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How many two-digit integers do not have any digits that are equal to e
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20 Sep 2022, 07:44
20 Sep 2022, 07:44
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Expert Reply
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Question Stats:
83% (00:54) correct
16% (00:36) wrong based on 6 sessions
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How many two-digit integers do not have any digits that are equal to each other?
(A) 90
(B) 81
(C) 80
(D) 75
(E) 72
(A) 90
(B) 81
(C) 80
(D) 75
(E) 72
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022) - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: How many two-digit integers do not have any digits that are equal to e
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24 Sep 2022, 05:45
24 Sep 2022, 05:45
1
Expert Reply
Two ways to do it.
1) Direct method
The tens place can be taken by any of the digits except 0, so 9 ways.
The one's place can be taken by any of the digits except the one used in the tens place, so 9 ways.
Total 9*9 or 81 ways.
2) Indirect
It is easy to count the numbers that have repeated digits - 11,22,33….99, so 9.
Total 2 digit number = 99-10+1=90.
Answer: 90-9=81
Answer: B
1) Direct method
The tens place can be taken by any of the digits except 0, so 9 ways.
The one's place can be taken by any of the digits except the one used in the tens place, so 9 ways.
Total 9*9 or 81 ways.
2) Indirect
It is easy to count the numbers that have repeated digits - 11,22,33….99, so 9.
Total 2 digit number = 99-10+1=90.
Answer: 90-9=81
Answer: B
gmatclubot
Re: How many two-digit integers do not have any digits that are equal to e [#permalink]
24 Sep 2022, 05:45
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