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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1434
Location: India
How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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5 00:00

Difficulty:   55% (hard)

Question Stats: 61% (02:28) correct 39% (03:06) wrong based on 88 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
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Aug 2009
Posts: 7755
How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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5
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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Senior Manager  G
Joined: 15 Feb 2017
Posts: 302
Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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Option B.i tried a very crude method of counting.pls suggest any other method

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Intern  B
Joined: 14 Jul 2018
Posts: 13
Location: India
Schools: ISB '20
GMAT 1: 710 Q47 V41 Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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Can anyone help me out with the solution for this?

Posted from my mobile device
Manager  B
Joined: 20 Aug 2015
Posts: 94
Location: India
GMAT 1: 710 Q50 V36 GPA: 3
Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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1
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
Senior Manager  D
Joined: 18 Jun 2018
Posts: 267
Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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1
1
chirag95 wrote:
Can anyone help me out with the solution for this?

Posted from my mobile device

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
Intern  B
Joined: 14 Jul 2018
Posts: 13
Location: India
Schools: ISB '20
GMAT 1: 710 Q47 V41 Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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Thanks guys, not sure why I got confused, the solution was fairly simple!

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VP  P
Joined: 07 Dec 2014
Posts: 1229
How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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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

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.
Manager  B
Joined: 29 Jan 2018
Posts: 54
Concentration: Marketing, Strategy
WE: Business Development (Retail)
Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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I didnt get it. Can someone please explain Intern  B
Joined: 31 May 2018
Posts: 1
Re: How many integers exist between 300 and 600 exclusive, such that all  [#permalink]

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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

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