Data Sufficiency

Well,
this is from OG 12
If . represents one of the operations +, -, and x, is k. (l+m)=(k.l) + (k.m) for all numbers k, l, and m?

(1) k.1 is not equal to 1.k for some numbers k.
(2) . represents subtraction

it says OA is D as it says substration can be only operation and we can get some value
Agreed
BUT
Lets take,
case 1) k=1,l=2 and m=3
1-(2+3) = (1-2)+(1-3) from question
-4=-3
not true answer NO

now take
k=m=n=0
(question doesnt say we cannot do that neither it says numbers are positive....it says for all numbers....0 is number as well)
0=0
true
Answer is YES

now how is answer D
It is still not giving concrete answer

thanks

As you calculated take first statement.
k = 0
k-1 != 1-k
where as if l,m = 1,1 respectively then k. (l+m)=(k.l) + (k.m)
k=1
where as if l,m = 2,3 then k. (l+m)!=(k.l) + (k.m) for subtraction and addition
k=1 and l=1,m=-1 then k. (l+m)!=(k.l) + (k.m) for multiplication.

with first statement we can decide whether they are equal or not.

consider second statement

if . represents subtraction then
k = 0
where as if l,m = 1,1 respectively then k. (l+m)=(k.l) + (k.m)
k=1
where as if l,m = 2,3 then k. (l+m)!=(k.l) + (k.m)

which is enough to decide statements are equal or not.
So I think we can decide with any one of the statements.

frank1 wrote:Well,
this is from OG 12
If . represents one of the operations +, -, and x, is k. (l+m)=(k.l) + (k.m) for all numbers k, l, and m?

(1) k.1 is not equal to 1.k for some numbers k.
(2) . represents subtraction

it says OA is D as it says substration can be only operation and we can get some value
Agreed
BUT
Lets take,
case 1) k=1,l=2 and m=3
1-(2+3) = (1-2)+(1-3) from question
-4=-3
not true answer NO

now take
k=m=n=0
(question doesnt say we cannot do that neither it says numbers are positive....it says for all numbers....0 is number as well)
0=0
true
Answer is YES

now how is answer D
It is still not giving concrete answer

thanks

You're misinterpreting the question, which asks:

Does k#(l+m) = (k#l) + (k#m) for ALL numbers k, l, and m?

If # represents multiplication:
k*l + k*m = (k*l) + (k*m) will be true for all values of k, l and m.

If # represents addition:
k+l+m = k+l + k+m will be true for some values (if k=0, for example) but not for ALL values of k, l, and m.

If # represents subtraction:
k-l-m = k-l + k-m will be true from some values (if k=0, for example) but not for ALL values of k, l. and m.

Since each statement indicates that # represents subtraction, we know that k-l-m = k-l + k-m will not be true for ALL values of k, l, and m. Thus, each statement is sufficient.

GMATGuruNY wrote: Since each statement indicates that # represents subtraction, we know that k-l-m = k-l + k-m will not be true for ALL values of k, l, and m. Thus, each statement is sufficient.

thanks guru for the response.

i think that is what my question is about
what if k=l=m=0
in that case the above statement will be true 0=0

i think as said earlier,i think question doesnt stop us from taking k=l=m=0

thanks
just a query

frank1 wrote:

GMATGuruNY wrote: Since each statement indicates that # represents subtraction, we know that k-l-m = k-l + k-m will not be true for ALL values of k, l, and m. Thus, each statement is sufficient.

thanks guru for the response.

i think that is what my question is about
what if k=l=m=0
in that case the above statement will be true 0=0

i think as said earlier,i think question doesnt stop us from taking k=l=m=0

thanks
just a query

Yes, if # represents subtraction, we could plug in k=l=m=0, in which case k-(l+m) = (k-l) + (k-m). But the answer to the question Does k-(l+m) = (k-l) + (k-m) for ALL numbers k, l, and m? will still be a definitive NO, because k-(l+m) = (k-l) + (k-m) is not true for ALL numbers k, l, and m.

Here's an analogy:

Does John eat ice cream every day?

If John eats ice cream on Tuesdays but not on Wednesdays, the answer to the question is NO: John does not eat ice cream every day.

The same reasoning holds true for the DS question above:

Does k#(l+m) = (k#l) + (k#m) for all numbers k, l, and m?

If k#(l+m) = (k#l) + (k#m) when k=l=m=0 but not when k=1, l=2, and m=3, then the answer to the question is NO: k#(l+m) = (k#l) + (k#m) is not true for all numbers k, l, and m.

Hi GMATGuruNY:
So it could be simply stated then when a question of this type asked in DS
Eg:Does k#(l+m) = (k#l) + (k#m) for all numbers k, l, and m?
No need to look into any of the conditions given as whatever the conditions would be we can Yes/No and the answer would be D always.

Hi All,

Can anyone please share any similar kind of questions.

Thanks in advance.

Regards,
Uva.

Brent@GMATPrepNow wrote:

Uva@90 wrote:Hi All,

Can anyone please share any similar kind of questions.

Thanks in advance.

Regards,
Uva.

Hi Uva,

Here are two similar questions:
- https://www.beatthegmat.com/operation-t45094.html
- https://www.gmatprepnow.com/module/gmat- ... ic?id=1058

Cheers,
Brent

Thanks Brent:)

You are always Helpful.

uniquer wrote:Hi GMATGuruNY:
So it could be simply stated then when a question of this type asked in DS
Eg:Does k#(l+m) = (k#l) + (k#m) for all numbers k, l, and m?
No need to look into any of the conditions given as whatever the conditions would be we can Yes/No and the answer would be D always.

That's a good point. Even, I was thinking the same, assuming the question format remains the same and we can anyway answer the statements with a definitive 'Yes' or 'No'.

Experts - Please correct if we are missing anything in our understanding. Is this a very broad assumption to make for such type of questions ?