DS #133 OG13th

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teresamichelle: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Feb 06, 2013 6:30 pm

by teresamichelle » Sat Jan 18, 2014 12:42 pm

I'm confused by this problem the explanation is very long & confusing for me. Is there another way to go about getting the right answer. Furthermore, I got other questions similar to this wrong, is there a place I can go to brush up on these types of problems?

If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y & z?

(1) the tens digit of x is equal to the sum of the tens digits of y and z.
(2) the units digit of x is equal to the sum of the units digits of y and z.

My choice: E (i guessed, didn't really understand the question)
Correct Answer: A

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Source: Beat The GMAT — Quantitative Reasoning | Sat Jan 18, 2014 12:42 pm

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

by Brent@GMATPrepNow » Sat Jan 18, 2014 12:58 pm

teresamichelle wrote: If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y & z?

(1) the tens digit of x is equal to the sum of the tens digits of y and z.
(2) the units digit of x is equal to the sum of the units digits of y and z.

Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?

Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308

Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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