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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
