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# W is a set of numbers {1, 2, 3, 4, 5}. How many numbers less

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Manager
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W is a set of numbers {1, 2, 3, 4, 5}. How many numbers less [#permalink]

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06 Jan 2005, 11:38
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W is a set of numbers {1, 2, 3, 4, 5}. How many numbers less than 500 can be arranged by using the set W, provided that repetitions are permitted?

A. 5
B. 10
C. 25
D. 100
E. 130

Director
Joined: 19 Nov 2004
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06 Jan 2005, 11:49
D) 100

- - -
For 100 th place, we can select 4 numbers 1,2,3,4 and for the other places we can select 5 numbers
4x5x5 = 100
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06 Jan 2005, 12:41
100.

first digit can't be 5 as it will exceed the 500 limit. So 1st digit can be selected in 4 ways and rest of them 5 ways and then 5 ways. So 4x5x5 = 100
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06 Jan 2005, 12:48
I wud say OA is wrong, what's the source and the explanation ?
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06 Jan 2005, 19:17
banerjeea_98 wrote:
I wud say OA is wrong, what's the source and the explanation ?

These are from the set of questions you have to pay for from the gmatclub site.

The OA is 130.
For 3 digit numbers- for the hundredths digit (4 numbers) x tens digit (5 numbers) x units digit (5 numbers) = 100
2 digit numbers- for tens digit (5 numbers) x units digit (5 numbers) = 5
1 digit numbers- 5 numbers
Total is 100+25+5=130
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07 Jan 2005, 09:32
Yes, stupid mistake, I assumed it is a 3 digit number only, didn't take single and double digits into consideration. 130 is correct.
07 Jan 2005, 09:32
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