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12 Jan 2022, 07:45
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E
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Difficulty:
95%
(hard)
Question Stats:
37% (02:05) correct
63%
(01:59)
wrong
based on 79
sessions
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How many numbers exceeding 999 and not exceeding 5000 can be formed, such that each digit is any of the first six whole numbers?
A. 600
B. 625
C. 820
D. 864
E. 865
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. 600
B. 625
C. 820
D. 864
E. 865
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Updated on: 12 Jan 2022, 09:28
Originally posted by IanStewart on 12 Jan 2022, 07:58.
Last edited by IanStewart on 12 Jan 2022, 09:28, edited 1 time in total.
Last edited by IanStewart on 12 Jan 2022, 09:28, edited 1 time in total.
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The number must be less than 5000, because our digits cannot be zero, so we have 4 choices for the thousands digit, and 6 choices for each of the remaining three digits, for 4*6*6*6 possible numbers in total. The units digit of that product will be 4, so D must be right (or you could multiply it out).
edit: I was assuming the question meant 'natural numbers' instead of 'whole numbers' -- you will never need to know what either of those terms mean for the GMAT, and I've confused the two my whole life.
The 'whole numbers' include zero, so we actually do need to include '5000' here as well, and the answer should be E.
edit: I was assuming the question meant 'natural numbers' instead of 'whole numbers' -- you will never need to know what either of those terms mean for the GMAT, and I've confused the two my whole life.
The 'whole numbers' include zero, so we actually do need to include '5000' here as well, and the answer should be E. 
12 Jan 2022, 09:22
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Answer is E.
Numbers are exceeding 999 and not exceeding 5000. This would mean that the range of numbers would be from 1000-5000. Digits are from 1-6.
Since there are a 4 place holders we can fill.
1-4,1-6,1-6,1-6,1-6 or 4x6x6x6=864
we would need to add one to account for 5000. So answer is 864+1=865
Numbers are exceeding 999 and not exceeding 5000. This would mean that the range of numbers would be from 1000-5000. Digits are from 1-6.
Since there are a 4 place holders we can fill.
1-4,1-6,1-6,1-6,1-6 or 4x6x6x6=864
we would need to add one to account for 5000. So answer is 864+1=865
