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

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

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

by AAPL » Mon Jun 04, 2018 5:27 am

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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!

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Source: Beat The GMAT — Problem Solving | Mon Jun 04, 2018 5:27 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Jun 04, 2018 6:21 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Mon Jun 04, 2018 9:55 am

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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jun 05, 2018 9:37 am

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]