In the system above, is s = 1 and q = 1 ?

Question

(\frac{K}{3})s + Tq = C

Ks + 12q = 21

Ps + 15q = R

In the system above, is  s = 1  and  q = 1 ?

(1)  C = 7

(2)  R = 24

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JerryAtDreamScore · Answer

Breaking Down the Info:

For s = q = 1 to be true, we need the following to be true as well:

\frac{K}{3} + T = C 
 K + 12 = 21 ,  K = 9 . (Hence  3 + T = C )
 P + 15 = R

Statement 1 Alone:

C = 7 is only one variable out of the many. Insufficient.

Statement 2 Alone:

R = 24 is only one variable out of the many. Insufficient.

Both Statements Combined:

We need K = 9 and T = 4 but this is not given. There are too many variables, so insufficient. Note if T is not 4, we will have no solution from the first two equations, and that could be the case.

Answer: E

aggt · Answer

Can you please share the solution ? How do we suffice s=1 and q=1 for the first equation without knowing the value of C?

MrkSkywalker · Answer

How can it be B? We get P = 9 if s and q are 1 but we can also say s = 3 and q = 1 and this would still work...

BhavyaJha · Answer

Hi  Bunuel

Can you provide solution please?
I believe answer should be E as there are more number of variables than equations.

IanStewart · Answer

I saw this question near the top of the year-end "hardest DS questions of the year" list, and I always get concerned test takers will use those lists thinking they'll be a good source of challenging questions. But the "hardest" questions on this forum -- in other words, the questions people have answered "incorrectly" most often -- are almost always prep company questions which are beyond the scope of the test, or which are incomprehensibly worded, or which have the wrong "OA" recorded on the forum. That's true here. From Statement 1, multiplying the first equation by 3 on both sides, then subtracting one equation from the other, you find that 4q = Tq, so either T = 4 or q = 0 (the post above from DreamScore is incorrect that there will be no solutions unless T = 4). We don't care about T when q is nonzero, so Statement 1 isn't useful. Using Statement 2, though, it's possible that s = 1, q = 1, k = 9 and p = 9, but it's also possible that s = 9, q = 1, k = 1 and p = 1, among other possibilities. So the answer here is E, and the answer currently listed as the "OA" ("B") is not the right answer to this question, which explains why, on a forum full of people who are very good at math, only 10% of people have answered this question "correctly".

I'd add that the situation for Verbal is even worse than for Quant -- the 'hardest' Verbal questions on this forum are universally dire practice problems -- CR problems with bad logic, SC questions that invent grammar rules that don't exist, etc. Especially for Verbal I'd advise test takers looking for hard practice to look at the hardest questions in official resources -- questions near the end of official books, or from the official advanced book, for example.

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=81491 GMAT-Club-Forum-ugwfp25y.png

Bunuel · Answer

testing links: https://gmatclub.com/forum/rules-for-po ... 33935.html

In the system above, is s = 1 and q = 1 ?

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