This one tricked me

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NeilWatson: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Wed Oct 30, 2013 7:54 am; Followed by:1 members

This one tricked me

by NeilWatson » Sun Apr 06, 2014 6:18 pm

If there are more than 2 numbers in a certain list, is each of the numbers in the list equal to 0?
1) The product of any 2 numbers in the list is equal to 0
2) The sum of any 2 numbers in the list is equal to 0

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 06, 2014 6:18 pm

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by [email protected] » Sun Apr 06, 2014 10:53 pm

Hi NeilWatson,

This DS question is perfect for TESTing Values.

We're told that we have a list of more than 2 numbers (meaning 3 or more numbers). We're asked if each of the numbers in the list is equal to 0. This is a YES/NO question.

Fact 1: The PRODUCT of ANY 2 numbers is equal to 0.

This means that at least one of the 2 numbers mentioned is 0.

Our list could contain:
0, 0, 0 and the answer to the question is YES
0, 0, 1 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: The sum of ANY 2 numbers is equal to 0.

This means that the 2 numbers are either both 0 or "opposites." Since the list is 3 or more numbers though, there's no way to guarantee that the sum would = 0 UNLESS all the numbers are ALL 0 (for example, IF we have -1, -1, 1, 1 we would NOT be able to guarantee that the sum of ANY 2 numbers is 0; this proves that all the numbers MUST = 0). So the answer to the question would be YES.
Fact 2 is SUFFICIENT

Final Answer: B

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

Contact Rich at [email protected]

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David@VeritasPrep: GMAT Instructor; Posts: 2193; Joined: Mon Feb 22, 2010 6:30 pm; Location: Vermont and Boston, MA; Thanked: 1186 times; Followed by:512 members; GMAT Score:770

by David@VeritasPrep » Mon Apr 07, 2014 2:33 pm

Very nice explanation from Rich!

It is important to be careful and not leap to the conclusion that the answer is C. Which many people do. (AT Veritas we say "No easy C's" because C can be a trap for many people).

I wanted to add one thing that might help here. This is a Yes/No question. Understand that Yes/No questions are more likely to be A B or D than are specific number questions.

I have verified this fact through examining official materials. You would expect three answer choices A B D to account for 60% of all answers. For yes/ no questions A B and D account for more than 70% and close to 75% of the answers in the Official Guide.

Now of course this is a small sample size, but it also makes sense. Think about yes/ no questions and what you are trying to answer, "Is x is positive?" "Is y a prime number?" "Is xy < 0?" or in this case "Is each of the numbers equal to zero?"

This requires less information than the standard specific number question, "What is the value of x?" It generally does not require as much knowledge to determine whether or not x is positive as it does to get one value of x."

So just remember going forward, when you see a yes/no question be sure that you are very careful to be exact as to what the question is asking, and lean a little bit in the direction of one statement alone. Sure the answer could easily be C or E but remember no "easy C's" only choose C (or E) if you have earned it!

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