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How many integers exist between 300 and 600 exclusive, such that all

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How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 07 Aug 2018, 00:36
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How many integers exist between 300 and 600 exclusive, such that all digits are distinct and from left to right, the digits are in strictly ascending order, i.e., hundreds place digit is less than tens place digit which in turn is less than ones place digit?

A. 28
B. 31
C. 35
D. 42
E. More than 50
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How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 08 Aug 2018, 08:42
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amanvermagmat wrote:
How many integers exist between 300 and 600 exclusive, such that all digits are distinct and from left to right, the digits are in strictly ascending order, i.e., hundreds place digit is less than tens place digit which in turn is less than ones place digit?

A. 28
B. 31
C. 35
D. 42
E. More than 50



Here is a way avoiding calculations..

Let's see between 300-400
Hundreds is 3 so other two will be any of 4,5,6,7,8,9, so 6 digits
Choose 2 out of 6 in 6C2=15 6C2 - this means we are choosing two and these two can be choosen only in one way.. say 4,7 can be only 47

400-500
The other two will be 5,6,7,8,9
Choose two out of 5 so 5C2=10

500-600
Choose 2 out of 4-(6,7,8,9), so 4C2=6
Total 15+10+6=31

B
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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 07 Aug 2018, 01:55
Option B.i tried a very crude method of counting.pls suggest any other method

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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 08 Aug 2018, 07:49
Can anyone help me out with the solution for this?

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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 08 Aug 2018, 08:18
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amanvermagmat wrote:
How many integers exist between 300 and 600 exclusive, such that all digits are distinct and from left to right, the digits are in strictly ascending order, i.e., hundreds place digit is less than tens place digit which in turn is less than ones place digit?

A. 28
B. 31
C. 35
D. 42
E. More than 50


The hundreds place digit can be 3, 4 or 5.

3XX --> When the tens place digit is 4, the number of digits possible in units place are 5,6,7,8,9 i.e. 5 in number. Similarly, when the tens place digit is 5, the number of digits possible in units place are 6,7,8,9 i.e. 4. Continuing this way, the number of such nos starting with 3 is 5+4+3+2+1 = 15.

Applying similar approach, the number of nos starting with 4 is 4+3+2+1 = 10, and the number of nos starting with 5 is 3+2+1 = 6

Total such nos 15+10+6 = 31
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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 08 Aug 2018, 08:30
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chirag95 wrote:
Can anyone help me out with the solution for this?

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OA:B

Case 1: 3 at hundreds place
a) 34X : 5 (X can be 5,6,7,8,9)
b) 35X : 4 (X can be 6,7,8,9)
c) 36X : 3 (X can be 7,8,9)
d) 37X : 2 (X can be 8,9)
e) 38X : 1 (X can be 9)
Total with 3 at hundred's place : 5+4+3+2+1 = 15

Case 2: 4 at hundreds place
a) 45X : 4 (X can be 6,7,8,9)
b) 46X : 3 (X can be 7,8,9)
c) 47X : 2 (X can be 8,9)
d) 48X : 1 (X can be 9)
Total with 4 at hundred's place : 4+3+2+1 = 10

Case 3: 5 at hundreds place
a) 56X : 3 (X can be 7,8,9)
b) 57X : 2 (X can be 8,9)
c) 58X : 1 (X can be 9)
Total with 5 at hundred's place : 3+2+1 = 6

Total (Case1+Case2+Case3) : 15+10+6 = 31
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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 08 Aug 2018, 09:18
Thanks guys, not sure why I got confused, the solution was fairly simple!

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How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post Updated on: 10 Aug 2018, 11:59
amanvermagmat wrote:
How many integers exist between 300 and 600 exclusive, such that all digits are distinct and from left to right, the digits are in strictly ascending order, i.e., hundreds place digit is less than tens place digit which in turn is less than ones place digit?

A. 28
B. 31
C. 35
D. 42
E. More than 50


such integers form a triangular sequence
to find the value of the nth term,
multiply n by n+1 and divide by 2
t1=1 (700s)
t2=3 (600s)
t3= 6 (500s)
t4=10 (400s)
t5=15 (300s)
t6=21 (200s)
t7=28 (100s)
6+10+15=31
B

Originally posted by gracie on 08 Aug 2018, 22:14.
Last edited by gracie on 10 Aug 2018, 11:59, edited 2 times in total.
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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 10 Aug 2018, 05:38
I didnt get it. Can someone please explain :(
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Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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New post 18 Sep 2018, 21:55
amanvermagmat wrote:
How many integers exist between 300 and 600 exclusive, such that all digits are distinct and from left to right, the digits are in strictly ascending order, i.e., hundreds place digit is less than tens place digit which in turn is less than ones place digit?

A. 28
B. 31
C. 35
D. 42
E. More than 50


Why can't I look at this problem this way
hundreds digit has only 3 options- 3,4 & 5
ten's digit will have 6 options - 4,5,6,7,8,9
units digit will have 5 options
so, total no. of posssible numbers=3x6x5
but, here we have counted 3! combinations of any three numbers.
so we divide by 6
(3x6x5)/6=15

what is wrong in this approach?
please help!!
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Re: How many integers exist between 300 and 600 exclusive, such that all &nbs [#permalink] 18 Sep 2018, 21:55
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How many integers exist between 300 and 600 exclusive, such that all

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