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Problem Solving Butler: April 2023 April 26 PS 1 PS 2

going to pin once again to keep it in recent chats

for-integers-a-b-c-and-d-if-the-value-of-ab-cd-1-c-429065.html Can anyone help me with this question?

I think the answer should be A, however they say that’s incorrect. b and d both are integers so both can only be equal to 1 or -1 if bd=1 so c=a, sufficient. However, b+d=3 is insufficient , we can check this with examples , b = 4 d =-1 , b+d =3 and b>d so c>a. But if b=1 and d=2, b+d = 3 but b<d so c<a. Please let me know if I missed something.

I think the answer should be E as both statement together doesnot give any concrete information about the relation between a and c even if we substitute the value of the respective numbers b and d from (i) we get b = 1/d or (b^2) = c/a (so we are not sure about the value of c/a which could be a fraction or a whole number (NOT sufficient) from. (ii) we get b = 3-d on substituting we get c/a = d/(3-d) which also doesn’t give a concrete value as the value of d is decisive (NOT sufficient) On combining both we cannot find any exact value of d which could suffice a single condition therefore both together not sufficient (E) should be the answer

but the question mentions that it is an integer so it cannot be a fraction

The answer to above question is E only as correctly described by u guys. I have a generic question. Is there any relationship between AM, GM, HM, mean and median? U can decide the case/ situation and illustrate your opinion.

Yes, we have many questions on relationships between mean and median and mode even sometimes depending on question, any kind of relationship can be drawn out, but I have attempted multiple questions with mean, median and mode, specially in D.S

That’s great 👍. However, my question was on broader aspect. Is there any relationship between AM GM HM mean and median AM means arithmetic mean, G is geometric mean etc

Harmonic Progression is rarely ever tested on GMAT, atleast I’ve not seen in over 2 years One relation that comes to mind is, "If numbers are in AP, then Mean = Median"

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