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Data Sufficiency

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Data Sufficiency

by RiyaR » Wed Sep 10, 2014 10:04 am
$&*^#=1995
In the correctly-worked multiplication problem above, each symbol represents a different nonzero digit. What is the value of ^?
(1) Ê  is prime
(2) â—Š is not prime
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by GMATGuruNY » Wed Sep 10, 2014 10:48 am
To make the problem easier to follow, let's replace the symbols with letters:
AB
CD
1995

In the correctly-worked multiplication problem above, A, B, C and D each represent a different nonzero digit. What is the value of C?
(1) D is prime
(2) B is not prime
1995 = 3*5*7*19.
For the product of AB and CD to have a units digit of 5, either B or D must be equal to 5.
Options for the 2-digit integer with a units digit of 5:
3*5=15, implying that the other integer = 7*19 = 133.
5*7=35, implying that the other integer = 3*19 = 57.
5*19=95, implying that the other integer = 3*7 = 21.

Only the option in red yields four distinct values for A, B, C and D.
Thus, two cases are possible:
Case 1: AB=95, CD=21
Case 2: AB=21, CD=95

Statement 1: D is prime
Only Case 2 is viable.
Thus, C=9.
SUFFICIENT.

Statement 2: B is not prime
Only Case 2 is viable.
Thus, C=9.
SUFFICIENT.

The correct answer is D.
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