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# Sean and George collect two kinds of kernels: apricot kernels and mang

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
Sean and George collect two kinds of kernels: apricot kernels and mang  [#permalink]

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05 Sep 2016, 07:22
00:00

Difficulty:

65% (hard)

Question Stats:

64% (02:46) correct 36% (02:35) wrong based on 83 sessions

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Sean and George collect two kinds of kernels: apricot kernels and mango kernels. If George has 4 apricot kernels, and together they have a total of 40 kernels (of both kinds,) then how many of these 40 kernels are mango kernels?

(1) The number of apricot kernels that Sean has is half the total number of mango kernels they have together.

(2) Sean has three times as many kernels as George has.

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Re: Sean and George collect two kinds of kernels: apricot kernels and mang  [#permalink]

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05 Sep 2016, 09:03
1
Bunuel wrote:
Sean and George collect two kinds of kernels: apricot kernels and mango kernels. If George has 4 apricot kernels, and together they have a total of 40 kernels (of both kinds,) then how many of these 40 kernels are mango kernels?

(1) The number of apricot kernels that Sean has is half the total number of mango kernels they have together.

(2) Sean has three times as many kernels as George has.

It's easier if represented in a table format:
Given

Consider 1)
This gives the value of $$a$$ and hence the number of mango kernels. Sufficient . Select A and D.

Consider 2)
Solving for $$b$$ gives the number of mango kernels of george, but not for sean. Sean can have only mango kernels or no mango kernels.
Not Sufficient.

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Joined: 07 Dec 2017
Posts: 799
Re: Sean and George collect two kinds of kernels: apricot kernels and mang  [#permalink]

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10 Mar 2018, 10:05
Bunuel wrote:
Sean and George collect two kinds of kernels: apricot kernels and mango kernels. If George has 4 apricot kernels, and together they have a total of 40 kernels (of both kinds,) then how many of these 40 kernels are mango kernels?

(1) The number of apricot kernels that Sean has is half the total number of mango kernels they have together.

(2) Sean has three times as many kernels as George has.

We'll translate the question stem into equations so we know what we need to do.
This is a Precise approach.

We'll write Ga, Gm for George's kernels and Sa,Sm for Sean's.
We're told that Ga = 4 and that Ga+Gm+Sa+Sm = 40 meaning that Gm+Sa+Sm=36.
We need to find out Gm+Sm

(1) tells us that 2Sa = Gm+Sm
Substituting into the above gives 3Sa = 36 so Sa = 12. Then Gm+Sm = 24.
Sufficient.

(2) tells us that Sa+Sm = 3(Ga+Gm)
Substituting gives us Gm + 3(Ga+Gm) = 36 which we cannot solve.
Insufficient.

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Re: Sean and George collect two kinds of kernels: apricot kernels and mang &nbs [#permalink] 10 Mar 2018, 10:05
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