Doubt with solving a question through "Math Strategy"

That the web may seem some ---------phenomenon, hardly rooted in the physical world, is a notion clearly ----------by the existence of “server farms”, sprawling forests of metal, figuratively sparking provide the backbone of the internet.

Options Blank (1)

(a) ethereal

(b)ephemeral

(c) Faddish

Option blank ii

(d)buttressed

(e)unsupported

(f)betrayed

I understand how to solve it through Idea contrast but not sure how to apply the “math strategy” over here. Can someone help, please?

Source: Magoosh

Share your contrast approach.

Identified “hardly” as the word contrasting the first blank , guess was some out of the world phenomenon, eliminated b and c got to (a). For second, identified support through a “,” sprawling forest of metal means , it is actually physically there, so it is not other worldly hence unsupported

What you just did is the math strategy, right?

You determined the support and contrasts between the ideas and the blank. That’s math strategy.

The “comma” after “phenomenon” creates support between the idea after it, and the idea before it (which includes the blank). So b1 must match “not physical world”.

“By” creates support for b2 which you aptly identified.

So, you’re “math strategizing”. You just need to add the logic words/punctuations.

thank you! You mean add as in (+) for the comma * (-) for the hardly = (-) for the first blank, I know from Greg’s videos that the negative doesn’t definitely mean a bad word if the sentence doesn’t flow, hence connotation based, is my understanding correct?

Close enough.

Idea 1 = “That the web…phenomenon”

Support/logic punctuation = comma (+)

Idea 2 = “not rooted in physical world” (‘hardly’ is not assigned a sign, it forms part of Idea 2)

Idea 1 × |logic punctuation| = Idea 2

The connotation bit you mentioned was spot on, so we can decide “Idea 2” is (+) or (-). We just have to be consistent with the equation.

We decide the sign for Idea 2 first because that’s a complete idea from which we can derive Idea 1.

Watch Math Strategy 1 - PrepSwift and the 3 subsequent math strategy videos for more on this if you need further clarity.