In the correctly-worked multiplication problem above, each

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.


In the correctly-worked multiplication problem above, each symbol represents a different nonzero digit. What is the value of ʞ?

(1) ʠ is prime

(2) ◊ is not prime

Transforming the original condition and the question, we have 1995=21*95=95*21. (Since all the digits have different values we can't have 35*57)
There are 4 variables and 1 equation, thus we need 3 more equations to match the number of variables and equations. Since there is 1 each in 1) and 2), E is likely the answer.
Using both 1)& 2) together, both gives us 21*95=1995 thus ʞ=9 and 1)=2). Therefore, D is the answer.

I spent a good amount of time on this problem.
But then I realized that GMAT is not the kind of exam where our math skills are tested. It's the reasoning.
So I thought about what could be the 2 line solution and then it struck me that I need to factor 1995.

GMAT is a reasoning test. The sooner we accept this the better the results will be.

Prime-factorisation of 1995 = 3 x 5 x 7 x 19

Statement 1
We are given that ʠ is prime
The only two-digit combination of the prime-factorisation that ensures ʠ is prime: €◊ = 21 and ʞʠ = 95. Hence, ʞ = 9, sufficient.

Statement 2
We are given that ◊ is not prime
The only two-digit combination of the prime-factorisation that ensures ◊ is not prime: €◊ = 21 and ʞʠ = 95. Hence, ʞ = 9, sufficient.

Answer is D

With alphametics, we first start with the big picture view and figure out what we can.

1995 = 3 * 5 * 7 * 19
We need to split 1995 into 2 factors of 2 digits each. 19 is already a 2 digit factor so to retain 2 digits, we can
- keep it as it is (but 3*5*7 becomes 3 digit) or
- we can multiply it by 3 to get 57 which means the other factor will be 5*7 = 35. So the two factors will be 57 and 35 but here they have 5 common digit though we are given that all digits of the two factors are distinct.
- we can multiply it by 5 to get 95 which means the other factor will be 3*7 = 21 (which is acceptable)

So the two factors are 21 and 95.
1 is not prime and 5 is.
Hence each statement alone is sufficient.

Answer (D)

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