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

Question

Each card in a deck has a positive integer written on one side. Bjorn and Dagmar each draw two cards and divide the number on the first card by the number on the second card to calculate their score. Did Bjorn get a higher score than Dagmar?

(1) If Bjorn had drawn the same two cards in the opposite order, his score would have been lower than Dagmar’s score.

(2) The first card Dagmar drew had a greater number than her second card.

KarishmaB · Accepted Answer

We know for Dagmar, F > S. e.g. the division of the two cards could be 9/3 = 3

For Bjorn, his score in reverse cards could be 2/4 or 2/16 etc 
So Bjorn's actual score could be 4/2 = 2 or 16/2 = 4. In one case, it is less than Dagmar's, in the other, it is greater.

So the answer should be (E).

If it is actually (C), please put up a screenshot of the question and solution. Not sure what I am missing.

OhsostudiousMJ · Answer

I Plugged in numbers to get the answer.

Asked B>D?
1) 1.1 Let B cards be 5,1 and D cards be 3,1. YES for any positive integer in place of 3!
 1.2 Let B cards be 5,1 and D cards be 1,6. NO for any positive integer>5 in place of 6!
Hence, insufficient.

2) Clearly, no data on B. Insufficient.

Combining 1 and 2, It suffices the statement 1.1 and hence sufficient.
  C  is the answer.

PriyankaPalit7 · Answer

chetan2u ,  Bunuel ,  VeritasKarishma ,  gmatbusters ,  amanvermagmat 
Can any of you please give the solution to this?

drakell · Answer

I got E as well. I can't figure out any way the answer is c.

Posted from my mobile device

chetan2u · Answer

Each card in a deck has a positive integer written on one side. Bjorn and Dagmar each draw two cards and divide the number on the first card by the number on the second card to calculate their score. Did Bjorn get a higher score than Dagmar?

(1) If Bjorn had drawn the same two cards in the opposite order, his score would have been lower than Dagmar’s score.
Let D's numbers be 3 and 2 so 3/2 =1.5..
B could be 2 and 1 in normal order, then reversed 1/2<1.5 but 2/1 > 1.5 OR B could be 3 and 2 in normal order, then reversed 2/3<1.5 but 3/2= 1.5
Insuff

(2) The first card Dagmar drew had a greater number than her second card.
So D's score is greater than 1
Insuff

Combined..
Let D's numbers be 3 and 2 so 3/2 =1.5..
B could be 2 and 1 in normal order, then reversed 1/2<1.5 but 2/1 > 1.5 OR B could be 3 and 2 in normal order, then reversed 2/3<1.5 but 3/2= 1.5
Insuff

so, answer will be E as pointed by VeritasKarishma

BUT yes, if statement 2 read

(2) The first card Dagmar drew had a ~~greater~~ lesser number than her second card.
This would mean D<1.

Combined
Reverse of B is less than D, that is \(\frac{1}{B}<D<1\)
So, \(\frac{1}{B}<1\) or 1<B (We can X-multiply as B is positive)
so sequence is D<1<B..
answer is YES and sufficient..

BunuelWannabe · Answer

Hi everyone,

I have already fixed the typo.

Thanks!

anandjain24 · Answer

Hi can anyone explain the meaning of the statements here. 
For 1 statement shouldn't the cards be same for B but in reverse order ie. 
D : 4 2
B : 2 4

Kindly correct me if I'm getting it wrong.

Posted from my mobile device

kaladin123 · Answer

The OA:

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.

Attachment:

table.JPG [ 17.82 KiB | Viewed 6474 times ]

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).

AkRaGMAT99 · Answer

I had taken values for the cards drawn by B and D as a, b and c, d respectively.

Now if a/b = 4/3 and c/d = 5/3, 
1. When the cards of B are reversed (3/4), they are still smaller than c/d, and statement 2 is also satisfied. 
2. If I consider a/b = 5/3 and c/d as 4/3, statement 2 is still met, and if B's cards are reversed (3/5), statement 1 still holds true.

Please let me know if my thinking is correct.

Thank you all!

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

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