OG 13th Data sufficiency #133

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

pchnts: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Oct 14, 2014 10:43 am

OG 13th Data sufficiency #133

by pchnts » Mon Nov 17, 2014 9:54 am

hello,

I have a problem with the solution of this question:

# 133:
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 and 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.

the answer to this question is A) - 1st statement is sufficient, but what if we would have sum of numbers 359 and 549, the sum of 5 +4 is nine but then the sum of hundreds digits wouldn't be 8.

thank you

Quote

Source: Beat The GMAT — Data Sufficiency | Mon Nov 17, 2014 9:54 am

GMAT/MBA Expert

[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 Nov 17, 2014 10:17 am

Hi pchnts,

Unfortunately, the example that you've described does NOT fit the restriction in Fact 1.

We're told that the TENS DIGIT of X = the sum of the TENS DIGITS of Y and Z

359 + 549 = 908

The tens digit of X is 0, the sum of the tens digits of Y and Z is 9. This is not a valid example.

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

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

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 Nov 17, 2014 10:50 am

pchnts 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 and 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

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Nov 17, 2014 10:57 am

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 and 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.

Let y = 2BC, z = 2EF, and x = HTU, so that the addition looks as follows:

2BC
2EF
HTU

When will it be true that H â‰ 2+2?
When we have to CARRY A 1 FROM THE TENS PLACE TO THE HUNDREDS PLACE.
To illustrate:

259
249
508

Here, because we have to carry a 1 from the tens place to the hundreds place, H = 2+2+1 = 5.

Question rephrased:

ABC
DEF
HTU

In the addition problem above, do we have to a carry a 1 from the tens place to the hundreds place?

Statement 1: The tens digit of x is equal to the sum of the tens
digits of y and z.
Since T = B+E, there is no need to carry a 1 to the hundreds place.
SUFFICIENT.

Statement 2: The units digit of x is equal to the sum of the
units digits of y and z.
Since U = C+F, we do not need to carry a 1 from the UNITS PLACE to the TENS PLACE.
But it cannot be determined whether we have to carry a 1 from the TENS PLACE to the HUNDREDS PLACE.
If T = B+E = 0+0 = 0, then there is no need to carry a 1 to the hundreds place:
If T = B+E = 9+9 = 18, then we must carry a 1 to the hundreds place.
INSUFFICIENT.

The correct answer is A.

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