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

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Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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New post Updated on: 10 Oct 2017, 10:59
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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.
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Re: Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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New post 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.

Answer: A.
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Re: Of the two-digit positive integers less than 52, how many have differe  [#permalink]

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New post 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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New post 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.

Answer: A.


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

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New post 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.

Answer: A.


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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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