Does this question have multiple answers?

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

torofish: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Nov 24, 2008 6:41 am

Does this question have multiple answers?

by torofish » Thu Jan 29, 2009 8:54 am

I got it from Kaplan Workshop on PS Basics.

Fence X is twice as long as Fence Y, and Fence Y is 2 feet shorter than Fence Z.
If 3 feet were added to each fence, which of the following must be true?

I.) X is twice as long as Y
II.) Y is 2 feet shorter than Z
III.) X is longer than Z

MY WAY

X = 12
Y = 6
Z = 8

so add 3

X = 15
Y = 8
Z = 11

Therefore,
I <-- not true
II <-- true
III <-- true

KAPLAN

X = 2
Y = 1
Z = 3

added 3

X = 5
Y = 4
Z = 6

I <-- not true
II <-- true
III <-- not ture

---------------

So, two answers?

Quote

Source: Beat The GMAT — Problem Solving | Thu Jan 29, 2009 8:54 am

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Thu Jan 29, 2009 9:24 am

The question asks what *must* be true, which means 'what would always be true no matter what numbers you choose'. With your example, you showed that II and III *could* be true, not that they are *always* true. As the numbers from the other solution illustrate, III is not *always* true; it's sometimes true, sometimes not.

This question does illustrate the danger of picking numbers for 'must be true' questions like the one above. If you plug in numbers and find that III is true, all you're proving is that III is true for the numbers you chose. You are not proving it's true for all numbers. Picking numbers can sometimes be useful, but you need to be careful about doing it.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Quote

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Thu Jan 29, 2009 9:30 am

I'm not sure if you can use numeric examples here, since I asks you if X is twice as long as Y after adding the three meters. We cannot know if there is a relationship between X and 3, so I wouldn't go to the numeric example...
Let's use what we have for now. And that is:
x = 2y
y+2 = z.

Now we add 3 meters to every fence. Let's analyze each statement and see if it is true or not.
1. x = 2y. While this is correct before adding the 3 meters, it is not after adding them. If it were, you get that 2(y+3) = x +3, which means that 2y+6 = x + 3. Since we know that x = 2y, this means that 6 = 3, which is obvious nonsense.
2. y+2 = z. Let's add the 3 meters to y an z. What do we get? Well, y + 3 + 2 = z + 3. This formula is consistent with the initial one, that y+2=z, so we assume it is correct.
3. After adding the three meters, we need to check if x + 3 is greater than z + 3, which is the same as asking if x is greater than z. Well, let's use our initial two equations. x = 2y and y + 2 = z, this means that x/2 + 2 = z. Is x greater than z? Well, we can't be sure. If you consider x = 2 as in the Kaplan explanation, then this is not true. But if you consider x = 6, then it certainly is true.

So I'd go with:
I. not true
II. true
III. not necessarily true

Since you are looking for smth [b]that must be true[/b], then your answer will be II.