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Of the two-digit positive integers less than 52, how many have differe

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Joined: 27 Jul 2016
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Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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Updated on: 10 Oct 2017, 10:59
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90% (00:51) correct 10% (01:04) wrong based on 61 sessions

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Of the two-digit positive integers less than 52, how many have different digits?

A 38
B 44
C 16
D 12
E 4

(The questions is from GMAT Toolkit app, yet there was no explanation on this exercise)

Originally posted by g1zmo on 10 Oct 2017, 09:57.
Last edited by g1zmo on 10 Oct 2017, 10:59, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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10 Oct 2017, 10:01
g1zmo wrote:
Of the two-digit positive integers less than 52, how many have different digits?

A 38
B 44
C 16
D 12
E 4

(The questions is from your app, yet there was no explanation on this exercise)

There are 42 two-digit positive integers less than 52, from 10 to 51 inclusive. Out of those 42, 4 have the same digits: 11, 22, 33, and 44. So, the answer is 42 - 4 = 38.

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GMAT 1: 770 Q51 V45
Re: Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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10 Oct 2017, 13:13
Of the two-digit positive integers less than 52, how many have different digits?

A 38
B 44
C 16
D 12
E 4

Use the rules for combinations/permutations to solve problems such as this. There are two spaces to fill and order matters. First find the number of possible values of different digit numbers 10 < but < 50. There are 4 possible values for the tens digit (1-4) according to the problem, and for each of these tens digit values there are 9 non-repeating possible digits (remember 0) so 9 x 4 = 36 possible values between 10 and 50. Then, add in the final two values that satisfy the problem, 50 and 51 to find that there are 38 two-digit positive integers less than 52 with different digits.
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Re: Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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14 Oct 2017, 16:56
Bunuel wrote:
g1zmo wrote:
Of the two-digit positive integers less than 52, how many have different digits?

A 38
B 44
C 16
D 12
E 4

(The questions is from your app, yet there was no explanation on this exercise)

There are 42 two-digit positive integers less than 52, from 10 to 51 inclusive. Out of those 42, 4 have the same digits: 11, 22, 33, and 44. So, the answer is 42 - 4 = 38.

Bunuel how did you find 42? I'm sorry I'm asking very basic things.
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Posts: 47112
Re: Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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15 Oct 2017, 01:50
1
1
SandhyAvinash wrote:
Bunuel wrote:
g1zmo wrote:
Of the two-digit positive integers less than 52, how many have different digits?

A 38
B 44
C 16
D 12
E 4

(The questions is from your app, yet there was no explanation on this exercise)

There are 42 two-digit positive integers less than 52, from 10 to 51 inclusive. Out of those 42, 4 have the same digits: 11, 22, 33, and 44. So, the answer is 42 - 4 = 38.

Bunuel how did you find 42? I'm sorry I'm asking very basic things.

The number of questions from 10 to 51 inclusive, is 51 - 10 + 1. Try to play with smaller numbers to see the logic behind this and derive general formula.
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Re: Of the two-digit positive integers less than 52, how many have differe &nbs [#permalink] 15 Oct 2017, 01:50
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