m is a positive integer, then \(m^3\) has how many digits?
stmnt1: \(m\) has 3 digits
==> \(10^2 <= m < 10^4\)
==> \(10^6 <= m^3 < 10^12\)
==> \(m^3\) can have minimum of 7 (i.e 6+1) and max of 11 digits (i.e. 12-1)
hence NOT suff.
stmnt2: m^2 has 5 digits
==> \(10^4 <= m^2 < 10^6\)
==> \(10^2 <= m < 10^3\)
==> \(10^6 <= m^3 < 10^9\)
==> \(m^3\) can have minimum of 7 (i.e 6+1) and max of 8 digits (i.e. 9-1)
hence NOT suff.
stmnt1&2 together: We can conclude that \(m^3\) can have minimum of 6 and max of 8 digits(i.e. 12-1) ==> m can have 7 or 8 digits
hence NOT suff.
Answer "E".
Regards,
Murali.
Kudos?
22 Dec 2010, 12:18
Kudos
Bookmarks
Runirish
1. m has 3 digits
When I look at such statements, I invariably think of the extremities. (as muralimba did above)
Smallest m = 100 which implies m^3 = 10^6 giving 7 digits.
Largest m = 999 but it is not easy to find its cube so I take a number close to it i.e. 1000 and find its cube which is 10^9 i.e. smallest 10 digit number. Hence 999^3 will have 9 digits.
Since we can have 7, 8 or 9 digits, this statement is not sufficient.
2. m^2 has 5 digits
Now try to forget what you read above. Just focus on this statement.
Smallest m^2 = 10000 which implies m = 100
Largest m^2 is less than 99999 which gives m as something above 300 but less than 400.
Now, if m is 100, m^3 = 10^6 giving 7 digits.
If m is 300, m^3 = 27000000 giving 8 digits.
Since we have 7 or 8 digits for m, this statement is not sufficient.
Now combining both, remember one important point - If one statement is already included in the other, and the more informative statement is not sufficient alone, both statements will definitely not be sufficient together.
e.g. statement 1 tells us that m has 3 digits. Statement 2 tells us that m is between 100 and 300 something, so statement 2 tells us that m has 3 digits (what statement 1 told us) and something extra (that its value lies between 100 and 300 something). Statement 2 is more informative and is not sufficient alone. Since statement 1 doesn't add any new information to statement 2, no way will they both together be sufficient.
Hence answer (E).
