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Susan's credit card number is 16 digits long. How many times

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Senior Manager
Joined: 30 May 2005
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Susan's credit card number is 16 digits long. How many times [#permalink]  03 Jul 2005, 22:04
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Susan's credit card number is 16 digits long. How many times does the digit 4 occur in it?

S1. The arithmetic mean of the 16 digits in the credit card number is 4.75

S2. The range of the 16 digits is 1
Manager
Joined: 28 Aug 2004
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but how are we sure that it ever occurs? I'll go with E.
SVP
Joined: 05 Apr 2005
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C seems ok because range is given..
Senior Manager
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OA is C

Range = 1 and Average = 4.75 implies that each digit is either a 4 or a 5.
Senior Manager
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AJB77 wrote:
OA is C

Range = 1 and Average = 4.75 implies that each digit is either a 4 or a 5.

plz AJB77
can you explain me why the range = 1 and Average = 4.75 implies that each digit is either a 4 or a 5.
thanks
regards

mandy
Senior Manager
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Mandy,

Can you construct a set of integers whose range is 1 and average = 4.75 that has a number other than 4 or 5?
Director
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C

x*4 + (16-x)*5 = 76
x = 4

Well I thought E ....But guys you really thought well.....
Senior Manager
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Re: DS - Credit card [#permalink]  21 Jul 2005, 14:07
HowManyToGo wrote:
AJB77 wrote:
Susan's credit card number is 16 digits long. How many times does the digit 4 occur in it?

S1. The arithmetic mean of the 16 digits in the credit card number is 4.75

S2. The range of the 16 digits is 1

C.
12 times.

HMTG.

plz HowManyToGo can you explain how you come to 12 TIMES
THANKS
Senior Manager
Joined: 04 May 2005
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The arithmetic mean of the 16 digits in the credit card number is 4.75

=> the total of the 16 digits is: 16 x 4.75 = 76

The range is 1, => only 4 and 5 are allowed

suppose all of them are 4, then we get the total:

16 x 4 = 64 => so we cannot have all 16 digits being 4

76 - 64 = 12 => we need to have exactly 12 of them being 5

so that: 4x4 + 12x5 = 76 = 4.75 x 16
Manager
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agree with C.
Another approach would be to see that the difference between 4 - 5 is 1 composed by 16 digits. Since the mean is 4.75 , this means that 75% of the digits are 5 and 25% are 4 ( thus 4 x 4 ) .
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