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# If M is a positive integer, then M^3 has how many digits? 1)

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If M is a positive integer, then M^3 has how many digits? 1) [#permalink]

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13 Jun 2008, 23:27
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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

Kudos [?]: 194 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4483 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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13 Jun 2008, 23:38
E

1) M has 3 digits --> M e (100,999) --> M^3 has from 6 to 8 digits. insufficient.
2) M^2 has 5 digits --> M e (~330,999) --> consider two integers: 400 and 900 ---> M^3 is 64*1000000 and 729*1000000. insufficient.

1)&2) the same as for 2). insufficient.
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13 Jun 2008, 23:43
on exam day i would go with B..

have no clue how to do this..

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14 Jun 2008, 21:19
Yeah I'm really boggled by this one as well. How do you calculate 999 * 3 on paper?
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Kudos [?]: 211 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4483 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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14 Jun 2008, 21:43
terp06 wrote:
Yeah I'm really boggled by this one as well. How do you calculate 999 * 3 on paper?

a few second.... 1000^3=10^9, but 999 is slightly lower than 10^9, therefore, 999 contains 8 digits.
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14 Jun 2008, 22:39
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walker wrote:
terp06 wrote:
Yeah I'm really boggled by this one as well. How do you calculate 999 * 3 on paper?

a few second.... 1000^3=10^9, but 999 is slightly lower than 10^9, therefore, 999 contains 8 digits.

1,000^3 has 10 digits (3 zeros 3 times plus 1) so 999^3 should have less than 10 digits. so it has 9 digits.
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Kudos [?]: 834 [1], given: 19

CEO
Joined: 17 Nov 2007
Posts: 3585

Kudos [?]: 4483 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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14 Jun 2008, 22:49
GMAT TIGER wrote:
1,000^3 has 10 digits (3 zeros 3 times plus 1) so 999^3 should have less than 10 digits. so it has 9 digits.

Thanks, Tiger! It is why I get Q50 in real GMAT.... oh these silly mistakes....
+1
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14 Jun 2008, 22:59
puma wrote:
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: take minimum and max. value for 3 digit integers
min value if m = 100, M^3 = 1,000,000, which has 7 digits.
min value if m = 999, M^3 = do not know exactly but should have 9 digits (since 1000^3 has 10 digits, 999 is slight lower than 1000. so 999^3 should have 9 digits).
not suff...

2: again min and max. values for m^2 that has 5 digits.
min value of m^2 = 10,000.00, m = 100 and m^3 = 1,000,000, which is the same as above in 1.
min value if m^2 = 99,999, m = 316 approx. again do not know exactly the value of m^3 but it should have either 9 or 8 digits. again not suff.

togather also do not know. so E.
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14 Jun 2008, 23:03
walker wrote:
GMAT TIGER wrote:
1,000^3 has 10 digits (3 zeros 3 times plus 1) so 999^3 should have less than 10 digits. so it has 9 digits.

Thanks, Tiger! It is why I get Q50 in real GMAT.... oh these silly mistakes....
+1

i too got Q50 with more careless and silly mistakes.
V doesnot go beyond 40. want to raise V above 40.

you deserve Q51 and V40+.

goodluck.

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Re: DS: digits   [#permalink] 14 Jun 2008, 23:03
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