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

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Joined: 05 Jan 2019
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Each card in a deck has a positive integer written on one side.  [#permalink]

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Updated on: 11 Apr 2019, 07:09
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Difficulty:

85% (hard)

Question Stats:

45% (02:16) correct 55% (01:42) wrong based on 53 sessions

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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.

Originally posted by BunuelWannabe on 09 Apr 2019, 12:17.
Last edited by BunuelWannabe on 11 Apr 2019, 07:09, edited 2 times in total.
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Re: Each card in a deck has a positive integer written on one side.  [#permalink]

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10 Apr 2019, 07:22
BunuelWannabe wrote:
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.

I Plugged in numbers to get the answer.

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.
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Re: Each card in a deck has a positive integer written on one side.  [#permalink]

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11 Apr 2019, 04:22
Can any of you please give the solution to this?
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Re: Each card in a deck has a positive integer written on one side.  [#permalink]

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11 Apr 2019, 05:52
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BunuelWannabe wrote:
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.

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.
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Re: Each card in a deck has a positive integer written on one side.  [#permalink]

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11 Apr 2019, 06:42
BunuelWannabe wrote:
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.

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.

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

Posted from my mobile device
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Each card in a deck has a positive integer written on one side.  [#permalink]

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11 Apr 2019, 07:05
1
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

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..
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Each card in a deck has a positive integer written on one side.  [#permalink]

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11 Apr 2019, 07:16
Hi everyone,

I have already fixed the typo.

Thanks!
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Re: Each card in a deck has a positive integer written on one side.  [#permalink]

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11 Apr 2019, 07:34
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
Re: Each card in a deck has a positive integer written on one side.   [#permalink] 11 Apr 2019, 07:34
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