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amanvermagmat
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How many integers exist between 300 and 600 exclusive, such that all 07 Aug 2018, 00:36
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58% (02:25) correct 42% (02:29) wrong based on 189 sessions

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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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B
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How many integers exist between 300 and 600 exclusive, such that all 08 Aug 2018, 08:42
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amanvermagmat
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
Show more


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

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How many integers exist between 300 and 600 exclusive, such that all 07 Aug 2018, 01:55
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Option B.i tried a very crude method of counting.pls suggest any other method

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How many integers exist between 300 and 600 exclusive, such that all 08 Aug 2018, 07:49
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Can anyone help me out with the solution for this?

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How many integers exist between 300 and 600 exclusive, such that all 08 Aug 2018, 08:18
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amanvermagmat
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
Show more

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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How many integers exist between 300 and 600 exclusive, such that all 08 Aug 2018, 08:30
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chirag95
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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How many integers exist between 300 and 600 exclusive, such that all 08 Aug 2018, 09:18
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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 Updated on: 10 Aug 2018, 11:59
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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amanvermagmat
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
Show more

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
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How many integers exist between 300 and 600 exclusive, such that all 10 Aug 2018, 05:38
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I didnt get it. Can someone please explain :(
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How many integers exist between 300 and 600 exclusive, such that all 18 Sep 2018, 21:55
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amanvermagmat
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
Show more

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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How many integers exist between 300 and 600 exclusive, such that all 15 Jul 2025, 05:38
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