STATENTS NEVER CONTRADICT - DS

[mww7786]

Hello Stacy, 8)

I hope things are going your way. This forum is an awesome way to network and get information.

HERE GOES. . .

#1 page 82 "Number Properties" book - MY QUESTION IS AT THE CONCLUSION/ INTERPRETATION STEP OF THE PROBLEM

Topic: Statements never contradict on Data sufficeincy

If y and n are positive integers, is yn divisible by 7?

1) n^2 -14n +49
2) n+2 is the first of 3 consecutive integers whose product is 990

Now: My question: when you determine that both are sufficeint since x=7, does this type of question indicate that both statements must be x=7
for both statements to be sufficeint. (in other words: will some DS questions have the answer: "both sufficeint" but have example s1) x=7
s2) x= OTHER #
OR, SHOULD BOTH STMNTS BE X=7 TO BE SUFFICEINT

-THE GENERAL PRINCIPAL IS THAT THE TWO STATMENTS WILL NEVER CONTRADICT??

[Guest]

The question may have been addressed to an indiv. but took the liberties...

#2) n+2 is first of three conse integers whose product is 990==> 9*10*11
Therefore n+2=9==> n=7

Hope this helps.

[StaceyKoprince]

It is true that the two statements will never contradict each other - but you can have a circumstance in which one variable can equal multiple numbers. So you could have one statement which says n^2 = 49, therefore n = +7 and -7, and then another statement which leads you only to n = +7; you would conclude that the n = +7 statement is sufficient. Alternatively, you could have one statement which gives you n = +7 or -7 and another statement which says n does NOT equal -7; you would conclude that the two statements together are sufficient. This is not considered contradictory because it is narrowing down your options; you use the info to get rid of one option but you still have at least one other option.

You would not have, however, a statement which tells you x = 7 (only) and then another statement which tells you that x does NOT equal 7. Or something that says x>0 and another that says x<0. Those types of statements are contradictory because there is no way to reconcile them - when you put them together, it just tells you that the problem is impossible - and they don't give us impossible problems on the test. (Well, some of them might seem impossible... )

[metman82]

Well I did a mistake when solving this problem with Statement (2).

I used prime factorization so I got:
990 = 2* 3^2 * 5 * 11
Therefore 990 is not divisible by 7.
I've forget that there is still a y.
Afterwards I have realized that you can combine the primefactors into-> 9,10,and 11
So n = 7
Therefore yn is divisble by 7.

[tim]

looks good to me. did you have a question about this one?