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acegmat123
Contains only one 7:

7XX: 1*10*10= 100

X7X: 9*1*10 = 90

XX7: 9*10*1 = 90

Contains two 7s:

77X: 1*1*10= 10

X77: 9*1*1 = 9

Contains three 7s:

777: 1

Total 200

B


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Be careful. You have....
Contains only one 7:

7XX: 1*10*10= 100

This configuration allows for more than one 7 since we're saying that the 2nd and 3rd digits can be ANY digit (including 7)
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acegmat123
Contains only one 7:

7XX: 1*10*10= 100

X7X: 9*1*10 = 90

XX7: 9*10*1 = 90

Contains two 7s:

77X: 1*1*10= 10

X77: 9*1*1 = 9

Contains three 7s:

777: 1

Total 200

B


Sent from my iPhone using GMAT Club Forum mobile app

Be careful. You have....
Contains only one 7:

7XX: 1*10*10= 100

This configuration allows for more than one 7 since we're saying that the 2nd and 3rd digits can be ANY digit (including 7)

Thanks GMATPerpNow. Completely overlooked that part.


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acegmat123
Contains two 7s:

77X: 1*1*9=9

X77: 8*1*1 = 8


There can be one more combination

7x7 : 1*9*1 = 9

So, the Total possibility wil be 243+9 = 252

Answer will (D)

PS : What say Brent ?
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Abhishek009
acegmat123
Contains two 7s:

77X: 1*1*9=9

X77: 8*1*1 = 8


There can be one more combination

7x7 : 1*9*1 = 9

So, the Total possibility wil be 243+9 = 252

Answer will (D)

PS : What say Brent ?

Bingo!
As we can see, accounting for every possible scenario is much more time-consuming than taking the TOTAL number of possible outcomes (that both adhere and break the rule) and then subtract the number of outcomes that break the rule.

Cheers,
Brent
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Abhishek009
acegmat123
Contains two 7s:

77X: 1*1*9=9

X77: 8*1*1 = 8


There can be one more combination

7x7 : 1*9*1 = 9

So, the Total possibility wil be 243+9 = 252

Answer will (D)

PS : What say Brent ?

Bingo!
As we can see, accounting for every possible scenario is much more time-consuming than taking the TOTAL number of possible outcomes (that both adhere and break the rule) and then subtract the number of outcomes that break the rule.

Cheers,
Brent

Yes you're right. Learnt a new method today.

9*10*10 - 8*9*9 = 900-648 = 252


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Let's calculate the numbers which don't have any 7 in their digits.
8×9×9=648
There are 900 numbers totally between 100 and 999
900-648=252
Option D

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