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Overlapping Sets

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Overlapping Sets

by swerve » Wed May 27, 2020 1:23 pm

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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.

The OA is A

Source: Economist GMAT
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Source: — Data Sufficiency |
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Re: Overlapping Sets

by deloitte247 » Fri May 29, 2020 9:35 am

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Given that: George has 4 apricot kernels
Total kernels = 40

Target question => How many of these 40 kernels are mango kernels?

Statement 1 => The number of apricot kernels that Sean has is half the total number of mango kernels they have together
Let the number of apricot kernels that Sean has = s
$$s=\frac{1}{2}\left(4+5\right)$$
$$s=\frac{4+5}{2}$$
$$2s=4+5$$
$$2s-5=4\ and\ s=4$$
Total apricot kernels = Sean's apricot kernels + George's apricot kernels = 4 + 4 = 8
Total mango kernels = 40 - 8 = 32
Statement 1 is SUFFICIENT


Statement 2 =>Sean has three times as many kernels George as has
Let the number of apricot kernels that Sean has = s
Let the number of mango kernels that George has = y
Let the number of mango kernels that Sean has = z
s + z = 3(4 + y)
s + z = 12 + 3y
Total mango kernels ( s + z ) cannot be evaluated with the expression obtained from this statement. Hence, statement 2 is NOT SUFFICIENT

Since statement 1 alone is SUFFICIENT
Answer = A
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