Each card in a deck has a positive integer written on one side.

Begin by creating variables for the cards that each player will draw:

\(b1\) = Bjorn’s first card
\(b2\) = Bjorn’s second card
\(d1\) = Dagmar’s first card
\(d2\) = Dagmar’s second card

Though the problem doesn’t explicitly talk about Fractions, the question itself can be translated as

\(\frac{b1}{b2}>\frac{d1}{d2}\)?

Glancing at the statements reveals that no actual values are given. Thus, it is very likely that you will need to Test Cases to evaluate the statements.

(1) INSUFFICIENT: Begin by translating the statement:

\(\frac{b2}{b1}<\frac{d1}{d2}\)

Algebraically, this inequality cannot be rearranged to recreate the inequality in the question, indicating this statement is likely insufficient. To verify that this statement is insufficient, you can test cases.

Given that this problem is about fractions, and all the card values are positive, think about how to create different cases. If the first card drawn is greater than the second card, then the score will be greater than 1. If the first card is less than the second card, then the score will be less than 1. On the other hand, fi the values of the cards are close together, the score will be closer to 1. If the values are far apart, the score will be farther away from 1.

In the scenarios below, Bjorn’s score changes from 3 to 13 when the order of his cards is reversed. You can create different answers to the question by changing whether Dagmar’s score is greater or less than 3, as long as Dagmar’s score is greater than 13.



It is possible to get both Yes and No as answers to the question. Statement (1) is INSUFFICIENT. Eliminate choices (A) and (D).


(2) INSUFFICIENT: Translate the statement: \(d1 > d2\)

Without any information about the cards Bjorn drew, this statement is insufficient to answer the question. Eliminate choice (B).

(1) AND (2) INSUFFICIENT: Even when both statements are used together, both Yes and No are possible answers to the question. Note that both cases used in Statement (1) work for both statements. Thus, they are still valid cases to test. Statements (1) and (2) are INSUFFICIENT.

The correct answer is (E).