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How many 3 digit positive integers with distinct digits

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How many 3 digit positive integers with distinct digits [#permalink] New post 05 Sep 2013, 23:09
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Question Stats:

57% (02:33) correct 43% (02:15) wrong based on 72 sessions
How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576
B. 520
C. 504
D. 432
E. 348
[Reveal] Spoiler: OA
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 05 Sep 2013, 23:21
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aparnaharish wrote:
How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576
B. 520
C. 504
D. 432
E. 348


A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive).
8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit).
8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 05 Sep 2013, 23:59
Bunuel wrote:
aparnaharish wrote:
How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576
B. 520
C. 504
D. 432
E. 348


A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive).
8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit).
8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.


Hi Bunuel,

why is this solution wrong?
9C1 options for the first digit (from 1 to 9 inclusive).
9C1 options for the Second digit (from 0 to 9 inclusive minus the one we used for the first digit).
7C1 options for the third digit (from 1 to 9 inclusive minus 2 digits we used for the first and the second digits)

Which gives
9*9*7=567

Where i am wrong???

Thanks in Advance,
Rrsnathan.
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 06 Sep 2013, 00:02
Expert's post
rrsnathan wrote:
Bunuel wrote:
aparnaharish wrote:
How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576
B. 520
C. 504
D. 432
E. 348


A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive).
8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit).
8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.


Hi Bunuel,

why is this solution wrong?
9C1 options for the first digit (from 1 to 9 inclusive).
9C1 options for the Second digit (from 0 to 9 inclusive minus the one we used for the first digit).
7C1 options for the third digit (from 1 to 9 inclusive minus 2 digits we used for the first and the second digits)

Which gives
9*9*7=567

Where i am wrong???

Thanks in Advance,
Rrsnathan.


If the second digit is 0, then you'll have 8 not 7 options for the third digit.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 06 Sep 2013, 00:46
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Perfectly clear!! Thank you very much!
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 06 Sep 2013, 09:21
Bunuel wrote:
aparnaharish wrote:
How many 3 digit positive integers with distinct digits are there, which are not multiples of 10?

A. 576
B. 520
C. 504
D. 432
E. 348

A number not to be a multiple of 10 should not have the units digit of 0.

XXX

9 options for the first digit (from 1 to 9 inclusive).
8 options for the third digit (from 1 to 9 inclusive minus the one we used for the first digit).
8 options for the second digit (from 0 to 9 inclusive minus 2 digits we used for the first and the third digits)

9*8*8=576.

Answer: A.

Hi Bunuel,

why is this solution wrong?
9C1 options for the first digit (from 1 to 9 inclusive).
9C1 options for the Second digit (from 0 to 9 inclusive minus the one we used for the first digit).
7C1 options for the third digit (from 1 to 9 inclusive minus 2 digits we used for the first and the second digits)

Which gives
9*9*7=567

Where i am wrong???

Thanks in Advance,
Rrsnathan.


If the second digit is 0, then you'll have 8 not 7 options for the third digit.

Hope it's clear.

It will still be wrong it is 9*9*8 and not 9*8*8...
still confused
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 17 Apr 2014, 03:26
Shouldn't it be 9x9x8?
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 17 Apr 2014, 03:32
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Re: How many 3 digit positive integers with distinct digits [#permalink] New post 20 Apr 2014, 21:07
I did in this way :

case 1: tens place is 0 : 8 x 1 x 9 = 72

case 2 : tens place is not 0 : 7 x 8 x9 = 504

therefore , total numbers = 72 + 504 = 576 ans.
Re: How many 3 digit positive integers with distinct digits   [#permalink] 20 Apr 2014, 21:07
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