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Traditionally, decision-making by managers that is reasoned step-by-step has been considered preferable to intuitive decision-making (opposing opinion). However, a recent study found that top managers used intuition significantly more than did most middle- or lower-level managers (premise). This confirms the alternative view that intuition is actually more effective than careful, methodical reasoning (conclusion).

The premise says the top managers used intuition more than most middle- or lower-level managers. The conclusion is that the intuition is mroe effective than methodical reasoning (or step-by-step reasoning).

Necessary assumption. Use negation.

If you negate E), you have:
Top managers are NOT more effective at decision-making than middle- or lower-level managers.
If this is the case, then the method used by top managers are not more effective than the method used by the middle- or lower-level mangers. And from the stimulus, we know that the top managers use intuition significantly more than most middle- or lower-level managers. So intuition is NOT more efficient than the step-by-step reasoning method, which is commonly used by all managers. Thus, the conclusion falls apart.

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The explanation for D) says:
If you negate D), the conclusion still might hold. Thus, according to the negation method, D) is not necessary.

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Majority = more than 50%.  

Negation: Not more than 50%; could be 50%, 49% . . .0%