To solve hard multi-blank GRE Text Completions, consider the subject of the blank and what is known about that subject to predict your own word(s) for the blanks one-at-a-time.

For the first blank
Subject: "greatest failing of positive psychology books" as pertains to "typical complexity"
Know: matches "replace typical complexity with breezy glibness"

As our prediction for the first blank we can simply reuse "replace".
(A) invoke - Does not match "replace" in this context. Eliminate Choice A.
(B) address - Does not match "replace" in this context. Eliminate Choice B.
(C) eschew - Matches "replace" in this context. Keep Choice C.

For the second blank
Subject: "advice of positive psychology books" as pertains to "this case" of "breezy glibness"
Know: matches "breezy glibness"

As our prediction for the second blank we can simply repurpose "glibness" into its simpler form "glib", which means overly simplistic.
(D) pat - Secondary definition of "trite" or "simple" matches the prediction. Keep Choice D.
(E) evocative - Reversal of the prediction. Eliminate Choice E.
(F) convoluted - Reversal of the prediction as "convoluted" is the opposite of "simple". Eliminate Choice F.

For the third blank
Subject: "our times"
Know: matches "succor public requires" and is opposite of "glibness"

As our prediction for the third blank we can simply take the opposite of "glibness" such as serious.
(G) heady - Broad reversal of the prediction. Eliminate Choice G.
(H) trying - Secondary adjectivial definition of "hard" or "difficult" matches the prediction. Keep Choice H.
(I) halcyon - Broad reversal of the prediction. Eliminate Choice I.

Read each of the kept choices into the sentence to ensure it creates a coherent meaning throughout the sentence. Once confirmed, select Choices C, D, and H.

They are talking about the failing of the deluge of positive psychology books. And in this case, it has got something to do with the "complexity typical of psychology books". Therefore, the only possible choice is eschew. For if they address it, or invoke it, it would be appropriate and correct, because the complexity is typical of psychology books. The fact that they replace the complexity with a glibness further tells us that the original complexity was dispensed with (eschewed).

Next the real failing is described - "they dispense advice that is so ______ and littered with platitudes....". We need a word that is a synonym or related to platitudes. Pat (glib and unconvincing) is the only correct choice, as it is related to platitudes (cliches which have lost their force and meaning) and is also a synonym of glib - and we know that the book contains breezy glibness.

And next - "as to be so bereft of the very succor that the public requires during our ____ times". Only during difficult times that the public requires help, so the word for the blank can only be trying. Halcyon refers to golden period and heady means intoxicating or exhilarating, not the right word.

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