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stne
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How many three digit numbers greater than 330 can be formed Updated on: 07 Sep 2012, 05:14
Originally posted by stne on 07 Sep 2012, 04:00.
Last edited by Bunuel on 07 Sep 2012, 05:14, edited 1 time in total.
Edited the question.
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67% (02:05) correct 33% (02:02) wrong based on 247 sessions

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How many three digit numbers greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?

A. 72
B. 48
C. 120
D. 96
E. 76
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A
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EvaJager
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How many three digit numbers greater than 330 can be formed Updated on: 07 Sep 2012, 05:29
Originally posted by EvaJager on 07 Sep 2012, 04:21.
Last edited by EvaJager on 07 Sep 2012, 05:29, edited 1 time in total.
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stne
How many three digit numbers greater than 330? can be formed from the digits 1,2,3,4,5 and 6, if each digit can only be used once?

1)72
2)48
3)120
4)96
5)76
Show more

Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.

Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.

Total number of possible choices 80 - 8 =72.
Answer: A.
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How many three digit numbers greater than 330 can be formed 07 Sep 2012, 05:21
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stne
How many three digit numbers greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?

A. 72
B. 48
C. 120
D. 96
E. 76
Show more

Similar questions to practice:
of-the-three-digit-integers-greater-than-700-how-many-have-135188.html (from OG13);
how-many-odd-three-digit-integers-greater-than-800-are-there-94655.html (from GMAT Club Tests);
of-the-three-digit-integers-greater-than-660-how-many-have-128853.html;
of-the-three-digit-integers-greater-than-600-how-many-have-127390.html.

Hope it helps.
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How many three digit numbers greater than 330 can be formed 07 Sep 2012, 05:42
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EvaJager
stne
How many three digit numbers greater than 330? can be formed from the digits 1,2,3,4,5 and 6, if each digit can only be used once?

1)72
2)48
3)120
4)96
5)76

Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.

Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.

Total possible choice 80 - 8 =72.
Answer: A.
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Thank You Eva..
Thanks for opening up my mind

after seeing your solution I got my mistake



Here is another way to approach this question

so lets take two cases
first case: hundredth digit is 3 ,

hundred digit is 3 ,so one option only .
then tenth digit cannot be 1 and 2 ( as we cannot have 316 or 326 ,these are less than 330 )and also 3, as 3 has been used in hundredth position, so 3 options only, 4 ,5, 6.
and units digit can have 4 remaining options so 1*3*4 = 12 all digits greater then 330 but less than 400

second case : hundred digit is greater than 3 only 3 options 4,5,and 6

3*5*4= 60

we have 5 options for the second place because now the hundredth digit is more than 3 , so tenth digit can be any of the 5 remaining options.
(eg 413, 426, 436, etc )

so total 60 +12 = 72

Thank you Bunuel for the further links ....
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How many three digit numbers greater than 330 can be formed 08 Sep 2012, 09:03
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stne
How many three digit numbers greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?

A. 72
B. 48
C. 120
D. 96
E. 76
Show more


Here we can simply make cases

_ _ _
A B C ..
Now for A = 3 , B can only be 4,5,6 and c can be anything this implies no. of ways = 1*3*4 = 12
now for A = 4,5,6 B can be anything and so can be C , no of ways = 3*5*4 = 60
this is because the numbers can be repeated so after you ave filled one digit the second one has fewer options!

Answer = 60+12 = 72
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How many three digit numbers greater than 330 can be formed 03 Jun 2016, 08:50
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stne
How many three digit numbers greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?

A. 72
B. 48
C. 120
D. 96
E. 76
Show more

Total numbers greater than 330 will be= numbers starting with digit 3 + number starting with digit 4, 5 or 6

total numbers starting with digit 3 and >330= 1*3*4= 12

Total numbers starting with digits 4,5 or 6= 3*5*4= 60

60+12= 72 A is the answer
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How many three digit numbers greater than 330 can be formed 21 May 2024, 16:17
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I think you made a typo . The number cant be repeated. check the highlighted part.
mandyrhtdm

stne
How many three digit numbers greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?

A. 72
B. 48
C. 120
D. 96
E. 76

Here we can simply make cases

_ _ _
A B C ..
Now for A = 3 , B can only be 4,5,6 and c can be anything this implies no. of ways = 1*3*4 = 12
now for A = 4,5,6 B can be anything and so can be C , no of ways = 3*5*4 = 60
this is because the numbers can be repeated so after you ave filled one digit the second one has fewer options!

Answer = 60+12 = 72
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