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Each card in a deck has an integer written on it, and the integers on

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Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 11:52
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Each card in a deck has an integer written on it, and the integers on each of the 12 cards in the deck are consecutive. In a certain game, the number points awarded for each turn is determined by drawing two cards and multiplying the numbers shown on the cards. If the points awarded in three turns are 40, 72, and 60,all of the following could be the smallest numbered card in the deck EXCEPT

(A) -1
(B) 0
(C) 4
(D) 5
(E) 6
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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:07
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Hi Turkish,

As wordy and 'layered' as this question looks, if you recognize how the 'restrictions' interact with one another, and pay attention to the answer choices, then you can avoid most of the work.

We're told a number of facts about a game and the cards that you use to play the game:
1) There are 12 cards, each with an integer written on it
2) The integers are consecutive
3) After drawing 2 cards, you multiply the product of the two numbers on the cards
4) The scores 40, 72 and 60 are earned during three turns.

We're asked which of the answers could NOT be the smallest number in the deck.

Let's focus on the number 40....

Since we have to get to the number 40 by using the product of 2 integers that are within "range" of one another (remember there are only 12 integers and they are CONSECUTIVE), there are only a few possible options....

40 =
(1)(40) --> NOT an option, since 1 and 40 are not within 12 integers.
(2)(20) --> NOT an option either
(4)(10) --> This IS an option
(5)(8) --> This IS an option

To get the "40" score, you either need the 4 or the 5....so one or the other or both needs to be on one of the cards.

Thus, there's no way that the 6 can be the smallest card.

Final Answer:

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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:15
Turkish wrote:
Each card in a deck has an integer written on it, and the integers on each of the 12 cards in the deck are consecutive. In a certain game, the number points awarded for each turn is determined by
drawing two cards and multiplying the numbers shown on the cards. If the points awarded in three turns are 40, 72, and 60,all of the following could be the smallest numbered card in the deck EXCEPT
(A) -1
(B) 0
(C) 4
(D) 5
(E) 6


As 40 is the smallest score . Lets check it.
40 can be written as product of 1*40, 2*20, 4*10, 5*8
but given to us is 12 as highest number so only 4*10 or 5*8 combinations are possible. minimum can't be 6.

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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:28
EMPOWERgmatRichC wrote:
Hi Turkish,

As wordy and 'layered' as this question looks, if you recognize how the 'restrictions' interact with one another, and pay attention to the answer choices, then you can avoid most of the work.

We're told a number of facts about a game and the cards that you use to play the game:
1) There are 12 cards, each with an integer written on it
2) The integers are consecutive
3) After drawing 2 cards, you multiply the product of the two numbers on the cards
4) The scores 40, 72 and 60 are earned during three turns.

We're asked which of the answers could NOT be the smallest number in the deck.

Let's focus on the number 40....

Since we have to get to the number 40 by using the product of 2 integers that are within "range" of one another (remember there are only 12 integers and they are CONSECUTIVE), there are only a few possible options....

40 =
(1)(40) --> NOT an option, since 1 and 40 are not within 12 integers.
(2)(20) --> NOT an option either
(4)(10) --> This IS an option
(5)(8) --> This IS an option

To get the "40" score, you either need the 4 or the 5....so one or the other or both needs to be on one of the cards.

Thus, there's no way that the 6 can be the smallest card.

Final Answer:

GMAT assassins aren't born, they're made,
Rich


I reread your answer twice but still can't grasp one thing: how 0 and -1 can be the smallest number in this question?
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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:34
Lucky2783 wrote:
Turkish wrote:
Each card in a deck has an integer written on it, and the integers on each of the 12 cards in the deck are consecutive. In a certain game, the number points awarded for each turn is determined by
drawing two cards and multiplying the numbers shown on the cards. If the points awarded in three turns are 40, 72, and 60,all of the following could be the smallest numbered card in the deck EXCEPT

but given to us is 12 as highest number so only 4*10 or 5*8 combinations are possible. minimum can't be 6.

E


Hi Lucky2783,

You've correctly answered the question, but part of what you stated in your explanation in NOT correct. The prompt states that there are 12 cards, each has an integer written on it and the integers are consecutive. That means that the numbers are 12 consecutive integers, NOT that the largest integer is 12.

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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:41
2
Harley1980 wrote:

I reread your answer twice but still can't grasp one thing: how 0 and -1 can be the smallest number in this question?


Hi Harley1980,

My approach focused on proving that 6 could NOT be the smallest integer (rather than proving that the other 4 answers COULD be the smallest integer). Here's the proof that -1 and 0 each could have been the smallest integer though.....

Since we're dealing with 12 consecutive integers...

IF...
-1 was the smallest, then we'd have the numbers -1 to +10, inclusive
We could get 40 with (4)(10) or (5)(8)
We could get 72 with (8)(9)
We could get 60 with (6)(10)
Thus, -1 COULD be the smallest integer

IF....
0 was the smallest, then we'd have the numbers 0 to +11, inclusive
We could get 40 with (4)(10) or (5)(8)
We could get 72 with (8)(9)
We could get 60 with (6)(10)
Thus, 0 COULD be the smallest integer

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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:48
EMPOWERgmatRichC wrote:
Harley1980 wrote:

I reread your answer twice but still can't grasp one thing: how 0 and -1 can be the smallest number in this question?


Hi Harley1980,

My approach focused on proving that 6 could NOT be the smallest integer (rather than proving that the other 4 answers COULD be the smallest integer). Here's the proof that -1 and 0 each could have been the smallest integer though.....

Since we're dealing with 12 consecutive integers...

IF...
-1 was the smallest, then we'd have the numbers -1 to +10, inclusive
We could get 40 with (4)(10) or (5)(8)
We could get 72 with (8)(9)
We could get 60 with (6)(10)
Thus, -1 COULD be the smallest integer

IF....
0 was the smallest, then we'd have the numbers 0 to +11, inclusive
We could get 40 with (4)(10) or (5)(8)
We could get 72 with (8)(9)
We could get 60 with (6)(10)
Thus, 0 COULD be the smallest integer

GMAT assassins aren't born, they're made,
Rich


Thank you.
I missed the words "in the deck" and thought about cards that we have drawn.
But after your answer I have realised my mistake.
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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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New post 02 Apr 2015, 12:52
EMPOWERgmatRichC wrote:
Lucky2783 wrote:
Turkish wrote:
Each card in a deck has an integer written on it, and the integers on each of the 12 cards in the deck are consecutive. In a certain game, the number points awarded for each turn is determined by
drawing two cards and multiplying the numbers shown on the cards. If the points awarded in three turns are 40, 72, and 60,all of the following could be the smallest numbered card in the deck EXCEPT

but given to us is 12 as highest number so only 4*10 or 5*8 combinations are possible. minimum can't be 6.

E


Hi Lucky2783,

You've correctly answered the question, but part of what you stated in your explanation in NOT correct. The prompt states that there are 12 cards, each has an integer written on it and the integers are consecutive. That means that the numbers are 12 consecutive integers, NOT that the largest integer is 12.

GMAT assassins aren't born, they're made,
Rich

Thanks rich.

anyways we are looking for smallest number so 1-12 is correct set to choose.
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Re: Each card in a deck has an integer written on it, and the integers on  [#permalink]

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Re: Each card in a deck has an integer written on it, and the integers on   [#permalink] 21 Feb 2018, 14:44
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