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Digits

by tonebeeze » Fri Mar 25, 2011 3:14 pm
Is the four-digit number k less than 2400?

1. The product of the digits in k is 72

2. The hundreds digit is the largest digit in k

OA = E
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Source: — Data Sufficiency |
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by srcc25anu » Fri Mar 25, 2011 5:20 pm
stat 1: product of digits = 72
72 = 9*8 or 3^2 * 2^3
any combination of 3 twos, 2 threes and any number of ones will satisfy the statement
hence not sufficient

stat 2: hundred's digit = 9 (largest digit)
now thousands digit could be anything less than 9 (1,2,3,4,5,6,7,8)
hence not sufficient

together stat 1 and 2:
if hundredth digit = 9, other 3 digits must give a product 8 again there are multiple ways to get it
8 9 1 1
2 9 2 2
1 9 8 1 and so on

hence E
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