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# A deck of n cards contains exactly k marked cards.

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A deck of n cards contains exactly k marked cards. [#permalink]  12 Feb 2020, 09:35
Expert's post
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Question Stats:

85% (00:45) correct 14% (00:59) wrong based on 14 sessions
A deck of n cards contains exactly k marked cards. ($$k \neq 0$$ )

 Quantity A Quantity B The ratio of the number of unmarked cards in the deck to the number of marked cards in the deck $$\frac{n}{k }-1$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: A deck of n cards contains exactly k marked cards. [#permalink]  12 Feb 2020, 11:05
The number of unmarked cards in the deck equals to n - k.

The Quantity A then equals to (n-k)/k = n/k - 1. That exactly equals to Quantity B.

GRE Instructor
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Re: A deck of n cards contains exactly k marked cards. [#permalink]  16 Feb 2020, 06:28
Expert's post
Carcass wrote:
A deck of n cards contains exactly k marked cards. ($$k \neq 0$$ )

 Quantity A Quantity B The ratio of the number of unmarked cards in the deck to the number of marked cards in the deck $$\frac{n}{k }-1$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation

Main idea: (number of marked cards) + (number of unmarked cards) = n

The given information tells us that there are k marked cards.

So we get: k + (number of unmarked cards) = n
Subtract k from both sides of the equation to get: number of unmarked cards) = n - k

QUANTITY A: (number of unmarked cards)/(number of marked cards) $$= \frac{n - k}{k}$$

QUANTITY B: $$\frac{n}{k }-1$$

At this point you may already see that the two quantities are equal.
However, if we don't see it, we can always multiply both quantities by k to get:

QUANTITY A: $$n - k$$

QUANTITY B: $$n-k$$

Cheers,
Brent
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Re: A deck of n cards contains exactly k marked cards.   [#permalink] 16 Feb 2020, 06:28
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