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Of the three-digit integers greater than 700, how many have two digits

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Re: Of the three-digit integers greater than 700, how many have two digits [#permalink] New post   12 Apr 2018, 16:30
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Bunuel wrote:
Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90
(B) 82
(C) 80
(D) 45
(E) 36


We can solve this problem by analyzing the digits (0 to 9) that are being “doubled”.

If 0 is doubled, then the numbers can only be 800 and 900. So we have 2 numbers.

If 1 is doubled, then the numbers can only be 711, 811 and 911. So we have 3 numbers.

If 2, 3, 4, 5, or 6 is doubled, then we should have 3 numbers for each case since it’s analogous to 1 being doubled.

If 7 is doubled, then the numbers can only be 770, 771, 772, 773, 774, 775, 776, 778, 779; 707, 717, 727, 737, 747, 757, 767, 787, 797; 877, and 977. So we have a total of 20 numbers.

If 8 or 9 is doubled, then we should have 20 numbers for each case since it’s analogous to 7 being doubled.

Thus, altogether we have 2 + 6 x 3 + 3 x 20 = 2 + 18 + 60 = 80 such numbers.

Answer: C
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Re: Of the three-digit integers greater than 700, how many have two digits [#permalink] New post   06 Oct 2019, 05:08
We don't even have to solve this question. Just use the logic!!

Because of the symmetry, 3 digit integers that have two digits that are equal to each other and the remaining digit different from the other two from 700-799 is equal to that are from 800-899 or 900-999

Hence total 3 digit numbers greater than 700 have two digits that are equal to each other and the remaining digit different from the other two
= 3k-1 (as we have to exclude 700)

Only option C is in the form of 3k-1

Bunuel wrote:
Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90
(B) 82
(C) 80
(D) 45
(E) 36

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Question: 11
Page: 22
Difficulty: 650
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MasteringGMAT
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Re: Of the three-digit integers greater than 700, how many have two digits [#permalink] New post   08 Feb 2023, 22:30
Is this a 650 Difficulty level question?
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Bunuel
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Re: Of the three-digit integers greater than 700, how many have two digits [#permalink] New post   09 Feb 2023, 02:11
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Traj201090 wrote:
Is this a 650 Difficulty level question?


You can check the difficulty level of a question along with the stats on it in the first post. For this question Difficulty = 700-Level. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question.
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Re: Of the three-digit integers greater than 700, how many have two digits [#permalink] New post   03 Jun 2023, 21:17
Bunuel wrote:
Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

(A) 90
(B) 82
(C) 80
(D) 45
(E) 36


Arrangement method
9_ _ =(1*1*9 )*3!/2! = 27
same same different = 3!/2!
similarly for
8_ _ = 27
and 7 _ _ =27 but we want greater than 700 so minus 1 and the 27 will include 700 so minus 1 = 26

so
27+27+26 = 80
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Re: Of the three-digit integers greater than 700, how many have two digits [#permalink]
03 Jun 2023, 21:17
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