If P, Q, and R are distinct positive digits and the product

AAPL wrote:If P, Q, and R are distinct positive digits and the product of the two-digits integer PQ and PR is 221, what is the sum of the digits P, Q, and R?

A. 5
B. 11
C. 13
D. 21
E. 23

The OA is B.

Factor out 221
221 = 13*17

Thus, PQ = 13 and PR = 17 or viceversa

Thus P = 1, Q = 3 and R = 7
Sum = 1+3+7 = 11.

Hence, the correct answer is B.

Has anyone another strategic approach to solve this PS question? Regards!

That's a perfect approach.
The hardest part is looking for two 2-digit numbers that have a product of 221!!

Cheers,
Brent

Hi AAPL,

Your approach is spot-on. When dealing with these types of questions, Number Property rules and pattern-recognition can often be quite helpful (and can help you to work through the math in an efficient fashion).

First, we're multiplying two 2-digit numbers together and ending up with 221. The smallest possible 2-digit number is 10, so the larger of the two values won't be any bigger than 22 (and you can prove rather quickly that 22 is NOT an option; see below).

Second, since we're multiplying two numbers together and ending with an ODD number, we know that the 2 numbers MUST be ODD (since Odd x Odd = Odd).

Third, when multiplying numbers together, the "units digit" of the end result will be the product of the units digit of the numbers that you multiplied together. Here, we need a product that ends in a 1 AND we know that we're multiplying two ODD numbers together. There are only a few options: two numbers that both end in a 1, two numbers that both end in a 9 or one number that ends in a 3 and one that ends in a 7.

At this point, a bit of multiplication and/or division is all that's left.

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:If P, Q, and R are distinct positive digits and the product of the two-digits integer PQ and PR is 221, what is the sum of the digits P, Q, and R?

A. 5
B. 11
C. 13
D. 21
E. 23

Let’s break 221 into prime factors:

221 = 13 x 17

Since there are only two 2-digit numbers that multiply together to yield 221, we see that PQ must equal 13 and PR must equal 17 (or vice versa). So the sum of P, Q and R is 1 + 3 + 7 = 11.

Answer: B