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

Question

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

Dan · Answer

but how are we sure that it ever occurs? I'll go with E.

HIMALAYA · Answer

C seems ok because range is given..

AJB77 · Answer

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

mandy · Answer

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

AJB77 · Answer

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?

gmat2me2 · Answer

Well I thought E ....But guys you really thought well.....

mandy · Answer

plz HowManyToGo can you explain how you come to 12 TIMES

THANKS

qpoo · Answer

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

tobiastt · Answer

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 ) .

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards