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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
How many even 3 digit integers greater than 700 with distinct non zero
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22 Nov 2021, 06:50
22 Nov 2021, 06:50
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Expert Reply
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Question Stats:
40% (03:07) correct
60% (02:08) wrong based on 5 sessions
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How many even 3 digit integers greater than 700 with distinct non zero digits are there ?
A. 729
B. 243
C. 108
D. 88
E. 77
A. 729
B. 243
C. 108
D. 88
E. 77
Re: How many even 3 digit integers greater than 700 with distinct non zero
[#permalink]
24 Nov 2021, 10:21
24 Nov 2021, 10:21
Expert Reply
Notice that we are told that no digit in these numbers could be zero. So, we have only 9 digits to use for XYZ, where Z is an even number.
If the first digit (X) is 7 or 9 (2 values) then the third digit (Z) can take all 4 values (2, 4, 6, or 8) and the second digit (Y) can take 7 values (9 minus two digits we already used). So, for this case we have 2*4*7=56 numbers;
If the first digit (X) is 8 (1 value) then the third digit (Z) can take only 3 values (2, 4, or 6,) and the second digit (Y) can take 7 values (9 minus two digits we already used). So, for this case we have 1*3*7=21 numbers;
Total: 56+21=77 numbers.
Answer: E.
If the first digit (X) is 7 or 9 (2 values) then the third digit (Z) can take all 4 values (2, 4, 6, or 8) and the second digit (Y) can take 7 values (9 minus two digits we already used). So, for this case we have 2*4*7=56 numbers;
If the first digit (X) is 8 (1 value) then the third digit (Z) can take only 3 values (2, 4, or 6,) and the second digit (Y) can take 7 values (9 minus two digits we already used). So, for this case we have 1*3*7=21 numbers;
Total: 56+21=77 numbers.
Answer: E.
gmatclubot
Re: How many even 3 digit integers greater than 700 with distinct non zero [#permalink]
24 Nov 2021, 10:21
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